船舶与海洋结构动力分析中的动态刚度阵法研究
|
摘要
动态刚度阵法最早由Kolousek于20世纪40年代初提出，是解决工程中结构动力学问题的一个强有力工具，它尤其适合于需要获得更高阶固有频率和更高精度的结构动力特性分析问题。动态刚度阵法通常也被称为精确方法，这是因为它的单元刚度阵是从单元运动微分方程的解析解推导而来的，其中的各元素都是频率的超越函数，并同时具有质量和刚度属性。因而，动态刚度阵法可以通过极少的自由度数准确的计算出结构固有频率和振动响应，而且随着计算频率的升高，动态刚度阵法也无需进一步细划单元。采用动态刚度阵法计算结构动力特性时，可以按结构自然节点划分单元，单元组装方法与常规有限元方法完全相同。本文着重将动态刚度阵法引入并推广到船舶与海洋结构动力分析中，利用它对船舶总体振动特性、局部加筋板结构中高频动力特性以及海洋平台的智能控制进行研究。论文主要包括以下几个方面内容：
本文首次将动态刚度阵法应用于船舶总体振动特性和响应研究中，利用它来简化计算模型，提高计算速度和精度。考虑到垂向和水平振动时船体所带的附加水质量不同，所以可利用平面Timoshenko梁单元的动态刚度阵来分别计算两个方向的总振动固有频率和响应。本文采用动态刚度阵法结合Wittrick-Williams算法对299，500DWT超大型油船的总体振动固有特性进行预报，所得固有频率和固有振型通过模态叠加法来求解该船在螺旋桨激励下的总体振动响应，计算结果分别与一维梁有限元模型和三维全船有限元模型计算结果以及实测值进行比较，以验证本方法的精确性和有效性。研究表明，船舶总体振动的刚度主要取决于平行中体的惯性矩和剪切面积，而其沿船长方向的分布对它的固有频率影响较小，反而船舶质量沿船长分布情况对固有频率的影响较大。因此，如果按理论站的位置来划分船体梁的单元时，可能会因为一个舱室的质量分布在若干个站内，需要按力和力矩等效的原则来重新调整质量分布，而采用动态刚度阵法计算时，当船舶舱室较多时可直接按照舱室分布来划分单元，避免了对船舶质量分布的重新调整，简化了计算模型，方便了数据准备工作，而且还能同时保证各单元满足梁理论的要求，提高了工程需要阶数内固有频率计算结果的准确性，为船舶总体振动特性分析研究提供了一个快速而便捷的计算方法。
本文推导了考虑平面内振动影响的双向加筋Mindlin板动态刚度阵，为动态刚度阵法提供了一种新的单元类型，进而为研究加筋板间的能量传递开辟了一个新途径。本文以加筋中厚矩形板为研究对象，通过Hamilton原理建立考虑平面内振动影响的双向加筋Mindlin板运动微分方程，再利用方程的解析解来推导其动态刚度阵，所得动态刚度阵被用于加筋板的中高频动力特性问题研究之中。首先采用动态刚度阵法对L型加筋板间的耦合损耗因子进行计算，计算结果与实测值和有限元方法分别进行了比较，以验证本文方法的可行性、准确性和高效性；所得加筋板间的耦合损耗因子可与统计能量分析方法相结合，来更为准确地对船舶舱室噪声进行预报。此外，本文还利用动态刚度阵法研究了加筋板间的能量传输关系，讨论了平面内振动、剪切变形和转动惯量对加筋板间弯曲能量传输的影响，并给出了一些相关结论。
本文提出了一种新的基于动态刚度阵法的导管架式海洋平台模糊神经网络自适应预测逆控制模型。该模型是将实时采集的海洋平台所受波浪力提供给动态刚度阵建立的计算模型，通过它来快速而准确地计算出平台项部的响应，再将此响应作为模糊神经网络预测逆控制器的输入信号，由它预测出下一时刻平台顶部的控制力来对海洋平台振动响应进行控制；同时对控制后的平台响应进行实时测量，所得响应误差和扰动一起作为反馈自适应预测逆控制器的输入信号，它的输出力信号直接反馈到被控平台的项部，以此来消除被控对象的内部噪声和外部扰动。最后的数值算例结果表明，本文所提出的导管架式海洋平台主动控制模型既能很好地解决控制系统中存在的时滞问题，又具有较强的抗干扰能力，可以有效地控制海洋平台的振动响应。
本文研究表明，动态刚度阵法凭借着所需单元少、计算速度快、计算精度高以及适用频率范围广等特点，可以用来便捷高效地计算结构的动力特性，在船舶与海洋结构动力分析中有着广阔的应用前景。利用该方法对船舶总体振动特性分析过程中可以提高计算精度，简化计算模型，是一个不可多得的简便实用工具。毫无疑问，本文所推导的双向加筋Mindlin板单元的动态刚度阵为动态刚度阵法提供了一个新的单元类型，为研究加筋板间中高频区域内的动力特性提供了一个强有力的工具。所提出的基于动态刚度阵法的导管架式海洋平台主动控制模型，为海洋平台的主动振动控制提供了一个新思路。
The concept of the dynamic stiffness matrix (DSM) method was first developed byKolousek. It is a powerful means of solving vibration problems in structural engineering,particularly when higher frequencies and better accuracies are required. Thismethod is basedon exact shape functions obtained from the solution of the element differential equations. Sothe method provides the researcher with much better model accuracy compared to finiteelement or other approximate methods. The resulting element matrix features exactly themass and stiffness properties of the element and leads to a transcendental eigenvalue problem.Since the element properties are derived exactly, no matter what the frequency is, the resultsobtained by this method are exact, without mesh refinement as the frequency increases. In thispaper the DSM method is introduced to the dynamic analysis for ship and offshore structures.It is used to analyze the vibration characteristic of ship hull, calculate the dynamiccharacteristics of stiffened plate in high-frequency range and control the vibrational responsesof offshore platforms. The present work is divided into the following parts.
The DSM technique is applied to compute overall vibrational characteristics of hullgirder in this paper. The analytical expressions of dynamic stiffness matrix of a Timoshenkobeam for transverse vibration are presented in which all the effects of rotatory inertia andshear deformation are taken into account in the formulation. The resulting dynamic stiffnessmatrix combined with the Wittrick-Williams algorithm is used to compute natural frequenciesand mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solvedby the mode superposition method. The computational results are compared with thoseobtained from other approximate methods and experiment. It is shown that with the DSMmethod, the mesh division can be determined by the cabin arrangement to avoid recalculatingweight distribution, simplify computational model and make the data preparation moreconvenient. In addition, this method can make each element meet the requirements of beamtheory, get more accurate calculation results in the ranges needed by engineering and furnish afast and simple method to carry out overall dynamic analysis for ship.
A dynamic stiffness matrix is presented for the analysis of stiffened moderate thick platein this paper. The plate differential equations are based on Mindlin thick plate theory andinclude the in,plane vibrations. The stiffeners are taken to be smeared over the surface of theelement by energy equivalent, and Hamilton's principle is used to derive the appropriate modifications which must be made to the plate differential equations. The resulting dynamicstiffness matrix provides the DSM method a new element type, and can be used to analyzeenergy transmission between stiffened plates in middle and high frequency ranges. In thispaper, the coupling loss factors of the junction are calculated by the DSM method, and thecalculated results are compared with those obtained by other numerical methods andexperiment to verify the effectiveness and feasibleness of the presented method. On the otherhand, the calculated coupling loss factors can be directly used by the statistical energyanalysis method to predict more accurate noise levels of ship cabin. In addtion, the DSMtechnique is applied to calculate the energy flow of the coupled stiffened plates. The effects ofshear deformation and rotary inertia and the in-plane vibrations are also discussed, and someuseful conclusions are drawn in this paper.
In this paper, a new active control scheme for jacket offshore platforms, based on theDSM method, is presented. According to the characteristic of DSM method in quick accuratemodeling, the actual model of controlled platform can be considered by the artificialintelligence control algorithm. In the DSM based fuzzy neural network (FNN) adaptivepredictive inverse control (APIC) scheme, a real time measurement of the random waveforces is made by the pressure transducers which are placed on the leg of the offshoreplatform. And then the responses on the top of the platform under these random wave forcesare quickly and accurately calculated by the DSM method. The calculated responses are takenas the input signals of FNN adaptive predictive inverse controller, through which the controlforce for the imminent time of the platform is forecasted. Moreover, a feedback adaptivepredictive inverse, controller is designed for the purpose of disturbance canceling and errorreduction. The numerical results obtained in this paper show that the DSM based FNN APICscheme which has excellent anti-disturbance capability is feasible and effective, and canfinally overcome the time delay.
The study shows that the DSM method has a comprehensive application in the dynamicanalysis of ship and offshore structures. With the advantages of few elements, higheraccuracy and speed, not only can the natural frequency and structural response be calculatedeffectively, but also the dynamic characteristics of structures can be solved in a wide range offrequencies by using DSM method. It is a powerful tool to analyze overall vibrationcharacteristics of ship with higher accuracy and simplified computational model. It is nodoubt that the dynamic stiffness matrix for stiffened Mindlin plate deduced in this paperextends element type of DSM method and provides a useful way to investigate energytransmission between stiffened plates with middle and high frequencies, which expandsapplied range of traditional methods. The presented DSM based FNN APIC scheme undoubtedly provides an efficient way to reduce the vibration responses for jacket offshoreplatforms.
