随机与谐和联合激励下分数阶非线性系统的统计线性化方法

Statistical linearization method for nonlinear Duffing oscillator under combined random and harmonic excitations

提出了一种计算随机与谐和联合激励下非线性分数阶系统响应二阶矩的统计线性化方法。假定位移响应可写为确定性均值和零均值随机分量之和的形式,原运动微分方程可化为关于均值分量的确定性微分方程和关于随机分量的随机微分方程组合。分别利用谐波平衡法和统计线性化方法对上述两类方程求解后,可得响应的确定性均值与随机分量。Monte Carlo模拟证实了该方法的有效性。

A statistical linearization method for calculating the second-order moment of a non-linear oscillator endowed with frac⁃tional derivative damping under combined random and harmonic excitations is proposed.Assuming the system response to be writ⁃ten as the sum of a deterministic mean component and a zero-mean random component,the motion differential equation can be sep⁃arated into two coupled differential equations of the deterministic and random parts.The method of harmonic balance and the meth⁃od of statistical linearization are used to solve the two differential equations respectively to access the deterministic and random com⁃ponents of the response.The effectiveness of the method is verified by Monte Carlo simulation.