矩形薄板的振动与声辐射研究及其控制
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摘要
近年来,噪声成了一个重要的环境问题,引起了众多专家学者的广泛关注,也是目前的一个研究重点。作为一门新兴的学科,有源噪声控制技术在最近的几十年时间里发展很快,由于传统的被动噪声控制在低频段存在缺陷,因此可以利用它来弥补不足。结构声有源控制基于辐射模态的理论,它避免了振动模态中复杂的耦合项,简化了计算。本文以对边固定对边自由矩形板为研究对象,在对其进行振动分析的基础上,对其声辐射模态控制进行了研究。
论文主要研究内容有：
(1)应用振型叠加法,推导了对边固定对边自由矩形薄板在简谐激励下的位移、速度关系式,分别利用MATLAB编程计算和有限元模拟证明了理论推导的结果。并由速度分布式得出了板周围空间声压分布的近似解。
(2)基于声辐射模态理论,分析对边固定对边自由矩形板的各阶辐射模态以及辐射效率随频率的变化趋势,并研究了该种情况下声辐射模态和振动模态的对应关系。
(3)根据辐射模态的特性,提出了抵消前N阶声辐射模态伴随系数法和声功率最小化法两种控制方法,并比较了两种方法的控制效果。最后讨论了激振力与控制力位置对控制效果的影响。
With the development of social economy, noise has been obtained widespread provenance as one of the significant environmental issues. In the past decades, the active noise control has been developed rapidly as a newly arisen discipline, which are expected to overcome the disadvantages of traditional passive noise control techniques in low-frequency stage. Based on the radiation modes, method of active structural acoustic control can avoid the complicated coupling of vibration modal and simplify the calculation and control burden. However, all the existing research production of radiation modes originate from rectangular plates with all four sides simply supported, while noise control about plates with one pair of opposite sides fixed and other two opposite sides free has not been reported yet.
The current study is summarized as follows:
(1)Based on the modal superposition method, the displacement and velocity formula of plate with two opposite edges fixed and other two free under excitation are deduced by theoretical analysis. Meanwhile, the finite element simulating and MATLAB programming and calculation are also used to confirm the results. Further, approximate solution for sound pressure distribution around the plate is obtained by velocity distribution. All conclusions above can provide a theoretical basis for a further study on sound radiation of plate with two opposite edges fixed and other two free.
(2) By the theory of radiation mode, the changing trend about radiation modal、radiation efficiency of each step versus frequency is established. In addition, the correspondence relationship between radiation mode and structure vibration mode are analyzed systemically.
(3) Aiming at radiation modal characteristics, two control methods of canceling acoustic radiation coefficient of the first N steps and minimizing acoustic power are presented and then compared for controlling effect. The influence of control effect with different position of exciting force and controlling force is also analyzed preliminarily.
The research results show that in low-frequency sound control method based on the radiation mode can reduce the acoustic power of plates with two opposite edges fixed and other two free sharply. And reasonable controlling forces locations will greatly improve the control effect.
论文主要研究内容有：
(1)应用振型叠加法,推导了对边固定对边自由矩形薄板在简谐激励下的位移、速度关系式,分别利用MATLAB编程计算和有限元模拟证明了理论推导的结果。并由速度分布式得出了板周围空间声压分布的近似解。
(2)基于声辐射模态理论,分析对边固定对边自由矩形板的各阶辐射模态以及辐射效率随频率的变化趋势,并研究了该种情况下声辐射模态和振动模态的对应关系。
(3)根据辐射模态的特性,提出了抵消前N阶声辐射模态伴随系数法和声功率最小化法两种控制方法,并比较了两种方法的控制效果。最后讨论了激振力与控制力位置对控制效果的影响。
With the development of social economy, noise has been obtained widespread provenance as one of the significant environmental issues. In the past decades, the active noise control has been developed rapidly as a newly arisen discipline, which are expected to overcome the disadvantages of traditional passive noise control techniques in low-frequency stage. Based on the radiation modes, method of active structural acoustic control can avoid the complicated coupling of vibration modal and simplify the calculation and control burden. However, all the existing research production of radiation modes originate from rectangular plates with all four sides simply supported, while noise control about plates with one pair of opposite sides fixed and other two opposite sides free has not been reported yet.