本文首次将动态刚度阵法应用于船舶总体振动特性和响应研究中，利用它来简化计算模型，提高计算速度和精度。考虑到垂向和水平振动时船体所带的附加水质量不同，所以可利用平面Timoshenko梁单元的动态刚度阵来分别计算两个方向的总振动固有频率和响应。本文采用动态刚度阵法结合Wittrick-Williams算法对299，500DWT超大型油船的总体振动固有特性进行预报，所得固有频率和固有振型通过模态叠加法来求解该船在螺旋桨激励下的总体振动响应，计算结果分别与一维梁有限元模型和三维全船有限元模型计算结果以及实测值进行比较，以验证本方法的精确性和有效性。研究表明，船舶总体振动的刚度主要取决于平行中体的惯性矩和剪切面积，而其沿船长方向的分布对它的固有频率影响较小，反而船舶质量沿船长分布情况对固有频率的影响较大。因此，如果按理论站的位置来划分船体梁的单元时，可能会因为一个舱室的质量分布在若干个站内，需要按力和力矩等效的原则来重新调整质量分布，而采用动态刚度阵法计算时，当船舶舱室较多时可直接按照舱室分布来划分单元，避免了对船舶质量分布的重新调整，简化了计算模型，方便了数据准备工作，而且还能同时保证各单元满足梁理论的要求，提高了工程需要阶数内固有频率计算结果的准确性，为船舶总体振动特性分析研究提供了一个快速而便捷的计算方法。
本文推导了考虑平面内振动影响的双向加筋Mindlin板动态刚度阵，为动态刚度阵法提供了一种新的单元类型，进而为研究加筋板间的能量传递开辟了一个新途径。本文以加筋中厚矩形板为研究对象，通过Hamilton原理建立考虑平面内振动影响的双向加筋Mindlin板运动微分方程，再利用方程的解析解来推导其动态刚度阵，所得动态刚度阵被用于加筋板的中高频动力特性问题研究之中。首先采用动态刚度阵法对L型加筋板间的耦合损耗因子进行计算，计算结果与实测值和有限元方法分别进行了比较，以验证本文方法的可行性、准确性和高效性；所得加筋板间的耦合损耗因子可与统计能量分析方法相结合，来更为准确地对船舶舱室噪声进行预报。此外，本文还利用动态刚度阵法研究了加筋板间的能量传输关系，讨论了平面内振动、剪切变形和转动惯量对加筋板间弯曲能量传输的影响，并给出了一些相关结论。
本文提出了一种新的基于动态刚度阵法的导管架式海洋平台模糊神经网络自适应预测逆控制模型。该模型是将实时采集的海洋平台所受波浪力提供给动态刚度阵建立的计算模型，通过它来快速而准确地计算出平台项部的响应，再将此响应作为模糊神经网络预测逆控制器的输入信号，由它预测出下一时刻平台顶部的控制力来对海洋平台振动响应进行控制；同时对控制后的平台响应进行实时测量，所得响应误差和扰动一起作为反馈自适应预测逆控制器的输入信号，它的输出力信号直接反馈到被控平台的项部，以此来消除被控对象的内部噪声和外部扰动。最后的数值算例结果表明，本文所提出的导管架式海洋平台主动控制模型既能很好地解决控制系统中存在的时滞问题，又具有较强的抗干扰能力，可以有效地控制海洋平台的振动响应。
本文研究表明，动态刚度阵法凭借着所需单元少、计算速度快、计算精度高以及适用频率范围广等特点，可以用来便捷高效地计算结构的动力特性，在船舶与海洋结构动力分析中有着广阔的应用前景。利用该方法对船舶总体振动特性分析过程中可以提高计算精度，简化计算模型，是一个不可多得的简便实用工具。毫无疑问，本文所推导的双向加筋Mindlin板单元的动态刚度阵为动态刚度阵法提供了一个新的单元类型，为研究加筋板间中高频区域内的动力特性提供了一个强有力的工具。所提出的基于动态刚度阵法的导管架式海洋平台主动控制模型，为海洋平台的主动振动控制提供了一个新思路。
The concept of the dynamic stiffness matrix (DSM) method was first developed byKolousek. It is a powerful means of solving vibration problems in structural engineering,particularly when higher frequencies and better accuracies are required. Thismethod is basedon exact shape functions obtained from the solution of the element differential equations. Sothe method provides the researcher with much better model accuracy compared to finiteelement or other approximate methods. The resulting element matrix features exactly themass and stiffness properties of the element and leads to a transcendental eigenvalue problem.Since the element properties are derived exactly, no matter what the frequency is, the resultsobtained by this method are exact, without mesh refinement as the frequency increases. In thispaper the DSM method is introduced to the dynamic analysis for ship and offshore structures.It is used to analyze the vibration characteristic of ship hull, calculate the dynamiccharacteristics of stiffened plate in high-frequency range and control the vibrational responsesof offshore platforms. The present work is divided into the following parts.
The DSM technique is applied to compute overall vibrational characteristics of hullgirder in this paper. The analytical expressions of dynamic stiffness matrix of a Timoshenkobeam for transverse vibration are presented in which all the effects of rotatory inertia andshear deformation are taken into account in the formulation. The resulting dynamic stiffnessmatrix combined with the Wittrick-Williams algorithm is used to compute natural frequenciesand mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solvedby the mode superposition method. The computational results are compared with thoseobtained from other approximate methods and experiment. It is shown that with the DSMmethod, the mesh division can be determined by the cabin arrangement to avoid recalculatingweight distribution, simplify computational model and make the data preparation moreconvenient. In addition, this method can make each element meet the requirements of beamtheory, get more accurate calculation results in the ranges needed by engineering and furnish afast and simple method to carry out overall dynamic analysis for ship.
A dynamic stiffness matrix is presented for the analysis of stiffened moderate thick platein this paper. The plate differential equations are based on Mindlin thick plate theory andinclude the in,plane vibrations. The stiffeners are taken to be smeared over the surface of theelement by energy equivalent, and Hamilton's principle is used to derive the appropriate modifications which must be made to the plate differential equations. The resulting dynamicstiffness matrix provides the DSM method a new element type, and can be used to analyzeenergy transmission between stiffened plates in middle and high frequency ranges. In thispaper, the coupling loss factors of the junction are calculated by the DSM method, and thecalculated results are compared with those obtained by other numerical methods andexperiment to verify the effectiveness and feasibleness of the presented method. On the otherhand, the calculated coupling loss factors can be directly used by the statistical energyanalysis method to predict more accurate noise levels of ship cabin. In addtion, the DSMtechnique is applied to calculate the energy flow of the coupled stiffened plates. The effects ofshear deformation and rotary inertia and the in-plane vibrations are also discussed, and someuseful conclusions are drawn in this paper.
In this paper, a new active control scheme for jacket offshore platforms, based on theDSM method, is presented. According to the characteristic of DSM method in quick accuratemodeling, the actual model of controlled platform can be considered by the artificialintelligence control algorithm. In the DSM based fuzzy neural network (FNN) adaptivepredictive inverse control (APIC) scheme, a real time measurement of the random waveforces is made by the pressure transducers which are placed on the leg of the offshoreplatform. And then the responses on the top of the platform under these random wave forcesare quickly and accurately calculated by the DSM method. The calculated responses are takenas the input signals of FNN adaptive predictive inverse controller, through which the controlforce for the imminent time of the platform is forecasted. Moreover, a feedback adaptivepredictive inverse, controller is designed for the purpose of disturbance canceling and errorreduction. The numerical results obtained in this paper show that the DSM based FNN APICscheme which has excellent anti-disturbance capability is feasible and effective, and canfinally overcome the time delay.
The study shows that the DSM method has a comprehensive application in the dynamicanalysis of ship and offshore structures. With the advantages of few elements, higheraccuracy and speed, not only can the natural frequency and structural response be calculatedeffectively, but also the dynamic characteristics of structures can be solved in a wide range offrequencies by using DSM method. It is a powerful tool to analyze overall vibrationcharacteristics of ship with higher accuracy and simplified computational model. It is nodoubt that the dynamic stiffness matrix for stiffened Mindlin plate deduced in this paperextends element type of DSM method and provides a useful way to investigate energytransmission between stiffened plates with middle and high frequencies, which expandsapplied range of traditional methods. The presented DSM based FNN APIC scheme undoubtedly provides an efficient way to reduce the vibration responses for jacket offshoreplatforms.
引文
[1] 金咸定，赵德有．船体振动学．上海：上海交通大学出版社，2000．
[2] 袁昌华．潜艇低速航行时的一种水下噪声源．舰船性能研究，1990，2：69-73．
[3] Kolousek V. Anwendung des gesetzes der virtuellen verschiebungen und des reziprozitatssatzes in der stabwerksdynamik. Ingenieur-Archiv, 1941, 12: 363-370.
[4] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[5] Mohsin M E, Sadek E A. The distributed mass-stiffness technique for the dynamical analysis of complex frameworks. The Structural Engineer, 1968, 46(11): 345-351.
