指数多项式闭合法求带位移偶次方项非线性随机振子响应的概率解

Exponential Ploynomial Closure Procedure for the Probabilistic Solution of Nonlinear Stochastic Oscillator with Even Order Terms in Displacement

本文用指数多项式闭合(Exponential Polynomial Closure,EPC)法分析了具非零均值响应的带位移偶次方项非线性随机振子的响应概率密度函数解。给出了求解过程并通过算例分析验证了指数多项式闭合法在此情况下的有效性。数值结果显示,指数多项式闭合法得到的响应概率密度结果与蒙特卡洛模拟的结果符合较好,尤其是在概率密度函数的尾部区域。

The exponential polynomial closure（EPC） method was employed to analyze the probability density function of the responses of nonlinear stochastic oscillator with non-zero mean responses.The solution procedure was presented and an example was given to show the effectiveness of EPC method in this case.The numerical results show that the results obtained with EPC method agree well with those obtained with Monte Carlo simulation,specially in the tails of the probability density function of the responses.