The current study is summarized as follows:
(1)Based on the modal superposition method, the displacement and velocity formula of plate with two opposite edges fixed and other two free under excitation are deduced by theoretical analysis. Meanwhile, the finite element simulating and MATLAB programming and calculation are also used to confirm the results. Further, approximate solution for sound pressure distribution around the plate is obtained by velocity distribution. All conclusions above can provide a theoretical basis for a further study on sound radiation of plate with two opposite edges fixed and other two free.
(2) By the theory of radiation mode, the changing trend about radiation modal、radiation efficiency of each step versus frequency is established. In addition, the correspondence relationship between radiation mode and structure vibration mode are analyzed systemically.
(3) Aiming at radiation modal characteristics, two control methods of canceling acoustic radiation coefficient of the first N steps and minimizing acoustic power are presented and then compared for controlling effect. The influence of control effect with different position of exciting force and controlling force is also analyzed preliminarily.
The research results show that in low-frequency sound control method based on the radiation mode can reduce the acoustic power of plates with two opposite edges fixed and other two free sharply. And reasonable controlling forces locations will greatly improve the control effect.
引文
[1]倪振华.振动力学.西安：西安交通大学出版社.1986
[2]M. Levinson. Free vibrations of a simply supported rectangular plate:An exact elasticity solution. Journal of Sound and Vibration,1985, 98(2):289-298
[3]T. F. Raske, A. L. Schlack. Dynamic response of plates due to moving loads, Journal of the Acoustical Society of America,1967,42 (3):625-635
[4]L. Fryba, Vibration of Solids and Structures under Moving Loads, Thomas Telford, London, UK,1999
[5]D. M. Yoshida, W. Weaver. Finite element analysis of beams and plates with moving loads, Publications, International Association of Bridges and Structural Engineering,1971,31:79-195
[6]J. A. Gbadeyan, S. T. Oni. Dynamic behavior of beams and rectangular plates under moving loads. Journal of Sound and Vibration,1995,182 (5):677-695
[7]G. Maidanik. Vibrational and radiative classification of modes of a baffled finite panel. Journal of Sound and Vibration,1974,34:447-455
[8]C. E. Wallace. Radiation resistance of rectangular panels. Journal of the Acoustical Society of America,1972,53:946-952
[9]E.G. Williams, J. D. Maynard, Numerical evaluation of the Rayleigh integral for planar radiators using the FFT, Journal of the Acoustical Society of America,1982,72 (6):2020-2030
[10]W.L.LI, H. J. GIBELING. Acoustic radiation from a rectangular plate reinforced by finite springs at arbitrary locations. Journal of Sound and vibration,1999,20(6):191-204
[11]姜哲,郭骅.由试验模态分析研究振动物体的辐射效率.振动与冲击,1992,4：44-49
[12]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
[13]梁剑,张重超.平板声辐射效率的级数表示.上海交通大学学报,1990,24(3)：16-22
[14]徐张明,王国治.水下结构振动与声辐射效率的研究.华东船舶工业学院学报,2000,14(1)：38-42
[15]黎胜,赵德有.用有限元/边界元进行结构的声辐射模态分析.声学学报.2001,26(2)：174—179
[16]陈克安.有源噪声控制.北京：国防工业出版社.2003
[17]Lueg P. Process of silencing sound oscillation, German patent DRP No.655508,1933
[18]Lueg P. Process of silencing sound oscillation, US patent No.655508,1933