[6] Cheng F Y. Vibrations of Timoshenko beams and frameworks. Journal of the Structural Division, 1970, 3: 551-571.
[7] Howson W P, Williams F W. Natural frequencies of frames with axially loaded Timoshenko members, Journal of Sound and Vibration, 1973, 26(4): 503-515.
[8] Swannell P, Tranberg C H. Procedures for the forced, damped vibration analysis of structural frames using distributed parameter models. Computer Method in Applied Mechanics and Engineering, 1978, 16(3): 291-302.
[9] Lunden R, Akesson B A. Damped second-order Rayleigh-Timoshenko beam vibration in space an exact complex dynamic member stiffness matrix. International Journal for Numerical Methods in Engineering, 1983, 19: 431-449.
[10] Banerjee J R. Coupled bending-torsional dynamic stiffness matrix for beam elements. International Journal for Numerical Methods in Engineering, 1989, 28: 1283-1289.
[11] Banerjee J R, Fisher S A. Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements. International Journal for Numerical Methods in Engineering, 1992, 33: 739-751.
[12] Li Jun, Shen RongYing, Jin XianDing et al. Coupled bending and torsional vibration of axially loaded Bernoulli-Euler beams including warping effects. Applied Acoustics, 2004, 65: 153-170.
[13] Banerjee J R, Williams F W. Coupled bending-torsional dynamic stiffness matrix for Timoshenko beam elements. Computers and Structures, 1992, 42: 301-310.
[14] Banerjee J R, Williams F W. Coupled bending-torsional dynamic stiffness matrix of an axially loaded Timoshenko beam element. International Journal of Solids and Structures, 1994, 31: 749-762.
[15] Banerjee J R, Guo S, Howson W P. Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping. Computers and Structures, 1996, 59: 613-621.
[16] Li Jun, Shen RongYing, Jin XianDing et al. Bending-torsional coupled dynamic response of axially loaded composite Timoshenko thin-walled beam with closed cross-section. Composite Structures, 2004, 64: 23-35.
[17] Banerjee J R. Free vibration of sandwich beams using the dynamic stiffness method. Computers and Structures, 2003, 81: 1915-1922.
[18] Banerjee J R. Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam. Journal of Sound and Vibration, 2004, 270: 379-401.
[19] Banerjee J R Williams F W. Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams. International Journal for Numerical Methods in Engineering, 1985, 21: 2289-2302.
[20] Leung A Y T, Zhou W E. Dynamic stiffness analysis of non-uniform Timoshenko beams. Journal of Sound and Vibration, 1995, 181: 447-456.
[21] Williams F W, Kennedy D. Exact dynamic members stiffness for a beam on an elastic foundation. Earthquake Engineering Structural Dynamics, 1987, 15: 133-136.
[22] Leung A Y T. Natural shape functions of a compressed Vlasov element. Thin-walled Structures, 1991, 11: 431-438.
[23] Gupta S, Manohar C S. Dynamic stiffness method for circular stochastic Timoshenko beams: response variability and reliability analyses. Journal of Sound and Vibration 2002, 253(5): 1051-1085.
[24] Akesson B. PFVIBAT—a computer program for plane frame vibration analysis by exact method. International Journal for Numerical in Methods in Engineering, 1976, 10: 1221-1231.
[25] Akesson B, Tagnfors H. SFVIBAT—a computer program for space frame vibration analysis. 1980, Pub. 27, Chalmers University of Technology, Division of Solid Mechanics, Gothenburg.
[26] Gustafsson T, Carlsson K G. PFVIBAT—DAMP: computer program for harmonic vibration of plane frames considering damping. Report T47, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1977.
[27] Akesson B, Tagnfors H, Lunden R et al. SFVIBAT-DAMP: a computer program for damped space frame vibration analysis, 1987, Pub. 29, Chalmers University of Technology, Division of Solid Mechanics, Gothenburg.
[28] Banerjee J R, Williams F W. User's guide to the computer program BUNVIS (Buckling or Natural Vibration of Space Frames). Department of Civil Engineering and Building Technology, University of Wales Institute of Science and Technology, Report No.5, 1982.
[29] Anderson M S, Williams F W, Banerjee J et al. User manual for BUNVISHRG: an exact buckling and vibration program for lattice structures with repetitive geometry and substructuring option, NASA Technical Memo 87669, 1986.
[30] Banerjee J R. Use and capability of CALFUN-a program for calculation of flutter speed using normal modes. Proc. Int. 84 Athens Summer Conf. on Modelling and Simulation, Athens, Greece, 1984: 27-29.
[31] Wittrick W H. General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures. International Journal of Mechanical Sciences, 1968, 10: 949-966.
[32] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[33] Langley R S. Application of the dynamic stiffness method to the free and forced vibration of aircraft panels. Journal of Sound and Vibration, 1989, 135: 319-331.
[34] Bercin A N, Langley R S. Application of the dynamic stiffness technique to the in-plane vibration of plate structures. Computers and Structures, 1996, 59(5): 869-875.
[35] Bercin A N. Analysis of energy flow in thick plate structure. Computers and Structures, 1997, 62(4): 747-756.
[36] Leung A Y T, Zhou W E. Dynamic stiffness analysis of laminated composite plates. Thin-Walled Structures, 1996, 25(2): 109-133.
[37] Langley R S. A Dynamic stiffness technique for the vibration analysis of stiffened shell structures. Journal of Sound and Vibration, 1992, 156: 521-540.
[38] Bercin A N. Natural frequencies of cross-ply laminated singly curved panels. Mechanics Research Communications, 1996, 23(2): 165-170.
[39] Williams F W. Computation of natural frequencies and initial buckling stresses of prismatic plate assemblies. Journal of Sound and Vibration, 1972, 21(1): 87-106.
[40] Anderson M S, Stround W J, Durling B J et al. PASCO: structural panel analysis and sizing code—users manual. NASA Technical Memorandum 80182, Washington, D. C., 1980.
[41] Simpson A. On the solution of S(ω)=0 by a Newtonian procedure, Journal of Sound and Vibration, 1984, 97(1): 153-164.
[42] Williams F W, Kennedy D. Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently. International Journal for Numerical Methods in Engineering, 1988, 26: 1825-1841.
[43] Qi Zhaohui, Kennedy D, Williams F W. An accurate method for transcendental eigenproblems with a new criterion for eigenfrequencies. International Journal of Solids andStructures, 2004, 41: 3225-3242.
[44] 胡仲根，恽伟君，段根宝．动态子结构法中的非线性特征值计算．船舶工程，1982，2：13-20
[45] 叶建乔．二次特征矩阵表示的特征值有界性分析．力学学报，1995，27(3)：326-335．
[46] Leung A Y T. Dynamic stiffness method and substructures. New York: Springer, 1993.
[47] Hashemi S M, Richard M J. Free vibrational analysis of axially loaded bending-torsion coupled beams a dynamic finite element. Computers and Structures, 2000, 77: 711-724.
[48] Chen Sbilin, Geradin M, Lamine E. An improved dynamic stiffness method and modal analysis for beam-like structures. Computers and Structures, 1996, 60(5): 725-731.
[49] Gupta K K. Development of a finite dynamic element for free vibration analysis of two-dimensional structures. International Journal for Numerical Methods in Engineering, 1978, 12(8): 1311-1327.
[50] 陈显钧，赵令诚．弯曲板固有振动分析的动态有限元素法．振动与冲击，1982，2：1-11．
[51] 贺国京，陈大鹏．动态有限元法及其在薄板弯曲振动中的应用．长沙铁道学院学报，1999，17(1)：1-6．
[52] 张令弥．动态有限元模型修正技术及其在航空航天结构中的应用．强度与环境1994，2：10-17．
[53] 王静，赵德有，郑治国．用动态有限元法计算加筋板固有频率．大连理工大学学报，2001，41(1)：90-93．
[54] 金咸定．船舶结构动力学的进展与信息化．振动与冲击，2002，21(4)：1-6．
[55] Ozsoysal R. A review of recent ship vibration papers. The Shock and Vibration Digest, 2004, 36: 207-214.
[56] Lewis F M. The inertia of the water surrounding a vibration ship. Trans. SNAME, 1929, 37: 1-20.
[57] Orsero P, Armand J L. A numerical determination of the entrained water in ship vibrations. International Journal for Numerical Methods in Engineering, 1978, 13(1): 35-48.
[58] Zong Z, Lam K Y. Hydrodynamic influence on ship-hull vibration close to water bottom. Journal of Engineering Mathematics, 2000, 37(4):363-374.
[59] Xing J T, Price W G. Theory of Non-linear Elastic Ship-water Interaction Dynamics. Journal of Sound and Vibration, 2000, 230(4): 877-914.
[60] Zheng H, Liu G R, Tao J Set al. FEM/BEManalysis of diesel piston-slap inducedship hull vibration and underwater noise. Applied Acoustics, 2001, 62: 341-358.
[61] Alan Jennings. Added mass for fluid-structure vibration problems. International Journal for Numerical Methods in Fluids, 1985, 5(9): 817-830.
