结构非平稳随机响应方差数值计算方法

Calculation method of the variance matrix of structural non-stationary random responses

对受非平稳随机激励的工程结构,建立了在任意调制的演变随机白噪声和有色噪声激励下,结构响应方差矩阵的计算方法。提出了矩阵微分方程的数值解法,首先将矩阵微分方程转换为普通的代数微分方程,再应用常规的ODE求解器进行求解。该方法可以处理任意调制的演变随机白噪声或有色噪声,原理简明,易于掌握和应用。文中介绍了相应的关键计算步骤。数值仿真算例显示了该方法的正确性和可行性。

For an engineering structure exposed to non-stationary random excitations this paper established the matrix Lyapunov equation satisfied by its structural responses under arbitrary evolutionary white or colored random loads. A new calculation method is proposed to solve the time varying matrix Lyapunov equation, which includes two steps translating the equation to Ordinary Differential Equation（ODE） in common form, and solving it by an ODE solver. This method is simple and concise in theory, and suitable to deal with arbitrary random excitations. The calculation method is introduced in detail. The feasibility of the method is validated by comparing the results of Monte Carlo method and the proposed one for a numerical simulation example.