[19]P. A. Nelson, E. J. Elliott. Active control of sound. Academic Press, London,1992
[20]C. Deffayet, Nelson P A. Active control of low-frequency harmonic sound radiated by a finite panel. Journal of Acoustic Society of America,1988: 84(6):2192-2199
[21]陈克安,陈国跃,李双等.分布式位移传感下的有源声学结构误差传感策略.声学学报,2007,32(1)：42-48
[22]李双,陈克安.有源声学结构次级声源的布放规律研究.机械科学与技术,2006,35(11)：1351-1357
[23]陈克安,柯谱曼.基于平面声源实施结构声辐射有源控制的理论研究.声学学报,2003,28(4)：279-293
[24]伊善贞,费仁元,周大森等.次级声源安装角度对管道有源消声性能的影响研究.机械工程学报,2005,41(4)：63-68
[25]郭文勇,黄映云,朴甲哲.管道主动消声的次级声源设计.海军工程大学学报,2000,14(1)：69-71
[26]C. R. Fuller, C. A. Rogers, H. Robertshaw. Control of sound radiation with active adaptive structure. Journal of Sound and Vibration,1992,157, 19-39
[27]C. R. Fuller, C. H. Hansen, S. D. Snyder. Active control of sound radiation from a vibrating rectangular panel by sound sources and vibration inputs: an experimental comparison. Journal of the Acoustic Society of America, 1962,34:809-826
[28]C.R.Fuller. Active control of sound transmission/radiation from elastic plates by vibrational inputs analysis. Journal of the Acoustic Society of America,1990,136(1):1-15
[29]C. R. Fuller, C. H. Hansen, S. D. Snyder. Experiments on active control of sound radiation from a panel use a piezoelectric actuators. Journal of Sound and Vibration,1991,150:179-190
[30]孙蓓蓓,孙庆鸿.有源结构在次级力源作用下的模态抑制和重构.振动工程学报,1997,10(1)：35-41
[31]李普,孙庆鸿,陈南.结构振动声辐射的H∞控制实验研究.声学学报,2000,25(5)：472-475
[32]陈克安,马远良自适应有源消声与滤波-XLMS算法及实现.应用声学,1993,7(3)：26-30
[33]陈克安.自适应声学结构声压误差传感策略.振动工程学报,2004,17(3)：301-305
[34]陈克安,尹雪飞.基于近场声压传感的结构声辐射有源控制.声学学报,2005,30(1)：63-68
[35]G. V. Borgiotti. The Power radiated by a Vibrating Body in an Acoustic Fluid and its Determination from Boundary Measurements. Journal of the Acoustic Society of America,1990,88(4)1884-1893
[36]G. V. Borgiotti. The determination of the acoustic far field of a radiating body in an acoustic fluid from boundary measurements. Journal of the Acoustic Society of America,1993,93(5):2788-2797
[37]G. V. Borgiotti. Frequency independence property of radiation spatial filters. Journal of the Acoustic Society of America,1994,96(6): 3516-3524
[38]Angie Sarkissian. Acoustic radiation from finite structures. Journal of the Acoustic Society of America,1991,90(1):574-578
[39]K. A. Cunefare, M. N. Currey. On the Exterior Acoustic Radiation modes of structure. Journal of the Acoustic Society of America,1994, 96(4):2302-2312
[40]S. J. EIliott. Radiation Modes and the active control of sound power. Journal of the Acoustic Society of America,1993,94(4): 2194-2204
[41]Koorsh Naghshineh, G. H. Koopmann. Material tailoring of structure to achieve a minimum radiation condition. Journal of the Acoustic Society of America,1992,92(2):841-855
[42]Koorsh Naghshineh, G. H. Koopmann. A design method for achieving weak radiator structures using active vibration control. Journal of the Acoustic Society of America,1992,92(3):856-870
[43]Koorsh Naghshineh, G. H. Koopmann. Active control of sound power using acoustic basis functions surface velocity filter. Journal of the Acoustic Society of America,1993,93(5):2740-2752
[44]K. A. Cunfare, M. N. Currey. On the Exterior Acoustic Radiation Modes of Structure. Journal of the Acoustic Society of America,1994, 96(4):2302-2312
