板结构辐射声的声品质基础理论研究
|
摘要
由于结构辐射声是产品的主要噪声源之一,因此产品设计者和制造者经常面临着用户对其产品结构辐射噪声的负面评价,这种用户的反映就是结构辐射声品质问题。声品质是用户对产品辐射声接受度的心理感觉反映,也是产品一系列性能的综合反映;其包含响度、粗糙度、波动度等一系列参数,并以不同的感受影响着人类的听觉心理。另一方面,声品质还可应用于其他用途,例如可通过声波动度判断汽车传动系统工作状态的平顺性。因此,结构辐射声品质设计成为产品设计中的一个重要问题,这类问题的研究对低噪声产品的设计具有重要的理论意义和实用价值,对其他工程问题的解决也有着广阔的应用前景。
本文运用以解析法为主、结合数值计算的方法,对不同形式的板结构声辐射特性及其声品质进行了系统的研究。建立了有限大板结构在无障板情况下的声辐射模型,分析了刚性障板对声辐射的影响规律;建立了板结构声辐射解析模型,研究了不同边界对板结构声辐射的控制规律;利用Zwicker响度模型和修正的PEAQ(Perceptual Evaluation of Audio Quality)方法,建立了板结构辐射声响度预测模型;发展和完善了GDQ(Generalized Differential Quadrature)方法,建立了适用于具有复杂边界板结构的声辐射模型和声波动度预测模型,揭示了各因素对板结构辐射声波动度的影响规律;提出了主区域离散方法,建立了具有任意形状和边界条件的板结构声辐射模型和声粗糙度预测模型,揭示了各因素对板结构辐射声粗糙度的影响规律;基于刚度,建立了加筋板结构声辐射及其声响度预测模型,揭示了加强筋对板结构辐射声响度的影响规律;提出了一个新的研究领域——结构辐射声品质主动控制,研究了一种控制板结构辐射声响度的主动控制策略。通过本文的理论分析与数值计算,获取了一系列有价值的研究结果,为板结构声辐射及其声品质设计提供了理论依据,也为产品虚拟声设计奠定了基础。
与现有研究成果相比,本文的研究成果主要体现在以下几个方面:
建立了在无刚性障板时有限大板结构声辐射模型,提出了当边界条件中含有弹性边界时结构声辐射的解析求解方法,利用表示辐射声压和结构模态耦合系数的双重积分,通过计算所得的声强级结果与有刚性障板时结构声辐射的数值计算结果相对比,揭示了刚性障板对结构声辐射的影响规律。为进一步研究刚性障板对结构声辐射的影响,利用能量的观点,采用振动速度平方均值和声辐射效率为参考基准,揭示了有无障板两种情况下结构声辐射差异的原因。
建立了适用于不同边界条件的板结构声辐射解析模型,并研究了边界条件对结构声辐射及声响度的影响。以五种不同边界条件的板结构声辐射为例,利用本文推导所得的解析模型,通过数值计算对比分析了简支、固支、自由三种形式的边界条件及其组合形式对板结构声辐射的影响;分析了不同激励力位置和板厚对板结构声辐射的影响规律。另一方面,由于人类听觉对声音频率的选择接收特性,边界条件对结构辐射声响度的影响与对物理声的影响有很大不同。基于Zwicker响度模型和修正的PEAQ方法,利用数值计算结果,揭示了简支、固支、自由三种形式的边界条件对结构辐射声响度的影响规律。通过计入人类听觉对频率的选择性接收特性,分析了边界条件对声功率级、声功率密度和特征频带声强级的影响,揭示了边界条件对结构声辐射和声响度不同影响的差异来源。这些研究为结构辐射响度预测和设计提供了解析模型。
对于结构辐射声,当其周围声源所影响而被调制时,将产生两个均可独立处理的声品质参数:波动度和粗糙度。发展和完善了GDQ方法,建立了适用于具有复杂边界的结构声辐射及其声波动度的解析计算模型。利用本文所建立的板结构辐射声波动度解析模型,揭示了调制频率、调制度和板结构模态密度等参数对辐射声波动度的影响规律,为复杂边界条件下板结构辐射声波动度设计提供了预测方法。为研究更具一般意义的板结构形式,提出了主区域离散方法,建立了具有任意边界和形状的板结构声辐射及其声粗糙度解析计算模型。利用本文所建立的板结构辐射声粗糙度模型,揭示了调制音频率、声压级和板结构模态密度变化对辐射声粗糙度的影响规律。
利用分层三角法函数和修正的PEAQ方法,建立了一般形式的正交加筋板结构声辐射及其声响度解析模型。以三种不同加强筋形式的板结构为例,揭示了加强筋及其组合形式对辐射声响度的影响规律,分析了加强筋对声功率级及特征频带声强级的影响,说明了加强筋对物理声和声响度不同影响的差异原因,也研究了在加筋情况下板结构模态密度对结构辐射声响度的影响规律。研究结果为通过加强筋控制板结构辐射声响度提供了理论模型和预测方法。
研究了适用于结构辐射声响度的主动控制策略。利用声辐射模态理论,建立了适用于主动控制的辐射声响度模型,并据此提出了一种声响度主动控制策略。利用四种具有不同边界条件的矩形板结构,通过其辐射声响度计算结果,验证了该控制策略的有效性,并分析了不同边界条件对在同种控制策略表现在结果上的差异。这些研究结果为主动控制在结构辐射声品质设计中的应用提供了理论依据和预测方法,也表明了结构辐射声品质主动控制与结构振动主动控制和声辐射主动控制有着很大差异。
Due to the structural noise is one of the main noise sources, designers and manufacturers are often faced with negative reactions to the sound or noise radiated from the product. A typical response to such reactions is confusion due to the“structural sound quality”of the problem. For the product, sound represents a more complex set of attributes, both aesthetic and functional, the structural sound quality becomes a key problem in product design. Sound quality includes a series of parameters, such as loudness, fluctuation strength and roughness, etc. These parameters influence the human hearing sensation by different ways. On the other hand, sound quality has other useful applications in engineering. For example, one can judge the status of the automobile power transfer system by the help of the fluctuation strength radiated form it. Therefore, for low noise and high performance product design, the study on structural sound quality is crucial on theory. This study also has wide application future on other engineering problems.
Analytical method is the main method used in this dissertation. Integrated with numerical method, this dissertation does a deep study systemically for the radiated sound and sound quality from the plate or plate-like structures with different forms. At first, the structural sound radiation model is established for the un-baffled finite plates. Because the different boundary conditions have different effects on the radiated sound, the analytical model is prompted for the calculation of the sound radiated from the plates. Based on the Zwicker loudness model and the corrected PEAQ (Perceptual Evaluation of Audio Quality) method, a model of sound loudness, which is radiated from the plates, is established for forecasting. For calculating the sound radiated from plates with mixed boundary conditions, the GDQ (Generalized Differential Quadrature) method is developed and corrtected in this dissertation. Based on the GDQ method, the model of sound radiation and sound fluctuation strength from the plates with mixed boundary conditions are established. The parameters, which affect the radiated sound fluctuation strength, are also discussed. Using the main domain discretization method prompted in this dissertation, the model of the sound radiation and sound roughness from the plates with arbitrary geometry forms or arbitrary boundary conditions is established. For revealing the effects of the stiffeners and its combined forms on the sound loudness radiated from the stiffened plates, the model of sound radiation and sound loudness from the stiffened plates is established. A new research field, active control of structural sound quality, is prompted in this dissertation. Based on the theory of sound radiation mode, this dissertation develops an active control strategy to control the sound loudness radiated from the plates. Some valuable study results are obtained through the theoretical analysis and numerical calculation in this dissertation. These results provide the theoretical foundation stone for the design of the structural sound quality and the virtual product radiated sound design.
Comparing with the current research results, the features obtained in this dissertation are mainly as follows:
The model of the sound radiation characteristic from the un-baffled rectangular plates is established. An analytical method is prompted to calculate the sound radiated from the plate with elastic support boundary conditions. The sound power level radiated from the un-baffled plates is numerically calculated by using a double layer integral representation of the sound radiation pressure and the modal coupling coefficients. The sound power level radiated from the baffled rectangular plates with the same boundary conditions are calculated in numerical experiments for comparison. From the viewpoint of energy, average velocity square of the un-baffled and the baffled rectangular plates with different boundary conditions is calculated, respectively. The relationship of sound radiation efficiency between the un-baffled and the baffled rectangular plates is deduced.
The effects of boundary conditions on sound radiation characteristics from the rectangular plates are studied. Using analytical method, five different boundary conditions are analyzed and calculated in numerical experiments as examples. The results reveal the effects of simple support, free support and clamped support on the sound radiated from the rectangular plates. Rectangular plates with different point force location and different plate thickness are calculated for verifying the effects of boundary conditions. On the other hand, because of the frequency selectivity of human hearing, the effects of boundary conditions on sound quality are different from the one on physical sound. Based on the Zwicker’s loudness model and the corrected PEAQ method, the sound loudness radiated from the vibrating plates and the effects of simple support, clamped support and free support on sound loudness are separately studied. The effects of boundary conditions on sound intensity level, sound intensity density and critical-band level are also studied under the condition of taking the frequency selectivity of human hearing system into account. The transformation progress of sound intensity level to sound loudness radiated from the rectangular plates, which is caused by the human hearing frequency selectivity characteristic, is illustrated in this dissretation. The research results provide analytical method for the forecasting and design of the sound loudness radiated from the plates or plate-like strucutres.
For the structural sound, two separate psycho-acoustical parameters, sound fluctuation strength and sound roughness, appears when the radiated sound is modulated by other sounds. The generalized differential quadrature method is developed for calculating the sound radiated from the forced vibrating rectangular plates with mixed boundary conditions. The fluctuation strength of the radiated sound, which is modulated by another sound near the plates, is studied. The effects of the modulation frequency and the modulation degree on the sound fluctuation strength are revealed. The effects of the radiated sound frequency and the structural modal density are also studied and compared, respectively. The numerical results are presented to show the characteristics of the fluctuation strength of the modulated sound radiated from the rectangular plates with mixed boundary conditions. For further generalizing, this dissertation reveals the effects of the modulation-sound pressure level and the modulation-sound frequency on the modulated sound roughness radiated from the rectangular plates with non-uniform boundary conditions. A generalized method is developed to calculate the radiated sound from such plates. Using this method, the sound roughness is calculated and compared with different modulation-sound frequency and modulation-sound pressure level, including the radiated sound frequency. Moreover, the effect of the plate mode density on the sound roughness is also illustrated.
