随机振动响应方差的直接算法

Direct algorithm for variance of random vibration response

将动力学方程经过系统扩阶和模态变换构成李雅普诺夫方程,可直接求得大型有限元结构的平稳随机振动响应方差.用等效线性化方法处理杜芬系统后,求解李雅普诺夫方程可以得到一套高效高精度求解杜芬系统随机振动响应方差的方法.仿真对误差进行了估计,结果验证了方法的高效和精确性.

By using of extending order and modal transformation of dynamic equation, a Lyapunov equation was established, and the solution of the Lyapunov equation could be used to directly obtain stationary random vibration response variance of large-scale finite element structure. Duffing system was linearized by equivalent linearization method, and the Lyapunov equation was solved to get the variance of random vibration response of duffing system. The precision has been justified by simulation, showing that the presented method is efficient and precise.