[45]K. A. Cunfare. The Radiation Modes of Baffled Finite Plates. Journal of the Acoustic Society of America,1995,98(3):1570-1580
[46]姜哲.声辐射问题中的模态分析：Ⅰ理论.声学学报,2004,24(4)：374-378
[47]姜哲.声辐射问题中的模态分析：Ⅱ.实例.声学学报,2005,29(6)：507-515
[48]姜哲.声辐射问题中的模态分析：Ⅲ.声场重构.声学学报,2005,30(3)： 242-248
[49]姜哲.基于声辐射模态确定声功率.江苏大学报,2005,26(6)：537-541
[50]姜哲,吴卫国.基于时域声辐射模态的结构噪声主动控制研究.江苏大学学报,2004,25(5)：453-456
[51]毛崎波,姜哲.通过声辐射模态研究结构噪声的有源控制.江苏理工大学学报,2000,21(4)：1-6
[52]毛崎波,姜哲.通过声辐射模态研究结构声辐射的有源控制.声学学报,2001,26(3)：277-281
[53]毛崎波,姜哲.对声辐射模态的讨论.振动工程学报,2000,3(4)：633-637
[54]毛崎波,姜哲.通过压电传感器进行对简支梁声辐射有源控制.声学学报,2001,26(4):157-160
[55]毛崎波,姜哲.对声辐射模态法的改进.振动工程学报,2002,13(4)：633-637
[56]毛崎波,姜哲.简支矩形板声辐射的有源控制.声学技术,2002,21(3)：118-121
[57]顾检,姜哲.通过PVDF测量简支梁声辐射模态伴随系数.江苏理工大学学报,2001,22(6)：1-5
[58]吴锦武,姜哲.利用PVDF设计两维简支结构声辐射模态传感器.江苏大学学报,2002,23(6)：15-20
[59]王志,姜哲.对平板的速度分布及其对应辐射效率的探讨.江苏大学学报,1999,20(2)：13-16
[60]许肖梅.声学基础.北京：科学出版社,2003
[2]M. Levinson. Free vibrations of a simply supported rectangular plate:An exact elasticity solution. Journal of Sound and Vibration,1985, 98(2):289-298
[3]T. F. Raske, A. L. Schlack. Dynamic response of plates due to moving loads, Journal of the Acoustical Society of America,1967,42 (3):625-635
[4]L. Fryba, Vibration of Solids and Structures under Moving Loads, Thomas Telford, London, UK,1999
[5]D. M. Yoshida, W. Weaver. Finite element analysis of beams and plates with moving loads, Publications, International Association of Bridges and Structural Engineering,1971,31:79-195
[6]J. A. Gbadeyan, S. T. Oni. Dynamic behavior of beams and rectangular plates under moving loads. Journal of Sound and Vibration,1995,182 (5):677-695
[7]G. Maidanik. Vibrational and radiative classification of modes of a baffled finite panel. Journal of Sound and Vibration,1974,34:447-455
[8]C. E. Wallace. Radiation resistance of rectangular panels. Journal of the Acoustical Society of America,1972,53:946-952
[9]E.G. Williams, J. D. Maynard, Numerical evaluation of the Rayleigh integral for planar radiators using the FFT, Journal of the Acoustical Society of America,1982,72 (6):2020-2030
[10]W.L.LI, H. J. GIBELING. Acoustic radiation from a rectangular plate reinforced by finite springs at arbitrary locations. Journal of Sound and vibration,1999,20(6):191-204
[11]姜哲,郭骅.由试验模态分析研究振动物体的辐射效率.振动与冲击,1992,4：44-49
[12]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
[13]梁剑,张重超.平板声辐射效率的级数表示.上海交通大学学报,1990,24(3)：16-22
[14]徐张明,王国治.水下结构振动与声辐射效率的研究.华东船舶工业学院学报,2000,14(1)：38-42
[15]黎胜,赵德有.用有限元/边界元进行结构的声辐射模态分析.声学学报.2001,26(2)：174—179
[16]陈克安.有源噪声控制.北京：国防工业出版社.2003
[17]Lueg P. Process of silencing sound oscillation, German patent DRP No.655508,1933
[18]Lueg P. Process of silencing sound oscillation, US patent No.655508,1933
[19]P. A. Nelson, E. J. Elliott. Active control of sound. Academic Press, London,1992
[20]C. Deffayet, Nelson P A. Active control of low-frequency harmonic sound radiated by a finite panel. Journal of Acoustic Society of America,1988: 84(6):2192-2199
[21]陈克安,陈国跃,李双等.分布式位移传感下的有源声学结构误差传感策略.声学学报,2007,32(1)：42-48
[22]李双,陈克安.有源声学结构次级声源的布放规律研究.机械科学与技术,2006,35(11)：1351-1357
[23]陈克安,柯谱曼.基于平面声源实施结构声辐射有源控制的理论研究.声学学报,2003,28(4)：279-293
[24]伊善贞,费仁元,周大森等.次级声源安装角度对管道有源消声性能的影响研究.机械工程学报,2005,41(4)：63-68
[25]郭文勇,黄映云,朴甲哲.管道主动消声的次级声源设计.海军工程大学学报,2000,14(1)：69-71
[26]C. R. Fuller, C. A. Rogers, H. Robertshaw. Control of sound radiation with active adaptive structure. Journal of Sound and Vibration,1992,157, 19-39