This dissertation reveals the effects of the stiffeners on the radiated sound loudness from the stiffened rectangular plates. Based on the hierarchical trigonometric functions and the corrected PEAQ method, the sound loudness radiated from different stiffened plates and the effects of the stiffeners’form are studied, respectively. The effects of the stiffener on the radiated sound intensity level and the critical-band level are also studied. Due to the frequency selectivity of human hearing, the difference of the physical sound and the human hearing sensation are illustrated. Moreover, the effect of the mode density on the radiated sound loudness is also illustrated. The results provide theoretical model and a forecasting method for the controlling of the structural sound loudness by stiffeners.
A new research filed, active control of structural sound quality, is prompted. The active loudness control of the sound radiated from the rectangular plates is studied. Basing on the radiation modes, the sound loudness model is developed for the active loudness control. According to the radiation modes and the developed sound loudness model, an active loudness control strategy is prompted. By comparing the different boundary conditions on the edge of the plate, the effects of the boundary conditions on the active sound loudness control are also illustrated. The calculation results show that the radiated sound loudness is effectively controlled by the strategy. The results also reveal that, for the reason of the frequency selectivity of the human hearing, the active control of structural radiated sound loudness is quite different from the active control of structural vibration and the tradiational active control of noise.
本文运用以解析法为主、结合数值计算的方法,对不同形式的板结构声辐射特性及其声品质进行了系统的研究。建立了有限大板结构在无障板情况下的声辐射模型,分析了刚性障板对声辐射的影响规律;建立了板结构声辐射解析模型,研究了不同边界对板结构声辐射的控制规律;利用Zwicker响度模型和修正的PEAQ(Perceptual Evaluation of Audio Quality)方法,建立了板结构辐射声响度预测模型;发展和完善了GDQ(Generalized Differential Quadrature)方法,建立了适用于具有复杂边界板结构的声辐射模型和声波动度预测模型,揭示了各因素对板结构辐射声波动度的影响规律;提出了主区域离散方法,建立了具有任意形状和边界条件的板结构声辐射模型和声粗糙度预测模型,揭示了各因素对板结构辐射声粗糙度的影响规律;基于刚度,建立了加筋板结构声辐射及其声响度预测模型,揭示了加强筋对板结构辐射声响度的影响规律;提出了一个新的研究领域——结构辐射声品质主动控制,研究了一种控制板结构辐射声响度的主动控制策略。通过本文的理论分析与数值计算,获取了一系列有价值的研究结果,为板结构声辐射及其声品质设计提供了理论依据,也为产品虚拟声设计奠定了基础。
与现有研究成果相比,本文的研究成果主要体现在以下几个方面:
建立了在无刚性障板时有限大板结构声辐射模型,提出了当边界条件中含有弹性边界时结构声辐射的解析求解方法,利用表示辐射声压和结构模态耦合系数的双重积分,通过计算所得的声强级结果与有刚性障板时结构声辐射的数值计算结果相对比,揭示了刚性障板对结构声辐射的影响规律。为进一步研究刚性障板对结构声辐射的影响,利用能量的观点,采用振动速度平方均值和声辐射效率为参考基准,揭示了有无障板两种情况下结构声辐射差异的原因。
建立了适用于不同边界条件的板结构声辐射解析模型,并研究了边界条件对结构声辐射及声响度的影响。以五种不同边界条件的板结构声辐射为例,利用本文推导所得的解析模型,通过数值计算对比分析了简支、固支、自由三种形式的边界条件及其组合形式对板结构声辐射的影响;分析了不同激励力位置和板厚对板结构声辐射的影响规律。另一方面,由于人类听觉对声音频率的选择接收特性,边界条件对结构辐射声响度的影响与对物理声的影响有很大不同。基于Zwicker响度模型和修正的PEAQ方法,利用数值计算结果,揭示了简支、固支、自由三种形式的边界条件对结构辐射声响度的影响规律。通过计入人类听觉对频率的选择性接收特性,分析了边界条件对声功率级、声功率密度和特征频带声强级的影响,揭示了边界条件对结构声辐射和声响度不同影响的差异来源。这些研究为结构辐射响度预测和设计提供了解析模型。
对于结构辐射声,当其周围声源所影响而被调制时,将产生两个均可独立处理的声品质参数:波动度和粗糙度。发展和完善了GDQ方法,建立了适用于具有复杂边界的结构声辐射及其声波动度的解析计算模型。利用本文所建立的板结构辐射声波动度解析模型,揭示了调制频率、调制度和板结构模态密度等参数对辐射声波动度的影响规律,为复杂边界条件下板结构辐射声波动度设计提供了预测方法。为研究更具一般意义的板结构形式,提出了主区域离散方法,建立了具有任意边界和形状的板结构声辐射及其声粗糙度解析计算模型。利用本文所建立的板结构辐射声粗糙度模型,揭示了调制音频率、声压级和板结构模态密度变化对辐射声粗糙度的影响规律。
利用分层三角法函数和修正的PEAQ方法,建立了一般形式的正交加筋板结构声辐射及其声响度解析模型。以三种不同加强筋形式的板结构为例,揭示了加强筋及其组合形式对辐射声响度的影响规律,分析了加强筋对声功率级及特征频带声强级的影响,说明了加强筋对物理声和声响度不同影响的差异原因,也研究了在加筋情况下板结构模态密度对结构辐射声响度的影响规律。研究结果为通过加强筋控制板结构辐射声响度提供了理论模型和预测方法。
研究了适用于结构辐射声响度的主动控制策略。利用声辐射模态理论,建立了适用于主动控制的辐射声响度模型,并据此提出了一种声响度主动控制策略。利用四种具有不同边界条件的矩形板结构,通过其辐射声响度计算结果,验证了该控制策略的有效性,并分析了不同边界条件对在同种控制策略表现在结果上的差异。这些研究结果为主动控制在结构辐射声品质设计中的应用提供了理论依据和预测方法,也表明了结构辐射声品质主动控制与结构振动主动控制和声辐射主动控制有着很大差异。
Due to the structural noise is one of the main noise sources, designers and manufacturers are often faced with negative reactions to the sound or noise radiated from the product. A typical response to such reactions is confusion due to the“structural sound quality”of the problem. For the product, sound represents a more complex set of attributes, both aesthetic and functional, the structural sound quality becomes a key problem in product design. Sound quality includes a series of parameters, such as loudness, fluctuation strength and roughness, etc. These parameters influence the human hearing sensation by different ways. On the other hand, sound quality has other useful applications in engineering. For example, one can judge the status of the automobile power transfer system by the help of the fluctuation strength radiated form it. Therefore, for low noise and high performance product design, the study on structural sound quality is crucial on theory. This study also has wide application future on other engineering problems.
Analytical method is the main method used in this dissertation. Integrated with numerical method, this dissertation does a deep study systemically for the radiated sound and sound quality from the plate or plate-like structures with different forms. At first, the structural sound radiation model is established for the un-baffled finite plates. Because the different boundary conditions have different effects on the radiated sound, the analytical model is prompted for the calculation of the sound radiated from the plates. Based on the Zwicker loudness model and the corrected PEAQ (Perceptual Evaluation of Audio Quality) method, a model of sound loudness, which is radiated from the plates, is established for forecasting. For calculating the sound radiated from plates with mixed boundary conditions, the GDQ (Generalized Differential Quadrature) method is developed and corrtected in this dissertation. Based on the GDQ method, the model of sound radiation and sound fluctuation strength from the plates with mixed boundary conditions are established. The parameters, which affect the radiated sound fluctuation strength, are also discussed. Using the main domain discretization method prompted in this dissertation, the model of the sound radiation and sound roughness from the plates with arbitrary geometry forms or arbitrary boundary conditions is established. For revealing the effects of the stiffeners and its combined forms on the sound loudness radiated from the stiffened plates, the model of sound radiation and sound loudness from the stiffened plates is established. A new research field, active control of structural sound quality, is prompted in this dissertation. Based on the theory of sound radiation mode, this dissertation develops an active control strategy to control the sound loudness radiated from the plates. Some valuable study results are obtained through the theoretical analysis and numerical calculation in this dissertation. These results provide the theoretical foundation stone for the design of the structural sound quality and the virtual product radiated sound design.
Comparing with the current research results, the features obtained in this dissertation are mainly as follows:
The model of the sound radiation characteristic from the un-baffled rectangular plates is established. An analytical method is prompted to calculate the sound radiated from the plate with elastic support boundary conditions. The sound power level radiated from the un-baffled plates is numerically calculated by using a double layer integral representation of the sound radiation pressure and the modal coupling coefficients. The sound power level radiated from the baffled rectangular plates with the same boundary conditions are calculated in numerical experiments for comparison. From the viewpoint of energy, average velocity square of the un-baffled and the baffled rectangular plates with different boundary conditions is calculated, respectively. The relationship of sound radiation efficiency between the un-baffled and the baffled rectangular plates is deduced.
The effects of boundary conditions on sound radiation characteristics from the rectangular plates are studied. Using analytical method, five different boundary conditions are analyzed and calculated in numerical experiments as examples. The results reveal the effects of simple support, free support and clamped support on the sound radiated from the rectangular plates. Rectangular plates with different point force location and different plate thickness are calculated for verifying the effects of boundary conditions. On the other hand, because of the frequency selectivity of human hearing, the effects of boundary conditions on sound quality are different from the one on physical sound. Based on the Zwicker’s loudness model and the corrected PEAQ method, the sound loudness radiated from the vibrating plates and the effects of simple support, clamped support and free support on sound loudness are separately studied. The effects of boundary conditions on sound intensity level, sound intensity density and critical-band level are also studied under the condition of taking the frequency selectivity of human hearing system into account. The transformation progress of sound intensity level to sound loudness radiated from the rectangular plates, which is caused by the human hearing frequency selectivity characteristic, is illustrated in this dissretation. The research results provide analytical method for the forecasting and design of the sound loudness radiated from the plates or plate-like strucutres.
For the structural sound, two separate psycho-acoustical parameters, sound fluctuation strength and sound roughness, appears when the radiated sound is modulated by other sounds. The generalized differential quadrature method is developed for calculating the sound radiated from the forced vibrating rectangular plates with mixed boundary conditions. The fluctuation strength of the radiated sound, which is modulated by another sound near the plates, is studied. The effects of the modulation frequency and the modulation degree on the sound fluctuation strength are revealed. The effects of the radiated sound frequency and the structural modal density are also studied and compared, respectively. The numerical results are presented to show the characteristics of the fluctuation strength of the modulated sound radiated from the rectangular plates with mixed boundary conditions. For further generalizing, this dissertation reveals the effects of the modulation-sound pressure level and the modulation-sound frequency on the modulated sound roughness radiated from the rectangular plates with non-uniform boundary conditions. A generalized method is developed to calculate the radiated sound from such plates. Using this method, the sound roughness is calculated and compared with different modulation-sound frequency and modulation-sound pressure level, including the radiated sound frequency. Moreover, the effect of the plate mode density on the sound roughness is also illustrated.
