求解双线性单自由度复合随机系统

Solution to Bi-linear SDOF Compound Stochastic Vibration

在单自由度线性复合随机系统研究及Monte Carlo法模拟的基础上,引入求解随机问题的非线性改进随机摄动法,将双线性单自由度随机结构看成是均值结构及其变分,假定反应的概率分布类型为正态分布或均匀分布,从而将双线性复合随机微分方程展开为线性摄动随机微分方程,然后与虚拟激励法结合,迭代求解随机反应.算例的计算结果表明,将非线性改进随机摄动法与虚拟激励法结合,所得的非线性复合随机振动系统的随机反应还是较为准确的.为取得更精确的计算结果,反应的概率分布类型的正确选择很重要.

Based on the research of linear SDOF compound stochastic vibration and Monte Carlo simulation,non-linear improved stochastic perturbation method is adopted to solve single stochastic problem,and bi-linear SDOF stochastic structure is expanded to mean part and variation part.Then,the probability distribution type of stochastic response is assumed as normal distribution or uniform distribution.As a result,bi-linear compound stochastic differential equation is expanded to linear perturbation stochastic differential equations.Stochastic response is obtained with the pseudo excitation method and iteration.A case study shows that the combination of non-linear improved stochastic perturbation method with pseudo excitation method can get relatively accurate result of stochastic response of non-linear compound stochastic vibration system.For more accurate results,precise pre-estimate of the probability distribution type of stochastic response is very important.