[27]C. R. Fuller, C. H. Hansen, S. D. Snyder. Active control of sound radiation from a vibrating rectangular panel by sound sources and vibration inputs: an experimental comparison. Journal of the Acoustic Society of America, 1962,34:809-826
[28]C.R.Fuller. Active control of sound transmission/radiation from elastic plates by vibrational inputs analysis. Journal of the Acoustic Society of America,1990,136(1):1-15
[29]C. R. Fuller, C. H. Hansen, S. D. Snyder. Experiments on active control of sound radiation from a panel use a piezoelectric actuators. Journal of Sound and Vibration,1991,150:179-190
[30]孙蓓蓓,孙庆鸿.有源结构在次级力源作用下的模态抑制和重构.振动工程学报,1997,10(1)：35-41
[31]李普,孙庆鸿,陈南.结构振动声辐射的H∞控制实验研究.声学学报,2000,25(5)：472-475
[32]陈克安,马远良自适应有源消声与滤波-XLMS算法及实现.应用声学,1993,7(3)：26-30
[33]陈克安.自适应声学结构声压误差传感策略.振动工程学报,2004,17(3)：301-305
[34]陈克安,尹雪飞.基于近场声压传感的结构声辐射有源控制.声学学报,2005,30(1)：63-68
[35]G. V. Borgiotti. The Power radiated by a Vibrating Body in an Acoustic Fluid and its Determination from Boundary Measurements. Journal of the Acoustic Society of America,1990,88(4)1884-1893
[36]G. V. Borgiotti. The determination of the acoustic far field of a radiating body in an acoustic fluid from boundary measurements. Journal of the Acoustic Society of America,1993,93(5):2788-2797
[37]G. V. Borgiotti. Frequency independence property of radiation spatial filters. Journal of the Acoustic Society of America,1994,96(6): 3516-3524
[38]Angie Sarkissian. Acoustic radiation from finite structures. Journal of the Acoustic Society of America,1991,90(1):574-578
[39]K. A. Cunefare, M. N. Currey. On the Exterior Acoustic Radiation modes of structure. Journal of the Acoustic Society of America,1994, 96(4):2302-2312
[40]S. J. EIliott. Radiation Modes and the active control of sound power. Journal of the Acoustic Society of America,1993,94(4): 2194-2204
[41]Koorsh Naghshineh, G. H. Koopmann. Material tailoring of structure to achieve a minimum radiation condition. Journal of the Acoustic Society of America,1992,92(2):841-855
[42]Koorsh Naghshineh, G. H. Koopmann. A design method for achieving weak radiator structures using active vibration control. Journal of the Acoustic Society of America,1992,92(3):856-870
[43]Koorsh Naghshineh, G. H. Koopmann. Active control of sound power using acoustic basis functions surface velocity filter. Journal of the Acoustic Society of America,1993,93(5):2740-2752
[44]K. A. Cunfare, M. N. Currey. On the Exterior Acoustic Radiation Modes of Structure. Journal of the Acoustic Society of America,1994, 96(4):2302-2312
[45]K. A. Cunfare. The Radiation Modes of Baffled Finite Plates. Journal of the Acoustic Society of America,1995,98(3):1570-1580
[46]姜哲.声辐射问题中的模态分析：Ⅰ理论.声学学报,2004,24(4)：374-378
[47]姜哲.声辐射问题中的模态分析：Ⅱ.实例.声学学报,2005,29(6)：507-515
[48]姜哲.声辐射问题中的模态分析：Ⅲ.声场重构.声学学报,2005,30(3)： 242-248
[49]姜哲.基于声辐射模态确定声功率.江苏大学报,2005,26(6)：537-541
[50]姜哲,吴卫国.基于时域声辐射模态的结构噪声主动控制研究.江苏大学学报,2004,25(5)：453-456
[51]毛崎波,姜哲.通过声辐射模态研究结构噪声的有源控制.江苏理工大学学报,2000,21(4)：1-6
[52]毛崎波,姜哲.通过声辐射模态研究结构声辐射的有源控制.声学学报,2001,26(3)：277-281
[53]毛崎波,姜哲.对声辐射模态的讨论.振动工程学报,2000,3(4)：633-637
[54]毛崎波,姜哲.通过压电传感器进行对简支梁声辐射有源控制.声学学报,2001,26(4):157-160
[55]毛崎波,姜哲.对声辐射模态法的改进.振动工程学报,2002,13(4)：633-637
[56]毛崎波,姜哲.简支矩形板声辐射的有源控制.声学技术,2002,21(3)：118-121
[57]顾检,姜哲.通过PVDF测量简支梁声辐射模态伴随系数.江苏理工大学学报,2001,22(6)：1-5
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