[62] Zhou D, Cheung Y K. Vibration of vertical rectangular plate in contact with water on one side. Earthquake Engineering & Structural Dynamics, 2000, 29(5): 693-710.
[63] Xia Lijuan, Wu Weiguo, Jin, Xianding et al. Analysis Of fluid-structure-coupled vertical vibration for high-speed ships. Journal of Ship Mechanics, 2000, 4(3): 43-50.
[64] Guo Lie, Wu Shichong, He, Fujian. Prediction of local vibration characteristics of naval ship structures. Journal of Ship Mechanics, 2000, 4(6): 69-83.
[65] Sinha G. Transverse free vibration of stiffened plates/shells with elastically restrained edges by FEM. International Shipbuilding Progress, 2000, 47(450): 191-214.
[66] Li X, Chen Y. Free vibration analysis of orthotropic circular cylindrical shell under external hydrostatic pressure. Journal of Ship Research, 2002, 46(3): 201-207.
[67] Lyon R H, Dejone R G. Theory and application of statistical energy analysis. Boston: Butterworth-Heinemann, second edition, 1995.
[68] Lyon R H, Maidanik G. Power flow between linearly coupled oscillators. Journal of the Acoustical Society of America, 1962, 34: 623-629.
[69] New land D E. Power flow between a class of coupled oscillators. Journal of the Acoustical Society of America, 1969, 43: 553-559.
[70] Keane A J, Price W G. Statistical energy analysis of strongly coupled systems. Journal of Sound and Vibration, 1987, 117(2): 363-386.
[71] 明瑞森，孙进才．非保守耦合结构间耦合损耗因子的计算．西北工业大学学报，1989，7(1)：39-46．
[72] 孙进才．复杂结构的损耗因子和耦合损耗因子的测量方法．声学学报，1995，20(2)：127-134．
[73] 孙进才，王冲，孙朝晖．间接耦合机械结构之间的耦合损耗因子．声学学报，1995，20(1)：34-41．
[74] 孙朝晖，孙进才，王冲等．负损耗因子的成因分析．声学学报，1996，2l(5)：798-804．
[75] Sheng M P, Wang M Q, Sun J C. Effective internal loss factors and coupling loss factors for non-conservatively coupled systems. Journal of Sound and Vibration, 1998, 209(4): 685-694.
[76] Eichler E. Plate-edge admittances. Journal of the Acoustical Society of America, 1964, 36(2): 344-348.
[77] Cremer L, Heckl M, Ungar E E. Structure-borne Sound (2nd Edition). Berlin: Springer, 1988.
[78] McCollum M D, Cuschieri J M. Thick plate bending wave transmission using a mobility power flow approach. Journal of the Acoustical Society of America, 1990, 88(3): 1472-1479.
[79] McCollum M D, Cuschieri J M. Bending and in-plane wave transmission in thick connected plates using statistical energy analysis. Journal of the Acoustical Society of America, 1990, 88(3): 1480-1485.
[80] Bosmans I, Mees P, Yermeir G. Structure-borne sound transmission between thin orthotropic plates: analytical solutions. Journal of Sound and Vibration, 1996, 191(1):75-90.
[81] Bosmans I, Vermeir G, Mees P. Coupling loss factors for coupled anisotropic plates. Journal of Sound and Vibration, 2002, 250(2):351-355.
[82] 王宏伟，赵德有．平板与周期加筋阻尼板间耦合损耗因子的研究．船舶力学，2001，5(2)：55-61．
[83] Bie D A, Hamid S. In-situ determination of loss and coupling loss factors by the power injection method. Journal of Sound and Vibration, 1980, 70: 187-204.
[84] Clarkson B L, Ranky M F. On the measurement of the coupling loss factor of structural connections. Journal of Sound and Vibration, 1984, 94(2): 249-261.
[85] Cacciolati C, Guyader J L. Measurement of SEA coupling loss factors using point mobilities. Philosophical transactions-Royal Society of London A, 1994, 346: 465-475.
[86] Langhe K D, Sas P. Statistical analysis of the power injection method. Journal of the Acoustical Society of America, 1996, 100: 291-303.
[87] Simmons C. Structure-borne sound transmission through plate junctions and estimates of SEA coupling loss factors using the finite element method. Journal of Sound and Vibration, 1991, 144(2): 215-227.
[88] Stimpson G, Lalor N. SEA extension of an FE model to predict total engine noise. Proceedings of Inter-noise 92, Toronto, Canada, 1992, 557-560.
[89] Steel J A, Craik R J M. Statistical energy analysis of structure-borne sound transmission by finite element methods. Journal of Sound and Vibration, 1994, 178(4): 533-561.
[90] Fredo C R. A sea-like approach for the derivation of energy flow coefficients with a finite element model. Journal of Sound and Vibration, 1997, 199(4): 645-666.
[91] Shankar K, Keane A J. Vibrational energy flow analysis using a substructure approach: the application of receptance theory to FEA and SEA. Journal of Sound and Vibration, 1997, 201(4): 491-513.
[92] 陆文发，李林普，高明道．近海导管架平台．北京：海洋出版社，1992．
[93] 任贵永．海洋活动式平台．天津：天津大学出版社，1989．
[94] 金伟良．海洋工程中的若干力学问题．科技通报，1997，13(2)：86-92．
[95] 段梦兰．海洋平台结构的最新研究进展第9届ISOPE大会报告综述．海洋工程，2000，18(1)：86-90．
[96] 桂洪斌，金咸定，肖熙．海洋平台振动控制研究综述．中国海洋平台，2003，18(5)：19-25．
[97] 桂洪斌．船舶与海洋工程结构振动控制问题的若干探讨．上海交通大学船舶与海洋工程学院结构力学研究所博士后研究报告，2003．
[98] Lee H H. Stochastic analysis for offshore platform with added mechanical dampers. Ocean Engineering,1997,24(9):817-834.
[99] 欧进萍，邹向阳等．设置粘弹性耗能器的JZ20-2MUQ平台结构冰振控制．海洋工程，2000，18(3)：9-14．
[100] 欧进萍，龙旭，肖仪清等．导管架式海洋平台结构阻尼隔振体系及其减振效果分析．地震工程与工程振动，2002，22(3)：115-122．
[101] 陆建辉，彭临悔，李华军．固定式近海石油平台振动控制研究．中国造船，2000，41(3)：63-68．
[102] 孙树民．独桩平台波浪反应的调谐质量阻尼器控制研究．噪声与振动控制，2001，(4)：14-17．
[103] 孙树民．考虑流体—桩—土相互作用的独桩平台波浪响应的TMD控制研究．中国造船，2002，43(1)：52-57．
[104] 李宏男，马百存．固定式海洋平台利用TLD的减震研究．海洋工程，1996，14(3)：91-96．
[105] 韦林．近海平台的振动最优控制．北京：科学出版社，1992．
[106] 李华军，嵇春艳，吴永宁．随机波浪载荷作用下海洋平台的前馈—反馈振动控制研究．青岛海洋大学学报，2001，31(6)：917-924．
[107] LI H J, Jiang J, Cao H et al. The optimal design of TMD for offshore structures. China Ocean Engineering, 1999, 13(2): 133-144.
[108] Vincenzo G R G. Adaptive control of flow-induced oscillation inducing vortex effects. International Journal of Non-linear Mechanics, 1999, 34: 853-868.
[109] Ahmad S K, Ahmad S. Active control of non-linearly coupled TLP responseunder wind and wave environments. Computers & Structures, 1999, 70(7): 735-747.
[110] LI Huajun, Sau-Lon JAMES HU, Tomotsuka. Optimal active control of wave-induced vibration for offshore platforms. China Ocean Engineering, 2001, 15(1): 1-14.
[111] Suhardjo J, Kareem A. Feedback-feedforward control of offshore platforms under random waves. Earthquake Engineering and Structural Dynamics, 2001, 30(2): 213-235.
[112] Suhardjo J, Kareem A. Structural control of offshore platforms. Proceeding of 7th ISOPE, USA, Honolulu, 1997: 416-424.
[113] Abdel-Rohman M. Structural control of a steel jacket platform. Structural Engineering and Mechanics, 1996, 4(2): 125-138.
[114] Kawano, Kenji, Ishizawa et al. Active control effects on dynamic response of offshore structures. Proceedings of the 3rd ISOPE, Singapore, 1993: 594-598.
[115] 管友海，黄维平．MR阻尼器在海洋平台半主动振动控制中的应用．中国海洋平台，2002，17(3)：25-28．
[116] 孙树民，梁启智．隔震独桩平台地震反应的半主动磁流变阻尼器控制研究．振动与冲击，2001，20(3)：61-64．
[117] 周亚军．导管架海洋平台结构振动智能主动控制研究：(博士学位论文)．大连：大连理工大学，2004．
[118] 周志华，曹存根．神经网络及其应用．北京：清华大学出版社，2004．
[119] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[120] 高隽．人工神经网络原理及仿真实例．北京：机械工业出版社，2003．
[121] 丛爽．神经网络、模糊系统及其在运动控制中的应用．北京：中国科学技术大学出版社，2001．
[122] Wang Zidong, Shu Huisheng, Liu Xiaohui et al. Robust stability for stochastic hopfield neural networks with time delays. Nonlinear Analysis: Real World Applications, 2006, 7(5): 1119-1128.
