两类演变随机响应的计算

The Calculation of Two Typical Evolutionary Random Responses

应用微分方程理论推导出工程上常见的两类演变随机激励下的非平稳随机响应的计算公式 ,并把微分方程数值积分的Runge-Kutta方法引入非均匀调制随机激励下的演变随机响应计算问题中 ,使复杂的演变随机响应问题得到简便的解决。通过计算实例 ,并同复模态分析方法比较 ,说明了该方法的有效性和精确性。该方法具有公式简单、编程容易、计算速度快等优点。

Earthquake excitations to ground structures and road-undulation-induced excitations to vehicles travelling with variable speed are two kinds of nonstationary random excitations commonly encountered in engineering. Actually, both kinds of the nonstationary random processes are evolved from stationary ones, though through utterly different ways. The problems of response to both kinds of excitations have much in common. The calculation formulas of nonstationary random responses under two typical evolutionary random excitations are presented by using of the theory of differential equation. By introducing Runge-Kutta integration method, the problems of evolutionary random responses for nonuniform modulated random excitations can be solved simply. By comparing the obtained results with the results of complex modal analysis, it is shown that the present method is accurate enough and efficient. The method has many advantages, such as simple in formulation, easy in programming and fast in calculating, and the method might be hopefully applied to nonlinear systems, too, if accompanied by the statistical linearization technique.