This dissertation reveals the effects of the stiffeners on the radiated sound loudness from the stiffened rectangular plates. Based on the hierarchical trigonometric functions and the corrected PEAQ method, the sound loudness radiated from different stiffened plates and the effects of the stiffeners’form are studied, respectively. The effects of the stiffener on the radiated sound intensity level and the critical-band level are also studied. Due to the frequency selectivity of human hearing, the difference of the physical sound and the human hearing sensation are illustrated. Moreover, the effect of the mode density on the radiated sound loudness is also illustrated. The results provide theoretical model and a forecasting method for the controlling of the structural sound loudness by stiffeners.
A new research filed, active control of structural sound quality, is prompted. The active loudness control of the sound radiated from the rectangular plates is studied. Basing on the radiation modes, the sound loudness model is developed for the active loudness control. According to the radiation modes and the developed sound loudness model, an active loudness control strategy is prompted. By comparing the different boundary conditions on the edge of the plate, the effects of the boundary conditions on the active sound loudness control are also illustrated. The calculation results show that the radiated sound loudness is effectively controlled by the strategy. The results also reveal that, for the reason of the frequency selectivity of the human hearing, the active control of structural radiated sound loudness is quite different from the active control of structural vibration and the tradiational active control of noise.
引文
[1] F. Seybet, B. Soenark, F. J. Rizzo, D. J. Shippy. Application of the BIE method to sound radiation problems using an iso-parametric element. ASME Transactions. Journal of Vibration and Acoustics, 1984,106: 414～420
[2]赵键,谢壮宁,黄幼玲.自由场结构体声辐射研究.声学学报, 1994, 19 (1): 22-31
[3] A. F. Seybet, B. Soenark, F. J. Rizzo, D. J. Shippy. A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions. Journal of Acoustic Society of American, 1986, 80: 1241～1247
[4] P. M. Morse, H. Feshbach. Methods of Theoretical Physics. McGraw-Hill: New York, 1955
[5] J. T . Huntetal. Finite Element Approch to Acoustic Radiation from Elastic Structure. Journal of Acoustic Society of American, 1974, Vol.5 5(2): 1233-1238
[6]沈壕,孙洪生.工程声学中的有限元法.声学学报,第4期, 1981: 249-259.
[7] T. Yen, F. L. Dimggio. Forced Vibration of Submerged Spherical Shells. Journal of Acoustic Society of American, 1967,4(1):618～626
[8] A. W. Leissa. SP-160 Vibration of Plates. NASA: Washington DC, 1969
[9] A. W. Leissa. Recent Research and Plate Vibration, 1981-1985. Part 1: Classical Theory. The Shock and Vibration Digest, 1987, 19(3): 10-24
[10] A. W. Leissa. Recent Research and Plate Vibration, 1981-1985. Part 2: Complicating Effects. The Shock and Vibration Digest, 1987, 19(3): 10-24
[11] A. W. Leissa. Vibrations of Plates. Acoustical Society of America: New York, 1993
[12]黎胜.水下结构声辐射和声传输的数值分析及主动控制模拟研究.大连:大连理工大学博士学位论文, 2001
[13] C. M. Wang, V. Thevendran. Vibration Analysis of Annular Plates with Concentric Support Using a Variant of Rayleigh-Ritz Method. Journal of Sound and Vibration, 1993, 163(1): 137-149
[14] R. D. Mindlin. Influence of Rotatory Inertia and Shear on the Flexural Motion ofIsotropic, Elastic Plate. ASME Journal of Applied Mechanics, 1951, 18: 31-38
[15] R. D. Mindlin, H. Deresiewicz. Thickness-shear and Flexural Vibration of a Circular Disk. Journal of Applied Physics, 1954, 25(10): 1329-1332
[16] O. G. Mcgee, C.S. Huang and A.W. Lessia. Comprehensive Exact Solution for Free Vibration of thick Annular Sectorial Plates with Simply Supported Radial Edges. International Journal of Mechanics Science, 1995, 37(5): 537-566
[17]尹岗,陈花玲,陈天宁.薄板低频声辐射效率的研究.西安交通大学学报, 1999, 33: 108-110.
[18] T. I. Yamada, S. Aomura. Free Vibration of a Mindlin Plate of Varying Thickness. Journal of Sound and Vibration, 1979, 66(1): 187-197
[19] K. M. Liew, Y. Xiang, C.M. Wang. Flexural Vibration of Shear Deformable Plates on Ring Support. Computer Methods in Applied Mechanics and Engineering, 1993, 110: 301-315
[20] L. Rayleigh. The Theory of Sound, 2nd Edition. Dover: New York, 1985
[21] G. Maidanik. Response of a Ribbed Panels to Reverberant Acoustic Fields. Journal of Acoustical Society of America, 1962, 34(6): 809-826
[22] C. E. Wallace. Radiation Resistance of a Rectangular Panel. Journal of Acoustical Society of America, 1972, 51(3): 946-952
[23] L. D. Pope, R.C. Leibowitz. Intermodal Coupling Coefficients for a Fluid-Loaded Rectangular Plate. Journal of Acoustical Society of America, 1974, 56: 408-415
[24] N. S. Lomas, S.I. Hayek. Vibration and Acoustic Radiation of Elastically Supported Rectangular Plates. Journal of Sound and Vibration, 1977, 52: 1-25
[25] C. E. Wallace. Radiation Resistance of a Rectangular Panel. Journal of the Acoustical Society of America, 1972, 51: 946-952
[26] M. C. Gomperts. Radiation from Rigid Baffled Rectangular Plates with General Boundary Conditions. Acustica, 1974, 30: 320-327
[27] M. C. Gomperts. Sound Radiation from Baffled Thin Rectangular Plates. Acustica, 1977, 37: 93-102
[28] M. Heckl. Radiation from Plane Sound Sources. Acustica, 1977, 37: 155-166
[29] F. Fahy. Sound and Structural Vibration. Academic Press: London, 1985
[30] F. G. Leppington, E.G. Broadbent, K.H. Heron. The Acoustic Radiation Efficiency of Rectangular Panels. Proceedings of the Royal Society of London, 1982, A382:245-271
[31] H. Levine. On the Radiation Impendence of a Rectangular Piston. Journal of Sound and Vibration, 1983, 89: 447-455
[32] H. Levine. On the Short Wave Acoustic Radiation from Planar Panels or Beams of Rectangular Shape. Journal of the Acoustical Society of America, 1984, 76: 608-615
[33] R. Szilard. Theory and Analysis of Plates, Classical and Numerical Methods. Prentice-Hall: New Jersey, 1966
[34] N. Li. Forced vibration anaylsis of the clamped orthotropic rectangular plate by the superposition method. Journal of Sound and Vibration, 1992, 158: 307-316
[35] V. Z. Vlasov. Some new problems on shell and thin structures. National Advance Aeronautic, Naca Technical Memo, 1949, 1024
[36] Y. K. Cheung, D. Zhou. The free vibration of rectangular plates using a new set of beam function with the Rayleigh-Ritz method. Journal of Sound and Vibration 1999, 223(5): 703-722
[37] A. Mukherjee, M. Mukhopadhyay. Finite element for flexural vibration analysis of plates having various shapes and varying rigidities. Computational Structure 1986, 23(6): 807-812
[38] S Haldar, A.H. Sheikn, S.K. Sarkar. Finite element analysis of composite plates with elastically restrained edges. Journal of Reinforced Plast Composite 1999, 18(7): 626-641
[39] H. Takabatake, Y. Nagareda. Simplified analysis of elastic plates with edge beams. Computational Structure 1999, 70(2): 129-139
[40] T. P. Chang, H. C. Chang. Vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation. International Journal of Solids Structure 1997, 34(18): 2291-2301
[41] K. N. Saha., R.C. Kar, P.K. Datta. Free vibration analysis of rectangular Mindlin plates with elastic restraints uniformly distributed along the edges. Journal of Sound and Vibration 1996, 192(4): 885-904
[42] D. Zhou. Natural frequencies of elastically restrained rectangular plates using a set of static beam functions in the Rayleigh-Ritz method. Computational Structure 1995, 57(4): 731-735
[43] E. E. Lundquist, E. Stowell. Critical compressive stress for flat rectangular plates supported along all edges and elastically restrained against rotation along the unloaded edges. NACA Report, 1942
[44] C. C. Barlett. The vibration and buckling of a circular plate clamped on part of its boundary and simply supported on the remainder. Journal of Applied Mechanical and Mathematics, 1963, 16(4): 431-440
[45] T. Ota, M. Hamada. Fundamental frequencies of simply supported but partially clamped square plates. Bulletin of Japanese Society of Mechanical Engineering, 1963, 6(23): 397-403
[46] M. Hamada, Y. Inoue, H. Hashimoto. Buckling of simply supported but partially clamped rectangular plates uniformly compressed in one direction. Bulletin of Japanese Society of Mechanical Engineering, 1967, 10: 35-40
[47] L. M. Keer, B. Stahl. Eigenvalue problems of rectangular plates with mixed edge conditions. Journal of Applied Mechanical, 1972, 39: 513-520
[48] T. Mizusawa, J. W. Leonard. Vibration and buckling of plates with mixed boundary conditions. Engineering Structures, 1990, 12: 285-290
[49] K. M. Liew, K. C. Hung, M. K. Lim. Roles of domain decomposition method in plate vibrations: treatment of mixed discontinuous periphery boundaries. International Journal of Mechanical Sciences, 1993, 35(7): 615-632
[50] K. M. Liew, K. C. Hung, K. Y. Lam. On the use of the substructure method for vibration analysis of rectangular plates with discontinuous boundary conditions. Journal of Sound and Vibration, 1993, 163: 451-462
[51] K. M. Liew, K. C. Hung, M. K. Lim. Method of domain decomposition in vibration of mixed edge anisotropic plates. International Journal of Solid Structures, 1993, 30(23): 3281-3301
[52] K. M. Liew, K. C. Hung, M. K. Lim. On the use of the domain decomposition method for vibration of symmetric laminates have discontinuities at the same edge. Journal of Sound and Vibration, 1994, 178: 243-264
[53] K. C. Hung, K. M. Liew, M. K. Lim. A discrete element method for vibration analysis of mixed edge plates. Finite Elements Analysis and Design, 1994, 18: 319-328
[54] F. L. Liu, K. M. Liew. Static analysis of Reissner-Mindlin plates by differentialquadrature element method. ASME Journal of Applied Mechanical, 1998, 65: 705-710
[55] F. L. Liu, K. M. Liew. Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method. Journal of Sound and Vibration, 1999, 225: 915-934
[56] J. R. Wu, W. Liu. Vibration of rectangular plates with edge restraints and intermediate stiffeners. Journal of Sound and Vibration, 1988, 123: 103-113
