摘要
通过作者前文[2]的讨论,我们得到了随机振动离散分析方法的一个具有无条件稳定性和高精确度的递推公式—β递推格式。但由于在这个递推格式中存在一个增广矩阵求逆的问题,这就给它在实际应用中带来了一定的困难。本文通过等效变换,成功地克服了这一困难,避免了这个增广矩阵求逆,并完全应用了原动力体系质量阵、阻尼阵和刚度阵的对称、带状等特点,大大减少了计算所需的内存和工作量,从而使该方法很实用。
Discrete analysis method of random vibration is a numerical method for solving random vibration responses of a dynamic system by discre- tizing its dynamic differential equation in both space and time domains. It has many advantages over the analytical method,e.g.it is more ap- plicable in general cases.This method was firstly proposed by the authors three years ago.A Series of results for the theoretical bases of the method and its application have been obtained.A high accuracy (absolute accurate when stationary state is reached)and unconditionable stable recurrence formula——β recurrence formula was developed.And a number of applications of this for different kinds of structural damping and excitations were carried out. However,because there is a double sized inverse matrix existing in the recurrence formula,it requires much more computation work in real calculation.For solving this problem,this paper uses equivalent frans- formation,successfully overcomes this difficulty.Therefore,not only the calculation of the double sized inverse matrix is avoided,but also the synthetic and banded preperties of the mass,damping and stiffness matrixes of the original dynamic system are fully used.This helps to make the computation time greatly reduced,so that this method becomes more practical.At the end,two examples are given to verify the effec- tiveness of the formulas given in this paper.
关键词
随机振动
离散分析
计算
random vibration
discrete analysis
equivalent transformation
practical calculation
