多维激励下结构随机振动响应分析

基于随机振动方法，以谱函数分析的方式，给出了典型结构在多维激励下的振动响应计算公式。根据理论分析的结果，计算了多激励单轴向和多激励多轴向的算例。结果表明，对于线性结构，多维激励下结构振动的响应谱为轴向上各个激励点时响应谱的叠加，但由于各点激励下结构振动的振型函数不同，结构响应可能比单个激励点激励时响应大，也可能小；在一些情况下，结构响应会丢失反对称振型的响应。多维激励下振型函数对结构响应的影响，应该引起工程结构设计人员的重视。

Random Vibration Response Analysis of Structures under Multi-dimensional Excitation

Base on random vibration method, through spectrum function analysis, the random vibration response calculation of typical structures under multi-dimensional excitation was given. MESA and MESE examples were demonstrated according the theoretical analysis results. Numerical analysis results indicated that, for linear structures, the responses of multi-dimensional excitation are the sum of one-dimensional excitation; however for the difference of mode functions of each single exciter, the structural vibration responses may increase or decrease compared with that of single exciter; in special case, the responses of anti-symmetric mode can even disappear. The influence of structural vibration responses character under multi-dimensional excitation is worth of attention of the designers of engineering structures.