[57] P. A. A. Laura, R. Gutierrz. A note on transverse vibration of stiffened rectangular plates with edges elastically restrained against rotation. Journal of Sound and Vibration, 1981, 78: 139-144
[58] R. Bhat. Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz methods. Journal of Sound and Vibration, 1985, 102: 493-499
[59] R. Gutierrez, P. A. A. Laura. Transverse vibration of rectangular plates elastically restrained against rotation along the edges. Journal of Sound and Vibration, 1985, 101: 122-124
[60] K. Liew, Y. Xiang, S. Kitipornchai, M. Lim. Vibration of the rectangular mindlin plates with intermediate stiffeners. Journal of Sound and Vibration, 1994, 166: 529-535
[61] K. Liew, Y. Xiang, S. Kitipornchai, J. Meek. Formulation of mindlinengesser model for stiffened plate vibration. Computer Methods in Applied Mechanical Engineering, 1995, 120: 339-353
[62] Y. Xiang, S. Kitipornchai, K. Liew, M. Lim. Vibration of stiffened skew mindlin plates. Acta Mechanica, 1995, 112: 11-18
[63] A. Berry, J. Nicolas. Vibration and sound radiation of fluid-loaded stiffened plates with consideration of in-plane deformation. Journal of Acoustical Society of America, 1996, 100: 312-319
[64] H. Molaghasemi, I. Harik. Free vibration of stiffened sector plates. Journal of Sound and Vibration, 1996, 190: 726-732
[65] B. Mace. Periodically stiffened fluid-loaded plate, I: response to converted harmonic pressure and free wave propagation. Journal of Sound and Vibration, 1980, 73: 473-486
[66] B. Mace. Periodically stiffened fluid-loaded plate, II: response to line and point forces. Journal of Sound and Vibration, 1980, 73: 487-504
[67] B. Mace. Sound radiation from fluid loaded orthogonally stiffened plates. Journal of Sound and Vibration, 1981, 79: 439-452
[68] D. Mead. Plates with regular stiffening in acoustic media: vibration and radiation. Journal of Acoustical Society of America, 1990, 88: 391-401
[69] A. Berry, J. Nicolas. Structural acoustics and vibration behavior of complex panels. Applied Acoustics, 1994, 100: 185-215
[70] T. Koko, M. Olson. Vibration analysis of stiffened plates by super elements. Journal of Acoustical Society of America, 1992, 158: 149-167
[71] C. Chen, W. Liu, S. Chern. Vibration analysis of stiffened plates. Computer and Structure, 1994, 50: 471-480
[72] A. Cote. Modelisation vibroacoustique dens le domaine des moyennes frequences par elements finis de type P. Ph.D. Thesis, Universite de Sherbrooke, Candan, 1998
[73] D. Mead, D. Zhu, N. Bardell. Free vibration of an orthogonally stiffened flat plate. Journal of Sound and Vibration, 1988, 127: 19-48
[74] D. Mead, D. Zhu, N. Bardell. Free vibration analysis of flat plate using the hierarchical finite element method. Journal of Sound and Vibration, 1991, 151: 262-289
[75] O. Beslin, J. Nicolas. A hierarchical functions set for predicting very high order plate bending modes with any boundary conditions. Journal of Acoustical Society of America, 1996, 95: 2578-2589
[76] C. Guigou, C. R. Fuller. Active control of sound radiation from a semi-infinite elastic beam with a clamped edge. Journal of Sound and Vibration, 1993, 168(3): 507-523
[77] R.H. Lyon. Product Sound Quality- From Design to Perception. Internoise, 2004
[78] C.L. Fog, T.H. Pederson. Introduction to Product Sound Quality. Nordic Acoustical Meeting, 1998
[79] A. Miskiewicz. Psychoacoustics in the Automotive Industry. Acustica, 1999, 85: 646-649
[80] L.N. Solomon. Semantic reactions to systematically varied sounds. Journal of the Acoustical Society of America, 1959, 31: 986-990
[81] E.A. Bjork. The perceived quality of natural sounds. Acustica, 1985, 57: 185-188
[82] A. Zeitler, J. Hellbruck. Semantic attributes of environmental sounds and their correlations with psychoacoustic magnitude. ICA, Rome, Italy, 2001, 25-114
[83] C.E. Osgood. The natural and measurement of meaning. Psychological Bulletin, 1952, 49: 197-237
[84] N Chouard., T. Hempel. A semantic differential design especially developed for the evaluation of interior car sounds. Joint Meeting: ASA/EAA/DEGA, Berlin, Germany, 1999, JASA(105)1280
[85] L Kyncl., O. Jiricek. Psychoacoustic product sound quality evaluation. ICA, Rome, Italy, 2001, 25-90
[86] E. Zwicker, H. Fastl. Psychoacoustics: Facts and Models. Springer-Verlag: Berlin, 1990
[87] P. Susini, S. McAdams, S. Winsberg. A multidimensional technique for sound quality assessment. Acta Acustica, 1999, 85: 650-656
[88] S. Winsberg, G.D. Soete. A latent class approach for fitting the weighted Euclidean model, CLASCAL. Psychometrika, 1993, 58: 315-330
[89] S. Winsberg, G.D. Soete. A Thurstonian pairwise choice model with univariate and multivariate spline transformation. Psychometrika, 1993, 58: 233-256
[90] O. Maeda. Development of an engine evaluation meter. SAE Paper 870965
[91] M. Schneider. Development of vehicle sound quality: targets and methods. Transaction of SAE, 95:1283
[92] H. Schiffbanker. Development and application of an evaluation technique to assess the subjective character of engine noise. Transaction of SAE, 91:1081
[93] M. Hussain. Statistical evaluation of an annoyance index for engine noise recordings. Transaction of SAE, 91:1080
[94] M. Otto. Evaluation and analysis of automotive starter sounds. Journal of Noise Control Engineering, 1993, 41(3): 162-175
[95] V. A. Herman. An engine approach to sound quality. Transaction of SAE, 96:2491
[96] M. F. Rusell. Subjective assessment of diesel vehicle noise. Proceeding of FISITA 92 I.Mech.E.C389/044 925 187 Engineering for the Customer, 1992, 2
[97] R. Mark. New design techniques for improving diesel NVH characteristics. Diesel Progress, 1997, 7: 56-68
[98] H. Kinoshita. Development of new-generation high-performance 4.5-litter V8 Nissan engine. Transaction of SAE, 90: 0651
[99] S. Shoichiro. Improvement of engine sound quality through a new flywheel system flexibly mounted to crankshaft. Transaction of SAE, 90: 0391
[100]藤原奖,孙彦昕.三菱电机在降低吸尘器噪声和改进声质量方面的研究动向.家电科技, 2004, 7: 64-65
[101] S. Amman, J. Greenberg. Subjective evaluation and objective evaluation of automobile structure noise. Noise Control Engineering, 1999, 47(1): 44-49
[102] S. Kuo, D. Morgan. Active Noise Control. Wiley: New York, 1996
[103] S.J. Elliott, P.A. Nelson. Active noise control. IEEE Signal Processing Magazine, 1993, 10(4): 12-35
[104] G. Garnaka. Active noise control, the state of the art. Noise Control Engineering, 1982, 18: 100-110
[105] S.J. Elliott, C. Boucher, P.A. Nelson. The behavior of a multiple channel active control system. IEEE Transactions on Signal Processing, 1992, 40(5): 1041-1052
[106] C. R. Fuller. Analysis of active control of sound radiation from elastic plates by force inputs. Proceeding of Inter-Noise’88, Avignon, France, 1998, 1061-1064
[107] L. Meirovitch, M. A. Norris. Vibration Control. Proceeding of Inter-Noise’84, Honolulu, USA, 1984, 477-482
[108] C. R. Fuller. Active control of sound transmission/radiation from elastic plates by vibration inputs I: analysis. Journal of Sound and Vibration, 1990, 136: 1-15
[109] B. Wang. Active control of noise transmission through rectangular plates using multiple piezoelectric or point forces actuators. Journal of the Acoustical Society of America, 1991, 90: 2820-2830
[110] E. K. Dimitriadis, C. R. Fuller, C. A. Rogers. Piezoelectric actuators for distributed vibration excitation of thin plates. Transactions of the America Society of Mechanical Engineers, 1991, 113: 100-107
[111] E. K. Dimitriadis, C. R. Fuller. Active control of sound transmission through elastic plates using piezoelectric actuators. American Institute of Aeronautics and Astronautics Journal, 1991, 29: 1771-1777
[112] C. A. Fuller, S. J. Elliott, P. A. Nelson. Active Control of Vibration. London: Academic Press, 1996
[113] C. R. Fuller, C. A. Rogers, H. H. Robertshaw. Control of sound radiation with active/adaptive strucutres. Journal of Sound and Vibration, 1992, 57: 19-39
[114] M. E. Johnson. Active control of sound transmission. Ph.D. Thesis, 1996, Institute of Sound and Vibration Research, University of Southampton
[115] A. Preumont. Vibration Control of Active Structures, An Introduction. The Netherlands: Kluwer Academic Publishers, 1997
[116] M. E. Johnson, S. J. Elliott. Active control of sound radiation using volume velocity cancellation. Journal of the Acoustical Society of America, 1995, 94: 2174-2186
[117] S. J. Elliott, M. E. Johnson. Radiation modes and the active control of sound power. Journal of the Acoustical Society of America, 1993, 92: 2194-2204
[118] J. Rex, S. J. Elliott. The QWSIS- a new sensor for structural radiation control. Proceedings of the First International Conference on Motion and Vibration Control, Yokohama, Japan, 1992, 339-343
[119] M. E. Johnson, T. Sors, S. J. Elliott, B. Bafaely. Feedback control of broadband sound radiation using a volume velocity sensor. Proceeding of Active’97, Budapest, Hungary, 1997, 1007-1020
[120] J. P. Maillard, C. R. Fuller. Active control of sound radiation from cylinders with piezoelectric actuators and structural acoustic sensing. Proceedings of Active’97, Budapest, Hungary, 1997, 1021-1034
[121] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. I: theory and design. Journal of the Acoustical Society of America, 1994, 93: 3252-3261
[122] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. II: active radiation control of a simply supported beam. Journal of the Acoustical Society of America, 1994, 93: 3262-3272
[123] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. III: experiments on active broadband radiation control of a simply-supported beam. Journal of the Acoustical Society of America, 1995, 94: 2613-2621
[124] A. Preumont, A. Franscois, S. Dubru. Piezoelectric array sensing for real-time, broad-band sound radiation measurement. Journal of Vibration and Acoustics, 1999, 21: 446-452
[125] Leuseur. Rayonnment Acoustique des Structures. Editions Eyrolles: Paris, 1988
[126] Maidanik. Vibrational and radiative classifications of modes of a baffled finite panel. Journal of Sound and Vibration, 1974, 34: 447-455
[127] H.G. Davies. Acoustic radiation from fluid loaded rectangular plates. MIT Reports No.7: 1476-1