[123] Bianchini M, Maggini M, Scarselli Fetal. Recursive neural networks for processing graphs with labelled edges: theory and applications. Neural Networks, 2005, 18(8): 1040-1050.
[124] Narayanan A, Keedwell E C, Tatineni Set al. Single-layer artificial neural networks for gene expression analysis. Neurocomputing, 2004, 61: 217-240.
[125] Gob S L, Mandic D P. Recurrent neural networks with trainable amplitude of activation functions. Neural Networks, 2003, 16(8): 1095-1100.
[126] Venkataram P, Ghosal P, Vijay Kumar B P. Neural network based optimal routing algorithm for communication networks. Neural Networks, 2002, 15(10): 1289-1298.
[127] Wang Lixin. A course in fuzzy systems and control. Hong Kong: Prentice-Hall Inc., 1997.
[128] 李士勇．模糊控制·神经控制和智能控制论．哈尔滨：哈尔滨工业大学出版社，1998．
[129] 赵振宇，徐用懋．模糊理论和神经网络的基础与应用．北京：清华大学出版社，1996．
[130] 诸静．模糊控制理论与系统原理．北京：机械工业出版社，2005．
[131] Gavalec M. Solvability and unique solvability of max-min fuzzy equations. Fuzzy Sets and Systems, 2001, 124(3): 385-393.
[132] Quek C, Zhou R W. Structure and learning algorithms of a nonsingleton input fuzzy neural network based on the approximate analogical reasoning schema. Fuzzy Sets and Systems, 2006, 157(13): 1814-1831.
[133] Ferreira W P, Silveira M D C G, Lotufo A Pet al. Transient stability analysis of electric energy systems via a fuzzy ART-ARTMAP neural network. Electric Power Systems Research, 2006, 76(6-7): 466-475.
[134] Zhou Yunfei, Li Shuijin, Jin Rencheng. A new fuzzy neural network with fast learning algorithm and guaranteed stability for manufacturing process control: Fuzzy Sets and Systems, 2002, 132(2): 201-216.
[135] Widrow B, Walach E. Adaptive inverse control. New Jersey: Prentice-Hall Inc., 1996.
[136] 卢志刚，吴士昌，于灵慧．非线性自适应逆控制及其应用．北京：国防工业出版社，2004．
[137] 袁小芳，王耀南，杨辉前．基于支持向量机的非线性逆控制及仿真研究．湖南大学学报，2006，33(1)：71-74．
[138] 朱家强，朱纪洪，郭锁凤等．基于神经网络的鲁棒自适应逆飞行控制．控制理论与应用，2005，22(2)：182-188．
[139] Salman R. Neural networks of adaptive inverse control systems. Applied Mathematics and Computation, 2005, 163(2): 931-939.
[1] Kolousek V. Anwendung des gesetzes der virtuellen verschiebungen und des reziprozitatssatzes in der stabwerksdynamik. Ingenieur-Archiv, 1941, 12:363-370.
[2] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，2001．
[3] Banerjee J R, Williams F W. Vibration of composite beams—an exact method usiag symbolic computation. Journal of Aircraft, 1995, 32: 636-642.
[4] Leung A Y T. Dynamic stiffness method and substructures. New York: Springer, 1993.
[5] Cheng F Y. Vibrations of Timoshenko beams and frameworks. Journal of the Structural Division, 1970, 3: 551-571.
[6] Wittrick W H. General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures. International Journal of Mechanical Sciences, 1968, 10: 949-966.
[1] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[2] Williams F W, Howson W P. compact computation of natural frequencies and buckling loads of plane frames. International Journal for Numerical Methods in Engineering, 1977, 11: 1067-1081.
[3] Howson W P, Williams F W. Natural frequencies of frames with axially loaded Timoshenko members. Journal of Sound and Vibration, 1973, 26(4): 503-515.
[4] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[5] ANSYS User's Manual for Revision 5.1, ANSYS Inc., 1991.
[6] 金咸定，赵德有．船体振动学．上海：上海交通大学出版社，2000．
[1] 金咸定，赵德有．船体振动学．上海：上海交通大学出版社，2000．
[2] 马广宗，蔡承德，虞铣辉．船舶振动基础与实用计算．北京：人民交通出版社，1981．
[3] Lewis F M. The Inertia of the Water Surrounding a Vibrating Ship. Trans. SNAME, 1929, 37: 1-20.
[4] 赵德有，金维成等．渔船振动预报．大连：大连理工大学出版社，1993．
[5] 陆鑫森．高等结构动力学．上海：上海交通大学出版社，1992．
[6] Wittrick W H, Williams F W. A General algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[7] Cho Dae-Seung. Vibration analysis of 299,500 DWT crude oil tanker, Report No. T3000-1. Pusan: Research Institute of Industrial Technology Pusan NationaiUniversity, Oct. 2000.
[8] Zhao Deyou, Lin Ze, etc. Global vibration measurement report for IRAN DENA, Report No. GVM20040104-01. Dalian: Department of Naval Architecture Dalian University of Technology. Jan. 4, 2004.
[1] Mukherjee A, Mukhopadhyay M. A review of dynamic behavior of stiffened plates. The Shock and Vibration Digest, 1986, 18: 3-8.
[2] Kolousek V. Dynamic in Engineering Structures. London: Butterworths, 1973.
[3] 李俊，金咸定．Timoshenko薄壁梁弯扭耦合振动的动态传递矩阵法．振动与冲击，2001，20(4)：57-59．
[4] Banerjee J R. Free vibration of sandwich beams using the dynamic stiffness method. Computers and Structures, 2003, 81: 1915-1922.
[5] Banerjee J R. Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam. Journal of Sound and Vibration, 2004, 270: 379-401.
[6] Li Jun, Shen RongYing, Jin XianDing et al. Bending-torsional coupled dynamic response of axially loaded composite Timoshenko thin-walled beam with closed cross-section. Composite Structures, 2004, 64: 23-35.
[7] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[8] Langley R S. Application of the dynamic stiffness method to the free and forced vibration of aircraft panels. Journal of Sound and Vibration, 1989, 135: 319-331.
[9] Bercin A N, Langley R S. Application of the dynamic stiffness technique to the in-plane vibration of plate structures. Computers and Structures, 1996, 59(5): 869-875.
[10] Bercin A N. Analysis of energy flow in thick plate structure. Computers and Structures, 1997, 62(4): 747-756.
[11] Mindlin R D. Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18(1): 31-38.
[12] 王勖成．有限单元法．北京：清华大学出版社，2003．
[13] ANSYS User's Manual for Revision 5.1, ANSYS Inc., 1991.
[1] 姚德源，王其政．统计能量分析原理及其应用．北京：北京理工大学出版社，1995．
[2] Simmons C. Structure-borne sound transmission through plate junctions and estimates of the SEA coupling loss factors using the finite element method. Journal of Sound and Vibration, 1991, 144(2):.215-227.
[3] Lyon R H. Statistical Energy Analysis of Dynamical Systems: Theory and Applications. The MIT Press, 1975.
[4] Bies D A, Hamid S. In situ determination of coupling loss factors by the power injection method. Journal of Sound and Vibration, 1980, 70: 187-204.
[5] 孙进才．复杂结构的损耗因子和耦合损耗因子的测量方法．声学学报，1995，20：127-134．
[6] Cimerman B, Bharj T, Borello G. Overview of the experimental approach to statistical energy analysis. 1997 SAE Noise & Vibration Conference and Expedition, Traverse City, MI, Paper No. 97NV169.
[7] 李德葆，陆秋海．工程振动试验分析．北京：清华大学出版社，2004．
[1] 周亚军，赵德有．海洋平台结构振动控制综述．振动与冲击，2004，23(4)：40-43．
[2] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[3] 周志华．曹存根．神经网络及其应用．北京：清华大学出版社，2004．
[4] 高隽．人工神经网络原理及仿真实例．北京：机械工业出版社，2003．
[5] 丛爽．神经网络、模糊系统及其在运动控制中的应用．北京：中国科学技术大学出版社，2001．
[6] 李士勇．模糊控制·神经控制和智能控制论．哈尔滨：哈尔滨工业大学出版社，1998．
[7] 赵振宇，徐用懋．模糊理论和神经网络的基础与应用．北京：清华大学出版社，1996．
[8] 诸静．模糊控制理论与系统原理．北京：机械工业出版社，2005．
[9] Widrow B, Walach E. Adaptive Inverse Control. New Jersey: Prentice-Hall Inc., 1996.
[10] 卢志刚，吴士昌，于灵慧．非线性自适应逆控制及其应用．北京：国防工业出版社，2004．
[11] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[12] 聂武，刘玉秋．海洋工程结构动力分析．哈尔滨：哈尔滨工程大学出版社，2002．
[13] 王士同．模糊系统、模糊神经网络及应用程序设计．上海：上海科学技术文献出版社，1998．
[2] 袁昌华．潜艇低速航行时的一种水下噪声源．舰船性能研究，1990，2：69-73．
[3] Kolousek V. Anwendung des gesetzes der virtuellen verschiebungen und des reziprozitatssatzes in der stabwerksdynamik. Ingenieur-Archiv, 1941, 12: 363-370.
