位移偶次方项对非线性随机振子在泊松激励下概率解的影响  

EFFECT OF EVEN NONLINEARITY OF DISPLACEMENT ON THE PDF SOLUTIONS OF STOCHASTIC OSCILLATORS UNDER POISSON EXCITATION

作　　者：郭秀秀[1] 鄂国康[1] 

机构地区：[1]澳门特别行政区澳门大学土木与环境工程系

出　　处：《固体力学学报》2013年第S1期112-116,共5页Chinese Journal of Solid Mechanics

基　　金：澳门大学研究与发展行政办公室基金资助

摘　　要：本文分析了带位移偶次方项非线性随机振子在泊松激励下响应的概率密度函数解.用指数多项式闭合法(exponential-polynomial closure method)求解了Fokker-Planck-Kolmogorov方程控制的随机振子的平稳响应概率解,分析了不同类型的非线性振子.用蒙特卡洛模拟结果验证了指数多项式闭合法在此情况下的有效性和精确度.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.数值结果显示当振子带有位移偶次方非线性时,位移的均值总是非零,位移的概率密度分布关于均值是非对称的,而速度的均值等于零,速度的概率分布关于均值对称.数据结果进一步显示,位移的均值和位移的概率分布随着位移偶次方项的大小和正负而反向变化.The probabilistic solutions of nonlinear stochastic oscillators with even nonlinearity driven by Poisson white noise are investigated in this paper.The stationary probability density function(PDF)of the oscillator responses governed by the reduced Fokker-Planck-Kolmogorov equation is obtained with exponential polynomial closure(EPC)method.Different types of nonlinear oscillators are considered.Monte Carlo simulation is conducted to examine the effectiveness and accuracy of the EPC method in this case.It is found that the PDF solutions obtained with EPC agree well with those obtained with Monte Carlo simulation,especially in the tail regions of the PDFs of oscillator responses.Numerical analysis shows that the mean of displacement is nonzero and the PDF of displacement is nonsymmetric about its mean when there is even nonlinearity in displacement in the oscillator,while the mean of velocity always equals zero and the PDF of velocity is symmetrically distributed about its mean.Numerical analysis further shows that both the mean and the PDF of displacement changes with the even order term on displacement both in quantity and in sign.

关 键 词：指数多项式闭合(EPC)法 FOKKER-PLANCK方程 位移偶次方非线性 

分 类 号：O324[理学—一般力学与力学基础]