[128] H.G. Davies. Sound from turbulent boundary layer excited panels. Journal of Acoustical Society of America, 1971, 49: 878-889
[129] R. Graham. High frequency vibration and acoustic radiation of fluid loaded plates. Transactions of Royal Society, London, 1995, A 352: 1-43
[130] O. Mattei. Sound radiation by baffled and constrained plates. Journal of Sound and Vibration, 1995, 179(1): 63-77
[131] Atalla, J. Nicolas, C. Gauthier. Acoustic radiation of an un-baffled vibrating plate with general conditions. Journal of Acoustical Society of America, 1996, 99: 1484-1494
[132] Laulagnet. Sound radiation by a simply supported un-baffled plate. Journal of Acoustical Society of America, 1998, 103: 2451-2462
[133] R. Soni, R.K. Sankara. Vibration of non-uniform rectangular plates: a spline technique method of solution. Journal of Sound and Vibration 1974, 35(1): 35-45
[134] Filipich, P.A.A. Laura, R.D. Santos. A note on vibration of rectangular plates. Journal of Sound and Vibration 1977, 50(3): 445-454
[135] H. Gutierrez, P.A.A. Laura, R.O. Grossi. Vibration of rectangular plates of bi-linearly varying thickness and with boundary conditions. Journal of Sound and Vibration 1981, 75:323-328
[136] F.T.K. Au, M.F. Wang. Sound radiation from forced vibration of rectangular orthotropic plates under moving loads. Journal of Sound and Vibration, 2005, 281(3-5):1057-1075
[137] W.T. Thomson. Theory of vibration with applications. New Jersey: Prentice Hall. 1972
[138] C.C. Sung, J.T. Jan. The response of and sound power radiated by a clamped rectangular plate. Journal of Sound and Vibration, 1997, 207(3): 301-317
[139] F.T.K. Au, M.F. Wang. Sound radiation from forced vibration of rectangular orthotropic plates under moving loads. Journal of Sound and Vibration, 2005,281(3-5): 1057-1075
[140] W.L. Li, H.J. Gibeling. Acoustic radiation from a rectangular plates reinforced by springs at arbitrary locations. Journal of Sound and Vibration, 1999, 220(1): 117-133
[141] T. Takahagi, M. Nakai, Y. Tamai. Near Field Sound Radiation From Simply Supported Rectangular Plate. Journal of Sound and Vibration, 1995, 185(3): 455-471
[142] J. Park, L. Mongeau, T. Siegumnd. Influence of supported properties on the sound radiated from the vibration of rectangular plates. Journal of Sound and Vibration, 2003, 264(4): 775-794
[143] Yuh-Chun Hu, Shyh-Chin Huang. The frequency response and damping effect of three-layer thin shell. Computers and Structures, 2000, 76(5):577-591
[144] Y. Wonho. Enhanced Modified Bark Spectral Distortion (EMBSD): An Objective Speech Quality Measure Based on Audible Distortion and Cognition Model. PhD Thesis, Temple University, USA, 1999
[145] ITU-R Recommendation BS. 1387. Method for Objective Measurement of Perceived Audio Quality (PSQM). 1998
[146] T. Thiede. Perceptual Audio Quality Assessment Using a Non-linear Filter Bank. PhD Thesis, TU Berlin, 1999
[147] ITU-R Study Group 6. Draft Revision to BS. 1387, Method for Objective Measurement of Perceived Audio Quality, Document 6/BL/30-E. 2001
[148] P. Kabal. An Examination and Interpretation of ITU-RBS.1387: Perceptual Evaluation of Audio Quality. TSP Lab Technical Report, Dept. ECE, McGill University, 2002
[149] H. Fastl. Hearing: Physiological bases and Psychophysics. Berlin Heidelberg: Springer, 1993
[150] H. Fastl. The psychoacoustics of sound quality evaluation. Acustica, 1997, 83(5): 754-764
[151] J. Bemsen. Sound in design. Danish Design Center & DELTA Acoustics and Vibration, 1999
[152] M. A. Milosevic, A. M. Mitic, M. S. Milosevic. Parameters influencing noise estimation. Working and Living Environmental Protection, 2004, 2(4): 277-284
[153] J. Blauert, U. Jekosch. Sound quality evaluation: a multilayered problem. Antwerp: EEA Tutorium, 1996
[154] Y. Narita. Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions. Journal of Sound and Vibration, 1981, 77(3): 345-355
[155] Y. Hirano, K. Okazaki. Vibration of a circular plate having partly clamped or partly simply supported edges. Bullion of Japanese Society of Mechanics Engineering, 1976, 19: 610-618
[156] S.C. Fan, Y.K. Cheng. Flexural free vibration of rectangular plates with complex support conditions. Journal of Sound and Vibration, 1986, 23:45-55
[157] K.M. Liew, C.M. Wang. Vibration analysis of plates by the pb-2 Rayleigh-Ritz method: mixed boundary conditions, reentrant corners and internal curved supports. Mechanical Structure and Mechanics, 1992, 20: 281-292
[158] C.Y. Chia. Nonlinear vibration of anisotropic rectangular plates with non-uniform edge constraints. Journal of Sound and Vibration, 1985, 101: 539-550
[159] R. Bellman, B.G. Kashef, J. Casti. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 1972, 10: 40-52
[160] P.A.A. Laura, R.H. Gutierrez. Analysis of vibrating rectangular plates with non-uniform boundary conditions by using the differential quadrature method. Journal of Sound and Vibration, 1994, 173: 702-706
[161] C. Shu. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD thesis, University of Glasgow, Scotland, 1991
[162] C. Shu, H. Du. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids Structures, 1997, 34: 819-835
[163] C. Shu, H. Du. A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates. Journal of Solids Structures, 1997, 34: 837-846
[164] C. Shu, C.M. Wang. Treatment of mixed and non-uniform boundary conditions in GDQ vibration analysis of rectangular plates. Engineering Structures, 1999, 21:125-134
[165] G. Xie, D.J. Thompson, C.J.C. Jones. Mode count and modal density of structural systems: relationships with boundary conditions. Journal of Sound and Vibration, 2004, 27(3-5): 621-651
[166] E. Terhardt. On the perception of periodic sound fluctuations (roughness). Acustica, 1974, 30: 201-213
[167] R. Hoeldrich. An optimized model for the objective assessment of roughness sensations in vehicle noise. AVL - Sound Engineering Conference, Graz, July 22-27, 1999
[168] P. Daniel, R. Weber. Calculating psycho-acoustical roughness. Proceeding of Internoise, 1993, 251-165
[169] M. Pflueger, R. Hoeldrich, F. Brandl, W. Biemayer. Psychoacoustic measurement of roughness of vehicle interior noise. Proceeding of 137th Meeting of the Acoustical of American, Berlin, March 14-19,1999
[170] D. Bloger, N. Griffith. Multidimensional timbre analysis of shakuhachi honkyoku. Proceeding of the Conference on Interdisciplinary Musicology, Montreal, Spring 10-12, 2005
[171] F. Brandl, W. Biermayer. A new tool for the onboard objective assessment of vehicle interior noise quality. SAE Noise & Vibration Conference & Exposition, Traverse City, May 17-20, 1999
[172] W. Sethares. Tuning, timbre, spectrum, scale. London: Springer Verlag, 1998
[173] P. N. Vassilakis. Perceptual and physical properties of amplitude fluctuation and their musical significance. PhD. Thesis, 2001, University of California at Los Angeles
[174] K. M. Liew, C. M. Wang, Y. Xiang. Vibration of Mindlin plates-programming the p-version Ritz method. Amsterdam, The Netherlands: Elsevier Science Ltd, 1998
[175] G. H. Su, Y. Xiang. A non-discrete approach for analysis of plates with multiple subdomains. Engineering Structures, 2002, 24: 563-575
[176] K.M. Liew, Y. Xiang, S.Kitipomchai. Research on thick plate vibration: a literature survey. Journal of Sound and Vibration, 1995, 180(1): 163-176
[177] S.F. Ney, G.G. Kulkami. On the transverse free vibration of beam-slab type highway bridges. Journal of Sound and Vibration, 1972, 21: 249-261
[178] T. Baledra, N.E. Shanmugam. Free vibration of plates structures by grillage method. Journal of Sound and Vibration, 1985, 99: 333-350
[179] C.L. Kirk. Vibration of centrally stiffened rectangular plates. Journal of Royal Aeronautical Society, 1961, 65: 695-697
[180] K.M. Liew, Y. Xiang, S.Kitipomchai, J.L. Meek. Formulation of Mindlin-engesser model for stiffened plate vibration. Computer Methods in Applied Mechanics and Engineering, 1995, 120(3-4): 339-353
[181] Y. Xiang, S.Kitipomchai, K.M. Liew, M.K. Lim. Vibration of stiffened skew Mindlin plates. Acta Methanica, 1995, 112: 11-28
[182] Y. Xiang, K.M. Liew, S.Kitipomchai. Vibration of circular and annular plate with internal ring stiffeners. Journal of the Acoustical Society of America, 1996, 100(6): 3696-3705
[183] B.R. Long. A stiffness-type analysis of the vibration of a class of stiffened plates. Journal of Sound and Vibration, 1971, 16: 323-335
[184] G. Akus, R. Ali. Free vibration analysis of stiffened plates using finite difference method. Journal of Sound and Vibration, 1976, 48: 15-25
[185] G. Akus. Free vibration analysis of stiffened plates by including the effect of in-plane inertia. Journal of Applied Mechanics, 1982, 49: 206-212
[186] M. Guo, I.E. Harik. Stability of eccentrically stiffened plates. Thin-Walled Structures, 1992, 14: 1-20
[187] C. Chen, W. Liu, S. Chren. Vibration analysis of stiffened plates. Computer and Structure, 1994, 50: 471-480
[188] A. Beslin, J. Nicolas. Structural acoustics and vibration behavior of complex panels. Applied Acoustics, 1994, 100: 185-215
[189] M. Barrette, A. Berry, O. Beslin. Vibration of stiffened plates using hierarchical trigonometric functions. Journal of Sound and Vibration, 2000, 235(5): 727-747
[190] P. Vitiello, P.A. Nelson, M. Petyt. Numerical studies of the active control of sound transmission through double partitions. ISVR Techincal Report, 1989, No.183
[191] C.K. Lee. Theory of laminated piezoelectric plates for design of distributed sensors/actuators. Part I: governing equations and reciprocal relationships. Journal of the Acoustical Society of America, 1990, 87:114-1158
[192] S.J. Eillott. Signal processing for active control. London: Academic Press, 2001
[2]赵键,谢壮宁,黄幼玲.自由场结构体声辐射研究.声学学报, 1994, 19 (1): 22-31
[3] A. F. Seybet, B. Soenark, F. J. Rizzo, D. J. Shippy. A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions. Journal of Acoustic Society of American, 1986, 80: 1241～1247
[4] P. M. Morse, H. Feshbach. Methods of Theoretical Physics. McGraw-Hill: New York, 1955
[5] J. T . Huntetal. Finite Element Approch to Acoustic Radiation from Elastic Structure. Journal of Acoustic Society of American, 1974, Vol.5 5(2): 1233-1238
[6]沈壕,孙洪生.工程声学中的有限元法.声学学报,第4期, 1981: 249-259.
