板列弯曲振动及功率流分析的辛空间波传播方法

Bending Vibration and Power Flow Analysis of Plate Assemblies in the Symplectic Space

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.

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 flowthrough 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.）.