[4] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[5] Mohsin M E, Sadek E A. The distributed mass-stiffness technique for the dynamical analysis of complex frameworks. The Structural Engineer, 1968, 46(11): 345-351.
[6] Cheng F Y. Vibrations of Timoshenko beams and frameworks. Journal of the Structural Division, 1970, 3: 551-571.
[7] Howson W P, Williams F W. Natural frequencies of frames with axially loaded Timoshenko members, Journal of Sound and Vibration, 1973, 26(4): 503-515.
[8] Swannell P, Tranberg C H. Procedures for the forced, damped vibration analysis of structural frames using distributed parameter models. Computer Method in Applied Mechanics and Engineering, 1978, 16(3): 291-302.
[9] Lunden R, Akesson B A. Damped second-order Rayleigh-Timoshenko beam vibration in space an exact complex dynamic member stiffness matrix. International Journal for Numerical Methods in Engineering, 1983, 19: 431-449.
[10] Banerjee J R. Coupled bending-torsional dynamic stiffness matrix for beam elements. International Journal for Numerical Methods in Engineering, 1989, 28: 1283-1289.
[11] Banerjee J R, Fisher S A. Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements. International Journal for Numerical Methods in Engineering, 1992, 33: 739-751.
[12] Li Jun, Shen RongYing, Jin XianDing et al. Coupled bending and torsional vibration of axially loaded Bernoulli-Euler beams including warping effects. Applied Acoustics, 2004, 65: 153-170.
[13] Banerjee J R, Williams F W. Coupled bending-torsional dynamic stiffness matrix for Timoshenko beam elements. Computers and Structures, 1992, 42: 301-310.
[14] Banerjee J R, Williams F W. Coupled bending-torsional dynamic stiffness matrix of an axially loaded Timoshenko beam element. International Journal of Solids and Structures, 1994, 31: 749-762.
[15] Banerjee J R, Guo S, Howson W P. Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping. Computers and Structures, 1996, 59: 613-621.
[16] Li Jun, Shen RongYing, Jin XianDing et al. Bending-torsional coupled dynamic response of axially loaded composite Timoshenko thin-walled beam with closed cross-section. Composite Structures, 2004, 64: 23-35.
[17] Banerjee J R. Free vibration of sandwich beams using the dynamic stiffness method. Computers and Structures, 2003, 81: 1915-1922.
[18] Banerjee J R. Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam. Journal of Sound and Vibration, 2004, 270: 379-401.
[19] Banerjee J R Williams F W. Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams. International Journal for Numerical Methods in Engineering, 1985, 21: 2289-2302.
[20] Leung A Y T, Zhou W E. Dynamic stiffness analysis of non-uniform Timoshenko beams. Journal of Sound and Vibration, 1995, 181: 447-456.
[21] Williams F W, Kennedy D. Exact dynamic members stiffness for a beam on an elastic foundation. Earthquake Engineering Structural Dynamics, 1987, 15: 133-136.
[22] Leung A Y T. Natural shape functions of a compressed Vlasov element. Thin-walled Structures, 1991, 11: 431-438.
[23] Gupta S, Manohar C S. Dynamic stiffness method for circular stochastic Timoshenko beams: response variability and reliability analyses. Journal of Sound and Vibration 2002, 253(5): 1051-1085.
[24] Akesson B. PFVIBAT—a computer program for plane frame vibration analysis by exact method. International Journal for Numerical in Methods in Engineering, 1976, 10: 1221-1231.
[25] Akesson B, Tagnfors H. SFVIBAT—a computer program for space frame vibration analysis. 1980, Pub. 27, Chalmers University of Technology, Division of Solid Mechanics, Gothenburg.
[26] Gustafsson T, Carlsson K G. PFVIBAT—DAMP: computer program for harmonic vibration of plane frames considering damping. Report T47, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1977.
[27] Akesson B, Tagnfors H, Lunden R et al. SFVIBAT-DAMP: a computer program for damped space frame vibration analysis, 1987, Pub. 29, Chalmers University of Technology, Division of Solid Mechanics, Gothenburg.
[28] Banerjee J R, Williams F W. User's guide to the computer program BUNVIS (Buckling or Natural Vibration of Space Frames). Department of Civil Engineering and Building Technology, University of Wales Institute of Science and Technology, Report No.5, 1982.
[29] Anderson M S, Williams F W, Banerjee J et al. User manual for BUNVISHRG: an exact buckling and vibration program for lattice structures with repetitive geometry and substructuring option, NASA Technical Memo 87669, 1986.
[30] Banerjee J R. Use and capability of CALFUN-a program for calculation of flutter speed using normal modes. Proc. Int. 84 Athens Summer Conf. on Modelling and Simulation, Athens, Greece, 1984: 27-29.
[31] Wittrick W H. General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures. International Journal of Mechanical Sciences, 1968, 10: 949-966.
[32] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[33] Langley R S. Application of the dynamic stiffness method to the free and forced vibration of aircraft panels. Journal of Sound and Vibration, 1989, 135: 319-331.
[34] Bercin A N, Langley R S. Application of the dynamic stiffness technique to the in-plane vibration of plate structures. Computers and Structures, 1996, 59(5): 869-875.
[35] Bercin A N. Analysis of energy flow in thick plate structure. Computers and Structures, 1997, 62(4): 747-756.
[36] Leung A Y T, Zhou W E. Dynamic stiffness analysis of laminated composite plates. Thin-Walled Structures, 1996, 25(2): 109-133.
[37] Langley R S. A Dynamic stiffness technique for the vibration analysis of stiffened shell structures. Journal of Sound and Vibration, 1992, 156: 521-540.
[38] Bercin A N. Natural frequencies of cross-ply laminated singly curved panels. Mechanics Research Communications, 1996, 23(2): 165-170.
[39] Williams F W. Computation of natural frequencies and initial buckling stresses of prismatic plate assemblies. Journal of Sound and Vibration, 1972, 21(1): 87-106.
[40] Anderson M S, Stround W J, Durling B J et al. PASCO: structural panel analysis and sizing code—users manual. NASA Technical Memorandum 80182, Washington, D. C., 1980.
[41] Simpson A. On the solution of S(ω)=0 by a Newtonian procedure, Journal of Sound and Vibration, 1984, 97(1): 153-164.
[42] Williams F W, Kennedy D. Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently. International Journal for Numerical Methods in Engineering, 1988, 26: 1825-1841.
[43] Qi Zhaohui, Kennedy D, Williams F W. An accurate method for transcendental eigenproblems with a new criterion for eigenfrequencies. International Journal of Solids andStructures, 2004, 41: 3225-3242.
[44] 胡仲根，恽伟君，段根宝．动态子结构法中的非线性特征值计算．船舶工程，1982，2：13-20
[45] 叶建乔．二次特征矩阵表示的特征值有界性分析．力学学报，1995，27(3)：326-335．
[46] Leung A Y T. Dynamic stiffness method and substructures. New York: Springer, 1993.
[47] Hashemi S M, Richard M J. Free vibrational analysis of axially loaded bending-torsion coupled beams a dynamic finite element. Computers and Structures, 2000, 77: 711-724.
[48] Chen Sbilin, Geradin M, Lamine E. An improved dynamic stiffness method and modal analysis for beam-like structures. Computers and Structures, 1996, 60(5): 725-731.
[49] Gupta K K. Development of a finite dynamic element for free vibration analysis of two-dimensional structures. International Journal for Numerical Methods in Engineering, 1978, 12(8): 1311-1327.
[50] 陈显钧，赵令诚．弯曲板固有振动分析的动态有限元素法．振动与冲击，1982，2：1-11．
[51] 贺国京，陈大鹏．动态有限元法及其在薄板弯曲振动中的应用．长沙铁道学院学报，1999，17(1)：1-6．
[52] 张令弥．动态有限元模型修正技术及其在航空航天结构中的应用．强度与环境1994，2：10-17．
[53] 王静，赵德有，郑治国．用动态有限元法计算加筋板固有频率．大连理工大学学报，2001，41(1)：90-93．
[54] 金咸定．船舶结构动力学的进展与信息化．振动与冲击，2002，21(4)：1-6．
[55] Ozsoysal R. A review of recent ship vibration papers. The Shock and Vibration Digest, 2004, 36: 207-214.
[56] Lewis F M. The inertia of the water surrounding a vibration ship. Trans. SNAME, 1929, 37: 1-20.
[57] Orsero P, Armand J L. A numerical determination of the entrained water in ship vibrations. International Journal for Numerical Methods in Engineering, 1978, 13(1): 35-48.
[58] Zong Z, Lam K Y. Hydrodynamic influence on ship-hull vibration close to water bottom. Journal of Engineering Mathematics, 2000, 37(4):363-374.
[59] Xing J T, Price W G. Theory of Non-linear Elastic Ship-water Interaction Dynamics. Journal of Sound and Vibration, 2000, 230(4): 877-914.
[60] Zheng H, Liu G R, Tao J Set al. FEM/BEManalysis of diesel piston-slap inducedship hull vibration and underwater noise. Applied Acoustics, 2001, 62: 341-358.