[7] T. Yen, F. L. Dimggio. Forced Vibration of Submerged Spherical Shells. Journal of Acoustic Society of American, 1967,4(1):618～626
[8] A. W. Leissa. SP-160 Vibration of Plates. NASA: Washington DC, 1969
[9] A. W. Leissa. Recent Research and Plate Vibration, 1981-1985. Part 1: Classical Theory. The Shock and Vibration Digest, 1987, 19(3): 10-24
[10] A. W. Leissa. Recent Research and Plate Vibration, 1981-1985. Part 2: Complicating Effects. The Shock and Vibration Digest, 1987, 19(3): 10-24
[11] A. W. Leissa. Vibrations of Plates. Acoustical Society of America: New York, 1993
[12]黎胜.水下结构声辐射和声传输的数值分析及主动控制模拟研究.大连:大连理工大学博士学位论文, 2001
[13] C. M. Wang, V. Thevendran. Vibration Analysis of Annular Plates with Concentric Support Using a Variant of Rayleigh-Ritz Method. Journal of Sound and Vibration, 1993, 163(1): 137-149
[14] R. D. Mindlin. Influence of Rotatory Inertia and Shear on the Flexural Motion ofIsotropic, Elastic Plate. ASME Journal of Applied Mechanics, 1951, 18: 31-38
[15] R. D. Mindlin, H. Deresiewicz. Thickness-shear and Flexural Vibration of a Circular Disk. Journal of Applied Physics, 1954, 25(10): 1329-1332
[16] O. G. Mcgee, C.S. Huang and A.W. Lessia. Comprehensive Exact Solution for Free Vibration of thick Annular Sectorial Plates with Simply Supported Radial Edges. International Journal of Mechanics Science, 1995, 37(5): 537-566
[17]尹岗,陈花玲,陈天宁.薄板低频声辐射效率的研究.西安交通大学学报, 1999, 33: 108-110.
[18] T. I. Yamada, S. Aomura. Free Vibration of a Mindlin Plate of Varying Thickness. Journal of Sound and Vibration, 1979, 66(1): 187-197
[19] K. M. Liew, Y. Xiang, C.M. Wang. Flexural Vibration of Shear Deformable Plates on Ring Support. Computer Methods in Applied Mechanics and Engineering, 1993, 110: 301-315
[20] L. Rayleigh. The Theory of Sound, 2nd Edition. Dover: New York, 1985
[21] G. Maidanik. Response of a Ribbed Panels to Reverberant Acoustic Fields. Journal of Acoustical Society of America, 1962, 34(6): 809-826
[22] C. E. Wallace. Radiation Resistance of a Rectangular Panel. Journal of Acoustical Society of America, 1972, 51(3): 946-952
[23] L. D. Pope, R.C. Leibowitz. Intermodal Coupling Coefficients for a Fluid-Loaded Rectangular Plate. Journal of Acoustical Society of America, 1974, 56: 408-415
[24] N. S. Lomas, S.I. Hayek. Vibration and Acoustic Radiation of Elastically Supported Rectangular Plates. Journal of Sound and Vibration, 1977, 52: 1-25
[25] C. E. Wallace. Radiation Resistance of a Rectangular Panel. Journal of the Acoustical Society of America, 1972, 51: 946-952
[26] M. C. Gomperts. Radiation from Rigid Baffled Rectangular Plates with General Boundary Conditions. Acustica, 1974, 30: 320-327
[27] M. C. Gomperts. Sound Radiation from Baffled Thin Rectangular Plates. Acustica, 1977, 37: 93-102
[28] M. Heckl. Radiation from Plane Sound Sources. Acustica, 1977, 37: 155-166
[29] F. Fahy. Sound and Structural Vibration. Academic Press: London, 1985
[30] F. G. Leppington, E.G. Broadbent, K.H. Heron. The Acoustic Radiation Efficiency of Rectangular Panels. Proceedings of the Royal Society of London, 1982, A382:245-271
[31] H. Levine. On the Radiation Impendence of a Rectangular Piston. Journal of Sound and Vibration, 1983, 89: 447-455
[32] H. Levine. On the Short Wave Acoustic Radiation from Planar Panels or Beams of Rectangular Shape. Journal of the Acoustical Society of America, 1984, 76: 608-615
[33] R. Szilard. Theory and Analysis of Plates, Classical and Numerical Methods. Prentice-Hall: New Jersey, 1966
[34] N. Li. Forced vibration anaylsis of the clamped orthotropic rectangular plate by the superposition method. Journal of Sound and Vibration, 1992, 158: 307-316
[35] V. Z. Vlasov. Some new problems on shell and thin structures. National Advance Aeronautic, Naca Technical Memo, 1949, 1024
[36] Y. K. Cheung, D. Zhou. The free vibration of rectangular plates using a new set of beam function with the Rayleigh-Ritz method. Journal of Sound and Vibration 1999, 223(5): 703-722
[37] A. Mukherjee, M. Mukhopadhyay. Finite element for flexural vibration analysis of plates having various shapes and varying rigidities. Computational Structure 1986, 23(6): 807-812
[38] S Haldar, A.H. Sheikn, S.K. Sarkar. Finite element analysis of composite plates with elastically restrained edges. Journal of Reinforced Plast Composite 1999, 18(7): 626-641
[39] H. Takabatake, Y. Nagareda. Simplified analysis of elastic plates with edge beams. Computational Structure 1999, 70(2): 129-139
[40] T. P. Chang, H. C. Chang. Vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation. International Journal of Solids Structure 1997, 34(18): 2291-2301
[41] K. N. Saha., R.C. Kar, P.K. Datta. Free vibration analysis of rectangular Mindlin plates with elastic restraints uniformly distributed along the edges. Journal of Sound and Vibration 1996, 192(4): 885-904
[42] D. Zhou. Natural frequencies of elastically restrained rectangular plates using a set of static beam functions in the Rayleigh-Ritz method. Computational Structure 1995, 57(4): 731-735
[43] E. E. Lundquist, E. Stowell. Critical compressive stress for flat rectangular plates supported along all edges and elastically restrained against rotation along the unloaded edges. NACA Report, 1942
[44] C. C. Barlett. The vibration and buckling of a circular plate clamped on part of its boundary and simply supported on the remainder. Journal of Applied Mechanical and Mathematics, 1963, 16(4): 431-440
[45] T. Ota, M. Hamada. Fundamental frequencies of simply supported but partially clamped square plates. Bulletin of Japanese Society of Mechanical Engineering, 1963, 6(23): 397-403
[46] M. Hamada, Y. Inoue, H. Hashimoto. Buckling of simply supported but partially clamped rectangular plates uniformly compressed in one direction. Bulletin of Japanese Society of Mechanical Engineering, 1967, 10: 35-40
[47] L. M. Keer, B. Stahl. Eigenvalue problems of rectangular plates with mixed edge conditions. Journal of Applied Mechanical, 1972, 39: 513-520
[48] T. Mizusawa, J. W. Leonard. Vibration and buckling of plates with mixed boundary conditions. Engineering Structures, 1990, 12: 285-290
[49] K. M. Liew, K. C. Hung, M. K. Lim. Roles of domain decomposition method in plate vibrations: treatment of mixed discontinuous periphery boundaries. International Journal of Mechanical Sciences, 1993, 35(7): 615-632
[50] K. M. Liew, K. C. Hung, K. Y. Lam. On the use of the substructure method for vibration analysis of rectangular plates with discontinuous boundary conditions. Journal of Sound and Vibration, 1993, 163: 451-462
[51] K. M. Liew, K. C. Hung, M. K. Lim. Method of domain decomposition in vibration of mixed edge anisotropic plates. International Journal of Solid Structures, 1993, 30(23): 3281-3301
[52] K. M. Liew, K. C. Hung, M. K. Lim. On the use of the domain decomposition method for vibration of symmetric laminates have discontinuities at the same edge. Journal of Sound and Vibration, 1994, 178: 243-264
[53] K. C. Hung, K. M. Liew, M. K. Lim. A discrete element method for vibration analysis of mixed edge plates. Finite Elements Analysis and Design, 1994, 18: 319-328
[54] F. L. Liu, K. M. Liew. Static analysis of Reissner-Mindlin plates by differentialquadrature element method. ASME Journal of Applied Mechanical, 1998, 65: 705-710
[55] F. L. Liu, K. M. Liew. Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method. Journal of Sound and Vibration, 1999, 225: 915-934
[56] J. R. Wu, W. Liu. Vibration of rectangular plates with edge restraints and intermediate stiffeners. Journal of Sound and Vibration, 1988, 123: 103-113
[57] P. A. A. Laura, R. Gutierrz. A note on transverse vibration of stiffened rectangular plates with edges elastically restrained against rotation. Journal of Sound and Vibration, 1981, 78: 139-144
[58] R. Bhat. Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz methods. Journal of Sound and Vibration, 1985, 102: 493-499
[59] R. Gutierrez, P. A. A. Laura. Transverse vibration of rectangular plates elastically restrained against rotation along the edges. Journal of Sound and Vibration, 1985, 101: 122-124
[60] K. Liew, Y. Xiang, S. Kitipornchai, M. Lim. Vibration of the rectangular mindlin plates with intermediate stiffeners. Journal of Sound and Vibration, 1994, 166: 529-535
[61] K. Liew, Y. Xiang, S. Kitipornchai, J. Meek. Formulation of mindlinengesser model for stiffened plate vibration. Computer Methods in Applied Mechanical Engineering, 1995, 120: 339-353
[62] Y. Xiang, S. Kitipornchai, K. Liew, M. Lim. Vibration of stiffened skew mindlin plates. Acta Mechanica, 1995, 112: 11-18
[63] A. Berry, J. Nicolas. Vibration and sound radiation of fluid-loaded stiffened plates with consideration of in-plane deformation. Journal of Acoustical Society of America, 1996, 100: 312-319
[64] H. Molaghasemi, I. Harik. Free vibration of stiffened sector plates. Journal of Sound and Vibration, 1996, 190: 726-732
[65] B. Mace. Periodically stiffened fluid-loaded plate, I: response to converted harmonic pressure and free wave propagation. Journal of Sound and Vibration, 1980, 73: 473-486
[66] B. Mace. Periodically stiffened fluid-loaded plate, II: response to line and point forces. Journal of Sound and Vibration, 1980, 73: 487-504
