基于参数展开的同伦分析法在强非线性随机动力系统中的应用

Application of homotopy technique with the parameter expansion to strongly nonlinear stochastic dynamic systems

将基于参数展开的同伦分析法(PE-HAM)进行了推广,使之适用于谐和激励与随机噪声联合作用下的强非线性随机动力系统.通过构造合适的同伦映射,将对强非线性随机动力系统响应的求解转化为对一组线性随机微分方程的求解.进一步研究了受到谐和与Gauss白噪声激励的强非线性Duffing振子,由PE-HAM得到了该系统的解过程和稳态概率密度的解析表达式.数值模拟的结果说明了PE-HAM方法的精确性.

This paper extends the method of PE-HAM to strongly nonlinear stochastic dynamic system under harmonic and Gauss white noise excitations. By constructing an appropriate homotopy mapping, the original system is transformed into a set of linear stochastic differential equations. In addition, the strongly nonlinear Duffing oscillator subjected to harmonic and Gauss white noise excitations is investigated using the proposed method, and its approximate analytically solution process and steady-state probability density are obtained. Numerical simulation is employed to verify the theoretical result and good agreement is found.