随机激励下框架梁结构能量有限元分析

Energy Finite Element Analysis of Framed Structure under Random Excitations

提出了梁结构在随机激励下的能量流分析方程及能量响应和功率流的计算公式,给出了在同时考虑弯曲和纵波场的耦合梁结构条件下计算功率流耦合矩阵的一般方法,用能量有限元分析法对一个受到多个不相关随机激励的框架梁结构的能量响应及功率流进行了计算.结果反映了振动能量在结构内的分布和传递路径,并表明梁的纵波场在耦合梁的能量传递中起到重要作用.用统计能量分析法对该框架梁结构响应进行了求解,通过比较2种方法的计算结果,验证了随机激励下能量有限元分析方法的正确性.

For beam structure, the energy flow analysis （EFA） equation for the case of random loading and formulations of energy response and power flow were proposed. Derivation of the coupling matrix for coupled beams, which is required for built-up beam structures when EFA is implemented using finite element method, was given. The proposed method was applied to a planar frame structure subject to incoherent random excitations, and solutions of energy density and power flow were calculated. The results indicate that the energy of longitudinal wave field is of approximately the same level as that of bending wave field in some beams in relatively high frequency. Statistical energy analysis （SEA） was utilized to solve the same problem, and good agreement between the results from the two approaches validates the EFA formulations developed for situations where random excitation is applied.