[67] B. Mace. Sound radiation from fluid loaded orthogonally stiffened plates. Journal of Sound and Vibration, 1981, 79: 439-452
[68] D. Mead. Plates with regular stiffening in acoustic media: vibration and radiation. Journal of Acoustical Society of America, 1990, 88: 391-401
[69] A. Berry, J. Nicolas. Structural acoustics and vibration behavior of complex panels. Applied Acoustics, 1994, 100: 185-215
[70] T. Koko, M. Olson. Vibration analysis of stiffened plates by super elements. Journal of Acoustical Society of America, 1992, 158: 149-167
[71] C. Chen, W. Liu, S. Chern. Vibration analysis of stiffened plates. Computer and Structure, 1994, 50: 471-480
[72] A. Cote. Modelisation vibroacoustique dens le domaine des moyennes frequences par elements finis de type P. Ph.D. Thesis, Universite de Sherbrooke, Candan, 1998
[73] D. Mead, D. Zhu, N. Bardell. Free vibration of an orthogonally stiffened flat plate. Journal of Sound and Vibration, 1988, 127: 19-48
[74] D. Mead, D. Zhu, N. Bardell. Free vibration analysis of flat plate using the hierarchical finite element method. Journal of Sound and Vibration, 1991, 151: 262-289
[75] O. Beslin, J. Nicolas. A hierarchical functions set for predicting very high order plate bending modes with any boundary conditions. Journal of Acoustical Society of America, 1996, 95: 2578-2589
[76] C. Guigou, C. R. Fuller. Active control of sound radiation from a semi-infinite elastic beam with a clamped edge. Journal of Sound and Vibration, 1993, 168(3): 507-523
[77] R.H. Lyon. Product Sound Quality- From Design to Perception. Internoise, 2004
[78] C.L. Fog, T.H. Pederson. Introduction to Product Sound Quality. Nordic Acoustical Meeting, 1998
[79] A. Miskiewicz. Psychoacoustics in the Automotive Industry. Acustica, 1999, 85: 646-649
[80] L.N. Solomon. Semantic reactions to systematically varied sounds. Journal of the Acoustical Society of America, 1959, 31: 986-990
[81] E.A. Bjork. The perceived quality of natural sounds. Acustica, 1985, 57: 185-188
[82] A. Zeitler, J. Hellbruck. Semantic attributes of environmental sounds and their correlations with psychoacoustic magnitude. ICA, Rome, Italy, 2001, 25-114
[83] C.E. Osgood. The natural and measurement of meaning. Psychological Bulletin, 1952, 49: 197-237
[84] N Chouard., T. Hempel. A semantic differential design especially developed for the evaluation of interior car sounds. Joint Meeting: ASA/EAA/DEGA, Berlin, Germany, 1999, JASA(105)1280
[85] L Kyncl., O. Jiricek. Psychoacoustic product sound quality evaluation. ICA, Rome, Italy, 2001, 25-90
[86] E. Zwicker, H. Fastl. Psychoacoustics: Facts and Models. Springer-Verlag: Berlin, 1990
[87] P. Susini, S. McAdams, S. Winsberg. A multidimensional technique for sound quality assessment. Acta Acustica, 1999, 85: 650-656
[88] S. Winsberg, G.D. Soete. A latent class approach for fitting the weighted Euclidean model, CLASCAL. Psychometrika, 1993, 58: 315-330
[89] S. Winsberg, G.D. Soete. A Thurstonian pairwise choice model with univariate and multivariate spline transformation. Psychometrika, 1993, 58: 233-256
[90] O. Maeda. Development of an engine evaluation meter. SAE Paper 870965
[91] M. Schneider. Development of vehicle sound quality: targets and methods. Transaction of SAE, 95:1283
[92] H. Schiffbanker. Development and application of an evaluation technique to assess the subjective character of engine noise. Transaction of SAE, 91:1081
[93] M. Hussain. Statistical evaluation of an annoyance index for engine noise recordings. Transaction of SAE, 91:1080
[94] M. Otto. Evaluation and analysis of automotive starter sounds. Journal of Noise Control Engineering, 1993, 41(3): 162-175
[95] V. A. Herman. An engine approach to sound quality. Transaction of SAE, 96:2491
[96] M. F. Rusell. Subjective assessment of diesel vehicle noise. Proceeding of FISITA 92 I.Mech.E.C389/044 925 187 Engineering for the Customer, 1992, 2
[97] R. Mark. New design techniques for improving diesel NVH characteristics. Diesel Progress, 1997, 7: 56-68
[98] H. Kinoshita. Development of new-generation high-performance 4.5-litter V8 Nissan engine. Transaction of SAE, 90: 0651
[99] S. Shoichiro. Improvement of engine sound quality through a new flywheel system flexibly mounted to crankshaft. Transaction of SAE, 90: 0391
[100]藤原奖,孙彦昕.三菱电机在降低吸尘器噪声和改进声质量方面的研究动向.家电科技, 2004, 7: 64-65
[101] S. Amman, J. Greenberg. Subjective evaluation and objective evaluation of automobile structure noise. Noise Control Engineering, 1999, 47(1): 44-49
[102] S. Kuo, D. Morgan. Active Noise Control. Wiley: New York, 1996
[103] S.J. Elliott, P.A. Nelson. Active noise control. IEEE Signal Processing Magazine, 1993, 10(4): 12-35
[104] G. Garnaka. Active noise control, the state of the art. Noise Control Engineering, 1982, 18: 100-110
[105] S.J. Elliott, C. Boucher, P.A. Nelson. The behavior of a multiple channel active control system. IEEE Transactions on Signal Processing, 1992, 40(5): 1041-1052
[106] C. R. Fuller. Analysis of active control of sound radiation from elastic plates by force inputs. Proceeding of Inter-Noise’88, Avignon, France, 1998, 1061-1064
[107] L. Meirovitch, M. A. Norris. Vibration Control. Proceeding of Inter-Noise’84, Honolulu, USA, 1984, 477-482
[108] C. R. Fuller. Active control of sound transmission/radiation from elastic plates by vibration inputs I: analysis. Journal of Sound and Vibration, 1990, 136: 1-15
[109] B. Wang. Active control of noise transmission through rectangular plates using multiple piezoelectric or point forces actuators. Journal of the Acoustical Society of America, 1991, 90: 2820-2830
[110] E. K. Dimitriadis, C. R. Fuller, C. A. Rogers. Piezoelectric actuators for distributed vibration excitation of thin plates. Transactions of the America Society of Mechanical Engineers, 1991, 113: 100-107
[111] E. K. Dimitriadis, C. R. Fuller. Active control of sound transmission through elastic plates using piezoelectric actuators. American Institute of Aeronautics and Astronautics Journal, 1991, 29: 1771-1777
[112] C. A. Fuller, S. J. Elliott, P. A. Nelson. Active Control of Vibration. London: Academic Press, 1996
[113] C. R. Fuller, C. A. Rogers, H. H. Robertshaw. Control of sound radiation with active/adaptive strucutres. Journal of Sound and Vibration, 1992, 57: 19-39
[114] M. E. Johnson. Active control of sound transmission. Ph.D. Thesis, 1996, Institute of Sound and Vibration Research, University of Southampton
[115] A. Preumont. Vibration Control of Active Structures, An Introduction. The Netherlands: Kluwer Academic Publishers, 1997
[116] M. E. Johnson, S. J. Elliott. Active control of sound radiation using volume velocity cancellation. Journal of the Acoustical Society of America, 1995, 94: 2174-2186
[117] S. J. Elliott, M. E. Johnson. Radiation modes and the active control of sound power. Journal of the Acoustical Society of America, 1993, 92: 2194-2204
[118] J. Rex, S. J. Elliott. The QWSIS- a new sensor for structural radiation control. Proceedings of the First International Conference on Motion and Vibration Control, Yokohama, Japan, 1992, 339-343
[119] M. E. Johnson, T. Sors, S. J. Elliott, B. Bafaely. Feedback control of broadband sound radiation using a volume velocity sensor. Proceeding of Active’97, Budapest, Hungary, 1997, 1007-1020
[120] J. P. Maillard, C. R. Fuller. Active control of sound radiation from cylinders with piezoelectric actuators and structural acoustic sensing. Proceedings of Active’97, Budapest, Hungary, 1997, 1021-1034
[121] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. I: theory and design. Journal of the Acoustical Society of America, 1994, 93: 3252-3261
[122] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. II: active radiation control of a simply supported beam. Journal of the Acoustical Society of America, 1994, 93: 3262-3272
[123] J. P. Maillard, C. R. Fuller. Advanced time domain wave-number sensing for structural acoustic systems. III: experiments on active broadband radiation control of a simply-supported beam. Journal of the Acoustical Society of America, 1995, 94: 2613-2621
[124] A. Preumont, A. Franscois, S. Dubru. Piezoelectric array sensing for real-time, broad-band sound radiation measurement. Journal of Vibration and Acoustics, 1999, 21: 446-452
[125] Leuseur. Rayonnment Acoustique des Structures. Editions Eyrolles: Paris, 1988
[126] Maidanik. Vibrational and radiative classifications of modes of a baffled finite panel. Journal of Sound and Vibration, 1974, 34: 447-455
[127] H.G. Davies. Acoustic radiation from fluid loaded rectangular plates. MIT Reports No.7: 1476-1
[128] H.G. Davies. Sound from turbulent boundary layer excited panels. Journal of Acoustical Society of America, 1971, 49: 878-889
[129] R. Graham. High frequency vibration and acoustic radiation of fluid loaded plates. Transactions of Royal Society, London, 1995, A 352: 1-43
[130] O. Mattei. Sound radiation by baffled and constrained plates. Journal of Sound and Vibration, 1995, 179(1): 63-77
[131] Atalla, J. Nicolas, C. Gauthier. Acoustic radiation of an un-baffled vibrating plate with general conditions. Journal of Acoustical Society of America, 1996, 99: 1484-1494
