【摘要】 论文给出了一个求大规模非线性随机动力系统响应概率密度函数解的新方法,称之为子空间法.考察了此方法在求解大规模带位移项参数激励非线性随机动力系统响应概率密度函数的有效性.这里的概率密度函数解由Fokker-Planck-Kolmogorov(FPK)方程控制.该方法是基于将非线性随机动力系统状态变量空间分成两个子空间,然后在其中一个子空间上对FPK方程进行积分,采取一定措施后得到低维的FPK方程.该低维的FPK方程的维数可以人为确定,也可以取为二维,从而可以用现有的求解低维FPK方程的方法求得所需的概率密度函数解.文中给出了算例,用数值结果验证了子空间法的有效性.论文是采用作者曾提出的指数多项式闭合(EPC)法求解由子空间法降维的FPK方程.更多还原

【Abstract】 A new method named subspace method is presented in this paper for the probability density function of the responses of large-scale nonlinear stochastic dynamic systems.The effectiveness of this method is investigated when there are multiplicative excitations on displacement in the large-scale nonlinear stochastic dynamic system.The probability density function investigated here is governed by the Fokker-Planck-Kolmogorov(FPK) equation.This method is based on the idea that the state space of the system responses is separated into two subspaces,both sides of the FPK equation is integrated over one of the subspace,and then the dimension-deducted low-dimensional FPK equation is obtained.The number of the dimensions of the dimension-deducted FPK equation can be at choice and can be as less as two.Therefore,the available methods can be employed for solving the low-dimensional FPK equations.Numerical examples are given to verify the effectiveness of the presented subspace method and the dimension-deducted low-dimensional FPK equations are solved with the exponential polynomial closure(EPC) method which was proposed by the authors.更多还原