[61] Alan Jennings. Added mass for fluid-structure vibration problems. International Journal for Numerical Methods in Fluids, 1985, 5(9): 817-830.
[62] Zhou D, Cheung Y K. Vibration of vertical rectangular plate in contact with water on one side. Earthquake Engineering & Structural Dynamics, 2000, 29(5): 693-710.
[63] Xia Lijuan, Wu Weiguo, Jin, Xianding et al. Analysis Of fluid-structure-coupled vertical vibration for high-speed ships. Journal of Ship Mechanics, 2000, 4(3): 43-50.
[64] Guo Lie, Wu Shichong, He, Fujian. Prediction of local vibration characteristics of naval ship structures. Journal of Ship Mechanics, 2000, 4(6): 69-83.
[65] Sinha G. Transverse free vibration of stiffened plates/shells with elastically restrained edges by FEM. International Shipbuilding Progress, 2000, 47(450): 191-214.
[66] Li X, Chen Y. Free vibration analysis of orthotropic circular cylindrical shell under external hydrostatic pressure. Journal of Ship Research, 2002, 46(3): 201-207.
[67] Lyon R H, Dejone R G. Theory and application of statistical energy analysis. Boston: Butterworth-Heinemann, second edition, 1995.
[68] Lyon R H, Maidanik G. Power flow between linearly coupled oscillators. Journal of the Acoustical Society of America, 1962, 34: 623-629.
[69] New land D E. Power flow between a class of coupled oscillators. Journal of the Acoustical Society of America, 1969, 43: 553-559.
[70] Keane A J, Price W G. Statistical energy analysis of strongly coupled systems. Journal of Sound and Vibration, 1987, 117(2): 363-386.
[71] 明瑞森，孙进才．非保守耦合结构间耦合损耗因子的计算．西北工业大学学报，1989，7(1)：39-46．
[72] 孙进才．复杂结构的损耗因子和耦合损耗因子的测量方法．声学学报，1995，20(2)：127-134．
[73] 孙进才，王冲，孙朝晖．间接耦合机械结构之间的耦合损耗因子．声学学报，1995，20(1)：34-41．
[74] 孙朝晖，孙进才，王冲等．负损耗因子的成因分析．声学学报，1996，2l(5)：798-804．
[75] Sheng M P, Wang M Q, Sun J C. Effective internal loss factors and coupling loss factors for non-conservatively coupled systems. Journal of Sound and Vibration, 1998, 209(4): 685-694.
[76] Eichler E. Plate-edge admittances. Journal of the Acoustical Society of America, 1964, 36(2): 344-348.
[77] Cremer L, Heckl M, Ungar E E. Structure-borne Sound (2nd Edition). Berlin: Springer, 1988.
[78] McCollum M D, Cuschieri J M. Thick plate bending wave transmission using a mobility power flow approach. Journal of the Acoustical Society of America, 1990, 88(3): 1472-1479.
[79] McCollum M D, Cuschieri J M. Bending and in-plane wave transmission in thick connected plates using statistical energy analysis. Journal of the Acoustical Society of America, 1990, 88(3): 1480-1485.
[80] Bosmans I, Mees P, Yermeir G. Structure-borne sound transmission between thin orthotropic plates: analytical solutions. Journal of Sound and Vibration, 1996, 191(1):75-90.
[81] Bosmans I, Vermeir G, Mees P. Coupling loss factors for coupled anisotropic plates. Journal of Sound and Vibration, 2002, 250(2):351-355.
[82] 王宏伟，赵德有．平板与周期加筋阻尼板间耦合损耗因子的研究．船舶力学，2001，5(2)：55-61．
[83] Bie D A, Hamid S. In-situ determination of loss and coupling loss factors by the power injection method. Journal of Sound and Vibration, 1980, 70: 187-204.
[84] Clarkson B L, Ranky M F. On the measurement of the coupling loss factor of structural connections. Journal of Sound and Vibration, 1984, 94(2): 249-261.
[85] Cacciolati C, Guyader J L. Measurement of SEA coupling loss factors using point mobilities. Philosophical transactions-Royal Society of London A, 1994, 346: 465-475.
[86] Langhe K D, Sas P. Statistical analysis of the power injection method. Journal of the Acoustical Society of America, 1996, 100: 291-303.
[87] Simmons C. Structure-borne sound transmission through plate junctions and estimates of SEA coupling loss factors using the finite element method. Journal of Sound and Vibration, 1991, 144(2): 215-227.
[88] Stimpson G, Lalor N. SEA extension of an FE model to predict total engine noise. Proceedings of Inter-noise 92, Toronto, Canada, 1992, 557-560.
[89] Steel J A, Craik R J M. Statistical energy analysis of structure-borne sound transmission by finite element methods. Journal of Sound and Vibration, 1994, 178(4): 533-561.
[90] Fredo C R. A sea-like approach for the derivation of energy flow coefficients with a finite element model. Journal of Sound and Vibration, 1997, 199(4): 645-666.
[91] Shankar K, Keane A J. Vibrational energy flow analysis using a substructure approach: the application of receptance theory to FEA and SEA. Journal of Sound and Vibration, 1997, 201(4): 491-513.
[92] 陆文发，李林普，高明道．近海导管架平台．北京：海洋出版社，1992．
[93] 任贵永．海洋活动式平台．天津：天津大学出版社，1989．
[94] 金伟良．海洋工程中的若干力学问题．科技通报，1997，13(2)：86-92．
[95] 段梦兰．海洋平台结构的最新研究进展第9届ISOPE大会报告综述．海洋工程，2000，18(1)：86-90．
[96] 桂洪斌，金咸定，肖熙．海洋平台振动控制研究综述．中国海洋平台，2003，18(5)：19-25．
[97] 桂洪斌．船舶与海洋工程结构振动控制问题的若干探讨．上海交通大学船舶与海洋工程学院结构力学研究所博士后研究报告，2003．
[98] Lee H H. Stochastic analysis for offshore platform with added mechanical dampers. Ocean Engineering,1997,24(9):817-834.
[99] 欧进萍，邹向阳等．设置粘弹性耗能器的JZ20-2MUQ平台结构冰振控制．海洋工程，2000，18(3)：9-14．
[100] 欧进萍，龙旭，肖仪清等．导管架式海洋平台结构阻尼隔振体系及其减振效果分析．地震工程与工程振动，2002，22(3)：115-122．
[101] 陆建辉，彭临悔，李华军．固定式近海石油平台振动控制研究．中国造船，2000，41(3)：63-68．
[102] 孙树民．独桩平台波浪反应的调谐质量阻尼器控制研究．噪声与振动控制，2001，(4)：14-17．
[103] 孙树民．考虑流体—桩—土相互作用的独桩平台波浪响应的TMD控制研究．中国造船，2002，43(1)：52-57．
[104] 李宏男，马百存．固定式海洋平台利用TLD的减震研究．海洋工程，1996，14(3)：91-96．
[105] 韦林．近海平台的振动最优控制．北京：科学出版社，1992．
[106] 李华军，嵇春艳，吴永宁．随机波浪载荷作用下海洋平台的前馈—反馈振动控制研究．青岛海洋大学学报，2001，31(6)：917-924．
[107] LI H J, Jiang J, Cao H et al. The optimal design of TMD for offshore structures. China Ocean Engineering, 1999, 13(2): 133-144.
[108] Vincenzo G R G. Adaptive control of flow-induced oscillation inducing vortex effects. International Journal of Non-linear Mechanics, 1999, 34: 853-868.
[109] Ahmad S K, Ahmad S. Active control of non-linearly coupled TLP responseunder wind and wave environments. Computers & Structures, 1999, 70(7): 735-747.
[110] LI Huajun, Sau-Lon JAMES HU, Tomotsuka. Optimal active control of wave-induced vibration for offshore platforms. China Ocean Engineering, 2001, 15(1): 1-14.
[111] Suhardjo J, Kareem A. Feedback-feedforward control of offshore platforms under random waves. Earthquake Engineering and Structural Dynamics, 2001, 30(2): 213-235.
[112] Suhardjo J, Kareem A. Structural control of offshore platforms. Proceeding of 7th ISOPE, USA, Honolulu, 1997: 416-424.
[113] Abdel-Rohman M. Structural control of a steel jacket platform. Structural Engineering and Mechanics, 1996, 4(2): 125-138.
[114] Kawano, Kenji, Ishizawa et al. Active control effects on dynamic response of offshore structures. Proceedings of the 3rd ISOPE, Singapore, 1993: 594-598.
[115] 管友海，黄维平．MR阻尼器在海洋平台半主动振动控制中的应用．中国海洋平台，2002，17(3)：25-28．
[116] 孙树民，梁启智．隔震独桩平台地震反应的半主动磁流变阻尼器控制研究．振动与冲击，2001，20(3)：61-64．
[117] 周亚军．导管架海洋平台结构振动智能主动控制研究：(博士学位论文)．大连：大连理工大学，2004．
[118] 周志华，曹存根．神经网络及其应用．北京：清华大学出版社，2004．
[119] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[120] 高隽．人工神经网络原理及仿真实例．北京：机械工业出版社，2003．
[121] 丛爽．神经网络、模糊系统及其在运动控制中的应用．北京：中国科学技术大学出版社，2001．
[122] Wang Zidong, Shu Huisheng, Liu Xiaohui et al. Robust stability for stochastic hopfield neural networks with time delays. Nonlinear Analysis: Real World Applications, 2006, 7(5): 1119-1128.