[132] Laulagnet. Sound radiation by a simply supported un-baffled plate. Journal of Acoustical Society of America, 1998, 103: 2451-2462
[133] R. Soni, R.K. Sankara. Vibration of non-uniform rectangular plates: a spline technique method of solution. Journal of Sound and Vibration 1974, 35(1): 35-45
[134] Filipich, P.A.A. Laura, R.D. Santos. A note on vibration of rectangular plates. Journal of Sound and Vibration 1977, 50(3): 445-454
[135] H. Gutierrez, P.A.A. Laura, R.O. Grossi. Vibration of rectangular plates of bi-linearly varying thickness and with boundary conditions. Journal of Sound and Vibration 1981, 75:323-328
[136] F.T.K. Au, M.F. Wang. Sound radiation from forced vibration of rectangular orthotropic plates under moving loads. Journal of Sound and Vibration, 2005, 281(3-5):1057-1075
[137] W.T. Thomson. Theory of vibration with applications. New Jersey: Prentice Hall. 1972
[138] C.C. Sung, J.T. Jan. The response of and sound power radiated by a clamped rectangular plate. Journal of Sound and Vibration, 1997, 207(3): 301-317
[139] F.T.K. Au, M.F. Wang. Sound radiation from forced vibration of rectangular orthotropic plates under moving loads. Journal of Sound and Vibration, 2005,281(3-5): 1057-1075
[140] W.L. Li, H.J. Gibeling. Acoustic radiation from a rectangular plates reinforced by springs at arbitrary locations. Journal of Sound and Vibration, 1999, 220(1): 117-133
[141] T. Takahagi, M. Nakai, Y. Tamai. Near Field Sound Radiation From Simply Supported Rectangular Plate. Journal of Sound and Vibration, 1995, 185(3): 455-471
[142] J. Park, L. Mongeau, T. Siegumnd. Influence of supported properties on the sound radiated from the vibration of rectangular plates. Journal of Sound and Vibration, 2003, 264(4): 775-794
[143] Yuh-Chun Hu, Shyh-Chin Huang. The frequency response and damping effect of three-layer thin shell. Computers and Structures, 2000, 76(5):577-591
[144] Y. Wonho. Enhanced Modified Bark Spectral Distortion (EMBSD): An Objective Speech Quality Measure Based on Audible Distortion and Cognition Model. PhD Thesis, Temple University, USA, 1999
[145] ITU-R Recommendation BS. 1387. Method for Objective Measurement of Perceived Audio Quality (PSQM). 1998
[146] T. Thiede. Perceptual Audio Quality Assessment Using a Non-linear Filter Bank. PhD Thesis, TU Berlin, 1999
[147] ITU-R Study Group 6. Draft Revision to BS. 1387, Method for Objective Measurement of Perceived Audio Quality, Document 6/BL/30-E. 2001
[148] P. Kabal. An Examination and Interpretation of ITU-RBS.1387: Perceptual Evaluation of Audio Quality. TSP Lab Technical Report, Dept. ECE, McGill University, 2002
[149] H. Fastl. Hearing: Physiological bases and Psychophysics. Berlin Heidelberg: Springer, 1993
[150] H. Fastl. The psychoacoustics of sound quality evaluation. Acustica, 1997, 83(5): 754-764
[151] J. Bemsen. Sound in design. Danish Design Center & DELTA Acoustics and Vibration, 1999
[152] M. A. Milosevic, A. M. Mitic, M. S. Milosevic. Parameters influencing noise estimation. Working and Living Environmental Protection, 2004, 2(4): 277-284
[153] J. Blauert, U. Jekosch. Sound quality evaluation: a multilayered problem. Antwerp: EEA Tutorium, 1996
[154] Y. Narita. Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions. Journal of Sound and Vibration, 1981, 77(3): 345-355
[155] Y. Hirano, K. Okazaki. Vibration of a circular plate having partly clamped or partly simply supported edges. Bullion of Japanese Society of Mechanics Engineering, 1976, 19: 610-618
[156] S.C. Fan, Y.K. Cheng. Flexural free vibration of rectangular plates with complex support conditions. Journal of Sound and Vibration, 1986, 23:45-55
[157] K.M. Liew, C.M. Wang. Vibration analysis of plates by the pb-2 Rayleigh-Ritz method: mixed boundary conditions, reentrant corners and internal curved supports. Mechanical Structure and Mechanics, 1992, 20: 281-292
[158] C.Y. Chia. Nonlinear vibration of anisotropic rectangular plates with non-uniform edge constraints. Journal of Sound and Vibration, 1985, 101: 539-550
[159] R. Bellman, B.G. Kashef, J. Casti. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 1972, 10: 40-52
[160] P.A.A. Laura, R.H. Gutierrez. Analysis of vibrating rectangular plates with non-uniform boundary conditions by using the differential quadrature method. Journal of Sound and Vibration, 1994, 173: 702-706
[161] C. Shu. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD thesis, University of Glasgow, Scotland, 1991
[162] C. Shu, H. Du. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids Structures, 1997, 34: 819-835
[163] C. Shu, H. Du. A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates. Journal of Solids Structures, 1997, 34: 837-846
[164] C. Shu, C.M. Wang. Treatment of mixed and non-uniform boundary conditions in GDQ vibration analysis of rectangular plates. Engineering Structures, 1999, 21:125-134
[165] G. Xie, D.J. Thompson, C.J.C. Jones. Mode count and modal density of structural systems: relationships with boundary conditions. Journal of Sound and Vibration, 2004, 27(3-5): 621-651
[166] E. Terhardt. On the perception of periodic sound fluctuations (roughness). Acustica, 1974, 30: 201-213
[167] R. Hoeldrich. An optimized model for the objective assessment of roughness sensations in vehicle noise. AVL - Sound Engineering Conference, Graz, July 22-27, 1999
[168] P. Daniel, R. Weber. Calculating psycho-acoustical roughness. Proceeding of Internoise, 1993, 251-165
[169] M. Pflueger, R. Hoeldrich, F. Brandl, W. Biemayer. Psychoacoustic measurement of roughness of vehicle interior noise. Proceeding of 137th Meeting of the Acoustical of American, Berlin, March 14-19,1999
[170] D. Bloger, N. Griffith. Multidimensional timbre analysis of shakuhachi honkyoku. Proceeding of the Conference on Interdisciplinary Musicology, Montreal, Spring 10-12, 2005
[171] F. Brandl, W. Biermayer. A new tool for the onboard objective assessment of vehicle interior noise quality. SAE Noise & Vibration Conference & Exposition, Traverse City, May 17-20, 1999
[172] W. Sethares. Tuning, timbre, spectrum, scale. London: Springer Verlag, 1998
[173] P. N. Vassilakis. Perceptual and physical properties of amplitude fluctuation and their musical significance. PhD. Thesis, 2001, University of California at Los Angeles
[174] K. M. Liew, C. M. Wang, Y. Xiang. Vibration of Mindlin plates-programming the p-version Ritz method. Amsterdam, The Netherlands: Elsevier Science Ltd, 1998
[175] G. H. Su, Y. Xiang. A non-discrete approach for analysis of plates with multiple subdomains. Engineering Structures, 2002, 24: 563-575
[176] K.M. Liew, Y. Xiang, S.Kitipomchai. Research on thick plate vibration: a literature survey. Journal of Sound and Vibration, 1995, 180(1): 163-176
[177] S.F. Ney, G.G. Kulkami. On the transverse free vibration of beam-slab type highway bridges. Journal of Sound and Vibration, 1972, 21: 249-261
[178] T. Baledra, N.E. Shanmugam. Free vibration of plates structures by grillage method. Journal of Sound and Vibration, 1985, 99: 333-350
[179] C.L. Kirk. Vibration of centrally stiffened rectangular plates. Journal of Royal Aeronautical Society, 1961, 65: 695-697
[180] K.M. Liew, Y. Xiang, S.Kitipomchai, J.L. Meek. Formulation of Mindlin-engesser model for stiffened plate vibration. Computer Methods in Applied Mechanics and Engineering, 1995, 120(3-4): 339-353
[181] Y. Xiang, S.Kitipomchai, K.M. Liew, M.K. Lim. Vibration of stiffened skew Mindlin plates. Acta Methanica, 1995, 112: 11-28
[182] Y. Xiang, K.M. Liew, S.Kitipomchai. Vibration of circular and annular plate with internal ring stiffeners. Journal of the Acoustical Society of America, 1996, 100(6): 3696-3705
[183] B.R. Long. A stiffness-type analysis of the vibration of a class of stiffened plates. Journal of Sound and Vibration, 1971, 16: 323-335
[184] G. Akus, R. Ali. Free vibration analysis of stiffened plates using finite difference method. Journal of Sound and Vibration, 1976, 48: 15-25
[185] G. Akus. Free vibration analysis of stiffened plates by including the effect of in-plane inertia. Journal of Applied Mechanics, 1982, 49: 206-212
[186] M. Guo, I.E. Harik. Stability of eccentrically stiffened plates. Thin-Walled Structures, 1992, 14: 1-20
[187] C. Chen, W. Liu, S. Chren. Vibration analysis of stiffened plates. Computer and Structure, 1994, 50: 471-480
[188] A. Beslin, J. Nicolas. Structural acoustics and vibration behavior of complex panels. Applied Acoustics, 1994, 100: 185-215
[189] M. Barrette, A. Berry, O. Beslin. Vibration of stiffened plates using hierarchical trigonometric functions. Journal of Sound and Vibration, 2000, 235(5): 727-747
[190] P. Vitiello, P.A. Nelson, M. Petyt. Numerical studies of the active control of sound transmission through double partitions. ISVR Techincal Report, 1989, No.183
[191] C.K. Lee. Theory of laminated piezoelectric plates for design of distributed sensors/actuators. Part I: governing equations and reciprocal relationships. Journal of the Acoustical Society of America, 1990, 87:114-1158
[192] S.J. Eillott. Signal processing for active control. London: Academic Press, 2001