Bending Vibration and Power Flow Analysis of Plate Assemblies in the Symplectic Space
-
摘要: 基于波传播理论,在辛空间下研究了由矩形薄板组成的板列结构的自由波属性以及受迫振动问题.通过将薄板弯曲振动控制方程导入辛对偶体系,得到了薄板波传播参数以及各阶波形的辛解析解.根据波在各板之间的传播、反射以及透射关系和叠加原理得到问题的解.给出了辛空间波传播框架下各板动能、应变能以及板间功率流的计算表达式.相比传统波传播方法,该方法具有不受边界条件限制以及能够给出波模态辛解析解的特点.以一个三板组合结构为算例,通过与ABAQUS程序得到的有限元参考解进行对比,验证了所提出方法的高效性与精确性.由于完全基于理性推导,不涉及任何试函数的引入,因此该方法也可推广应用于由其他类型板(如中厚板、层合板等)组合的板列结构动力响应分析问题.Abstract: The free wave propagation and forced vibration of thin rectangular plate assemblies were investigated with the symplectic method based on wave propagation theory. The governing equations of bending vibration of the thin plates were introduced into the symplectic duality system firstly, then the wave propagation parameters and wave shapes were determined as analytical solution to the symplectic eigenvalue problem. And responses of the thin plates described in physical domain were transformed into wave coordinates. The amplitudes associated with the mode shapes were obtained through solving of the equations involving excitation, scattering and propagation. Superimposition of the wave amplitudes gave the physical responses. Expressions were derived for the mean power flow through the system and mean energy in the plate components. Compared with the traditional wave methods, the provided method is applicable for any combination of classical boundary conditions. The method was applied to the forced vibration of a built-up structure of 3 directly connected thin plates and the results were compared with those from the ABAQUS finite element software. A significant improvement on accuracy and computational efficiency is achieved. As the derivation of the formulae is rigorously rational, the provided method is also applicable for the dynamic analysis of plate assemblies composed of any other types of plates (such as moderately thick plates, and layered plates, etc.).
-
Key words:
- symplectic duality system /
- plate assembly /
- power flow
-
[1] Petyt M. Introduction to Finite Element Vibration Analysis [M]. Cambridge: Cambridge University Press, 2010. [2] Lyon R H, DeJong R G. Theory and Application of Statistical Energy Analysis [M]. Boston: Butterworth-Heinemann, 1995. [3] Woodhouse J. An introduction to statistical energy analysis of structural vibration[J]. Applied Acoustics,1981,14(6): 455-469. [4] Mace B R, Rosenberg J. The SEA of two coupled plates: an investigation into the effects of subsystem irregularity[J]. Journal of Sound and Vibration,1998,212(3): 395-415. [5] Silvester P. A general high-order finite-element analysis program waveguide[J]. Microwave Theory and Techniques, IEEE Transactions on,1969,17(4): 204-210. [6] Koshiba M, Maruyama S, Hirayama K. A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems[J]. Journal of Lightwave Technology,1994,12(3): 495-502. [7] Langley R S. Application of the dynamic stiffness method to the free and forced vibrations of aircraft panels[J]. Journal of Sound and Vibration,1989,135(2): 319-331. [8] Grice R M, Pinnington R J. A method for the vibration analysis of built-up structures—part I: introduction and analytical analysis of the plate-stiffened beam[J]. Journal of Sound and Vibration,2000,230(4): 825-849. [9] Wester E C N, Mace B R. Wave component analysis of energy flow in complex structures—part I: a deterministic model[J]. Journal of Sound and Vibration,2005,285(1): 209-227. [10] Ladevèze P, Arnaud L, Rouch P, Blanze C. The variational theory of complex rays for the calculation of medium-frequency vibrations[J]. Engineering Computations,2001,18(1/2): 193-214. [11] Vanmaele C, Vandepitte D, Desmet W. An efficient wave based prediction technique for plate bending vibrations[J]. Computer Methods in Applied Mechanics and Engineering,2007,196(33): 3178-3189. [12] Vergote K, Vanmaele C, Vandepitte D, Desmet W. An efficient wave based approach for the time-harmonic vibration analysis of 3D plate assemblies[J]. Journal of Sound and Vibration,2013,332(8): 1930-1946. [13] Mace B R, Duhamel D, Brennan M J, Hinke L. Finite element prediction of wave motion in structural waveguides[J]. Journal of the Acoustical Society of America,2005,117(5): 2835-2843. [14] Waki Y, Mace B R, Brennan M J. Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides[J]. Journal of Sound and Vibration,2009,327(1): 92-108. [15] Langley R S. A wave intensity technique for the analysis of high frequency vibrations[J]. Journal of Sound and Vibration,1992,159(3): 483-502. [16] Maxit L, Guyader J L. Extension of SEA model to subsystems with non-uniform modal energy distribution[J]. Journal of Sound and Vibration,2003,265(2): 337-358. [17] Nefske D J, Sung S H. Power flow finite element analysis of dynamic systems: basic theory and application to beams[J]. Journal of Vibration Acoustics Stress and Reliability in Design,1989,11(1): 94-100. [18] Shorter P J, Langley R S. Vibro-acoustic analysis of complex systems[J]. Journal of Sound and Vibration,2005,288(3): 669-699. [19] 姚伟岸, 钟万勰. 辛弹性力学[M]. 北京: 高等教育出版社, 2002.(YAO Wei-an, ZHONG Wan-xie. Symplectic Elasticity [M]. Beijing: Higher Education Press, 2002. (in Chinese)) [20] 钟万勰. 应用力学对偶体系[M]. 北京: 科学出版社, 2002.(ZHONG Wan-xie. Duality System in Applied Mechanics [M]. Beijing: Science Press, 2002. (in Chinese)) [21] 鲍四元, 邓子辰. 环扇形板弯曲问题中环向模拟为时间的辛体系[J]. 西北工业大学学报, 2004,22(6): 734-738.(BAO Si-yuan, DENG Zi-chen. Symplectic solutions of annular sector plate clamped along two circular edges with circumfluent coordinate treated as “time”[J]. Journal of Northwestern Polytechnical University,2004,22(6): 734-738.(in Chinese)) [22] 钟阳, 李锐, 田斌. 矩形中厚板自由振动问题的哈密顿体系与辛几何解法[J]. 动力学与控制学报, 2009,7(4): 302-307.(ZHONG Yang, LI Rui, TIAN Bin. On Hamilton system and new symplectic approach for free vibration of moderately thick rectangular plates[J]. Journal of Dynamics and Control,2009,7(4): 302-307.(in Chinese))
点击查看大图
计量
- 文章访问数: 1090
- HTML全文浏览量: 147
- PDF下载量: 761
- 被引次数: 0