结构非平稳随机响应分析的快速虚拟激励法

Fast pseudo-excitation method in structural non-stationary stochastic response analysis

虚拟激励法能够方便地应用于结构非平稳随机响应分析,但在每个离散频点处都涉及到虚拟激励作用下动力方程的时程积分,对于大型复杂结构,其计算量是难以接受的。将结构动力方程写成状态方程形式,采用精细积分法对状态方程进行数值求解,导出了结构动力响应关于离散时刻处激励的显式线性表达式。利用这一显式表达式,只需要变换离散时刻处的激励数值,就可以方便快捷地求出新的激励作用下的结构动力响应。效率分析和数值算例表明,相对于传统虚拟激励法,本文提出的改进算法在求解非平稳激励下结构随机振动方面具有更高的计算效率。

The pseudo-excitation method can be conveniently applied to structural non-stationary stochastic response analysis,but it is required to conduct a large amount of time integration of dynamic equations under different pseudo-excitations at each discrete point of the frequency domain concerned.For large-scale complicated structures,the computation costs for such repetitive time integrations are unacceptable.In this paper,dynamic equations are first transformed into the form of state equations and solved by the precise time integration method.An explicit linear expression is then deduced for structural dynamic responses due to the excitations at different time.Based on the above explicit expression,structural dynamic responses under different pseudo-excitations can be obtained conveniently and rapidly once the values of excitations at different time are given,without any time integration being required.Efficiency analysis and numerical examples show the proposed fast pseudo-excitation method has higher efficiency in non-stationary stochastic response analysis when compared with the traditional pseudo-excitation method.