基于混合摄动-伽辽金法的线性随机结构动力响应分析

Dynamic Response Analysis of Linear Random Structures Based on Mixed Perturbation-galerkin Method

在已知的Newmark-β法的基础上,将结构的随机运动方程转化为求解时域位移的准静态平衡方程。在蒙特卡罗模拟(MCS)的框架,结合混合摄动-伽辽金法提出了一种随机参数结构的动力分析方法——随机摄动-伽辽金法。然后,将随机摄动-伽辽金有限元法的计算结果与直接蒙特卡罗模拟的结果进行比较。数值算例表明,该方法在复合随机振动分析中具有很高的精度和效率。

Based on the known Newmark-β method,the stochastic motion equation of the structure was transformed into a quasi-static equilibrium equation for time domain displacement.In the framework of monte carlo simulation (MCS),combined with the mixed perturbation-galerkin method,a dynamic analysis method of random parameter structure was proposed.Then,the results of random perturbation-galerkin finite element method were compared with those of direct monte carlo simulation.Numerical examples showed that the method has high accuracy and efficiency in the analysis of complex random vibration.