耦合板结构随机能量有限元分析

摘要

For plate structures, the governing equation of energy flow analysis (EFA)for random loading case was proposed and the corresponding energy response as well as power flow were formulated. The procedure to calculate the coupling matrix of plate junction considering both flexural and in-plane wave fields was presented. The proposed method was utilized to predict the energy response and power flow of an L-shaped coupled plate structure subject to two uncorrelated broadband random forces. The results display the spatial variation of energy density and the pattern of power flow in the coupled structure. Statistical energy analysis (SEA) was employed to estimate the energy response of the same structure. Considerably well agreement between solutions from these two methods was observed and the application of EFA method in plate structures under random excitations was validated.%基于单频激励下导出的板的能量流分析方程,将其应用推广到板受随机激励的情形,提出了宽带随机激励下板的响应能量及功率流的计算公式.对考虑弯曲和纵波场耦合的板结构给出了计算能量有限元耦合矩阵的一般方法.用能量有限元法对受到两个不相关宽带白噪声激励力作用的L型板的能量响应和功率流进行了计算,结果反映了各波场的能量在空间上的分布和它们在各波场内的流动特性,其中弯曲波场的功率流显示出相向功率流发生汇集和改变流向的特点.对该耦合结构的响应用统计能量分析法进行了求解,其结果与能量有限元法计算结果间较好的一致性验证了随机激励下板的能量有限元分析应用的正确性.