[123] Bianchini M, Maggini M, Scarselli Fetal. Recursive neural networks for processing graphs with labelled edges: theory and applications. Neural Networks, 2005, 18(8): 1040-1050.
[124] Narayanan A, Keedwell E C, Tatineni Set al. Single-layer artificial neural networks for gene expression analysis. Neurocomputing, 2004, 61: 217-240.
[125] Gob S L, Mandic D P. Recurrent neural networks with trainable amplitude of activation functions. Neural Networks, 2003, 16(8): 1095-1100.
[126] Venkataram P, Ghosal P, Vijay Kumar B P. Neural network based optimal routing algorithm for communication networks. Neural Networks, 2002, 15(10): 1289-1298.
[127] Wang Lixin. A course in fuzzy systems and control. Hong Kong: Prentice-Hall Inc., 1997.
[128] 李士勇．模糊控制·神经控制和智能控制论．哈尔滨：哈尔滨工业大学出版社，1998．
[129] 赵振宇，徐用懋．模糊理论和神经网络的基础与应用．北京：清华大学出版社，1996．
[130] 诸静．模糊控制理论与系统原理．北京：机械工业出版社，2005．
[131] Gavalec M. Solvability and unique solvability of max-min fuzzy equations. Fuzzy Sets and Systems, 2001, 124(3): 385-393.
[132] Quek C, Zhou R W. Structure and learning algorithms of a nonsingleton input fuzzy neural network based on the approximate analogical reasoning schema. Fuzzy Sets and Systems, 2006, 157(13): 1814-1831.
[133] Ferreira W P, Silveira M D C G, Lotufo A Pet al. Transient stability analysis of electric energy systems via a fuzzy ART-ARTMAP neural network. Electric Power Systems Research, 2006, 76(6-7): 466-475.
[134] Zhou Yunfei, Li Shuijin, Jin Rencheng. A new fuzzy neural network with fast learning algorithm and guaranteed stability for manufacturing process control: Fuzzy Sets and Systems, 2002, 132(2): 201-216.
[135] Widrow B, Walach E. Adaptive inverse control. New Jersey: Prentice-Hall Inc., 1996.
[136] 卢志刚，吴士昌，于灵慧．非线性自适应逆控制及其应用．北京：国防工业出版社，2004．
[137] 袁小芳，王耀南，杨辉前．基于支持向量机的非线性逆控制及仿真研究．湖南大学学报，2006，33(1)：71-74．
[138] 朱家强，朱纪洪，郭锁凤等．基于神经网络的鲁棒自适应逆飞行控制．控制理论与应用，2005，22(2)：182-188．
[139] Salman R. Neural networks of adaptive inverse control systems. Applied Mathematics and Computation, 2005, 163(2): 931-939.
[1] Kolousek V. Anwendung des gesetzes der virtuellen verschiebungen und des reziprozitatssatzes in der stabwerksdynamik. Ingenieur-Archiv, 1941, 12:363-370.
[2] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，2001．
[3] Banerjee J R, Williams F W. Vibration of composite beams—an exact method usiag symbolic computation. Journal of Aircraft, 1995, 32: 636-642.
[4] Leung A Y T. Dynamic stiffness method and substructures. New York: Springer, 1993.
[5] Cheng F Y. Vibrations of Timoshenko beams and frameworks. Journal of the Structural Division, 1970, 3: 551-571.
[6] Wittrick W H. General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures. International Journal of Mechanical Sciences, 1968, 10: 949-966.
[1] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[2] Williams F W, Howson W P. compact computation of natural frequencies and buckling loads of plane frames. International Journal for Numerical Methods in Engineering, 1977, 11: 1067-1081.
[3] Howson W P, Williams F W. Natural frequencies of frames with axially loaded Timoshenko members. Journal of Sound and Vibration, 1973, 26(4): 503-515.
[4] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[5] ANSYS User's Manual for Revision 5.1, ANSYS Inc., 1991.
[6] 金咸定，赵德有．船体振动学．上海：上海交通大学出版社，2000．
[1] 金咸定，赵德有．船体振动学．上海：上海交通大学出版社，2000．
[2] 马广宗，蔡承德，虞铣辉．船舶振动基础与实用计算．北京：人民交通出版社，1981．
[3] Lewis F M. The Inertia of the Water Surrounding a Vibrating Ship. Trans. SNAME, 1929, 37: 1-20.
[4] 赵德有，金维成等．渔船振动预报．大连：大连理工大学出版社，1993．
[5] 陆鑫森．高等结构动力学．上海：上海交通大学出版社，1992．
[6] Wittrick W H, Williams F W. A General algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[7] Cho Dae-Seung. Vibration analysis of 299,500 DWT crude oil tanker, Report No. T3000-1. Pusan: Research Institute of Industrial Technology Pusan NationaiUniversity, Oct. 2000.
[8] Zhao Deyou, Lin Ze, etc. Global vibration measurement report for IRAN DENA, Report No. GVM20040104-01. Dalian: Department of Naval Architecture Dalian University of Technology. Jan. 4, 2004.
[1] Mukherjee A, Mukhopadhyay M. A review of dynamic behavior of stiffened plates. The Shock and Vibration Digest, 1986, 18: 3-8.
[2] Kolousek V. Dynamic in Engineering Structures. London: Butterworths, 1973.
[3] 李俊，金咸定．Timoshenko薄壁梁弯扭耦合振动的动态传递矩阵法．振动与冲击，2001，20(4)：57-59．
[4] Banerjee J R. Free vibration of sandwich beams using the dynamic stiffness method. Computers and Structures, 2003, 81: 1915-1922.
[5] Banerjee J R. Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam. Journal of Sound and Vibration, 2004, 270: 379-401.
[6] Li Jun, Shen RongYing, Jin XianDing et al. Bending-torsional coupled dynamic response of axially loaded composite Timoshenko thin-walled beam with closed cross-section. Composite Structures, 2004, 64: 23-35.
[7] Wittrick W H, Williams F W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. International Journal of Mechanical Sciences, 1974, 16(4): 209-239.
[8] Langley R S. Application of the dynamic stiffness method to the free and forced vibration of aircraft panels. Journal of Sound and Vibration, 1989, 135: 319-331.
[9] Bercin A N, Langley R S. Application of the dynamic stiffness technique to the in-plane vibration of plate structures. Computers and Structures, 1996, 59(5): 869-875.
[10] Bercin A N. Analysis of energy flow in thick plate structure. Computers and Structures, 1997, 62(4): 747-756.
[11] Mindlin R D. Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18(1): 31-38.
[12] 王勖成．有限单元法．北京：清华大学出版社，2003．
[13] ANSYS User's Manual for Revision 5.1, ANSYS Inc., 1991.
[1] 姚德源，王其政．统计能量分析原理及其应用．北京：北京理工大学出版社，1995．
[2] Simmons C. Structure-borne sound transmission through plate junctions and estimates of the SEA coupling loss factors using the finite element method. Journal of Sound and Vibration, 1991, 144(2):.215-227.
[3] Lyon R H. Statistical Energy Analysis of Dynamical Systems: Theory and Applications. The MIT Press, 1975.
[4] Bies D A, Hamid S. In situ determination of coupling loss factors by the power injection method. Journal of Sound and Vibration, 1980, 70: 187-204.
[5] 孙进才．复杂结构的损耗因子和耦合损耗因子的测量方法．声学学报，1995，20：127-134．
[6] Cimerman B, Bharj T, Borello G. Overview of the experimental approach to statistical energy analysis. 1997 SAE Noise & Vibration Conference and Expedition, Traverse City, MI, Paper No. 97NV169.
[7] 李德葆，陆秋海．工程振动试验分析．北京：清华大学出版社，2004．
[1] 周亚军，赵德有．海洋平台结构振动控制综述．振动与冲击，2004，23(4)：40-43．
[2] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[3] 周志华．曹存根．神经网络及其应用．北京：清华大学出版社，2004．
[4] 高隽．人工神经网络原理及仿真实例．北京：机械工业出版社，2003．
[5] 丛爽．神经网络、模糊系统及其在运动控制中的应用．北京：中国科学技术大学出版社，2001．
[6] 李士勇．模糊控制·神经控制和智能控制论．哈尔滨：哈尔滨工业大学出版社，1998．
[7] 赵振宇，徐用懋．模糊理论和神经网络的基础与应用．北京：清华大学出版社，1996．
[8] 诸静．模糊控制理论与系统原理．北京：机械工业出版社，2005．
[9] Widrow B, Walach E. Adaptive Inverse Control. New Jersey: Prentice-Hall Inc., 1996.
[10] 卢志刚，吴士昌，于灵慧．非线性自适应逆控制及其应用．北京：国防工业出版社，2004．
[11] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284.
[12] 聂武，刘玉秋．海洋工程结构动力分析．哈尔滨：哈尔滨工程大学出版社，2002．
[13] 王士同．模糊系统、模糊神经网络及应用程序设计．上海：上海科学技术文献出版社，1998．
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |