非平稳激励下结构随机振动时域分析法

RANDOM VIBRATION ANALYSIS OF STRUCTURES SUBJECTED TO NON-STATIONARY EXCITATIONS BY TIME DOMAIN METHOD

根据线性动力系统输入与输出之间的线性关系特性,探讨非平稳随机激励下结构随机振动的时域求解方法。把结构动力方程写成状态方程形式,同时把非平稳随机激励向量离散为一系列时间截口随机向量。采用精细积分法对状态方程进行数值求解,可建立任意离散时刻结构响应关于时间截口随机向量的显式线性表达式。基于该显式表达式:一方面可以直接利用一阶矩和二阶矩的运算规律计算任意离散时刻结构响应的均值和方差;另一方面也可进一步实施蒙特卡罗数值模拟,这除了可以得到结构响应的均值和方差时程外,还可以得到结构非平稳随机响应的演化概率密度函数。所提出的方法对随机激励方式没有任何限制,适用面广,且具有计算精度高、计算效率大幅提高以及获得响应统计信息全面等优点。数值算例显示了该文方法的上述优点。

According to linear characteristics of the relation between the input and output of linear dynamic systems,the time domain method is investigated for random vibration analysis of structures subjected to non-stationary random excitations.Equations of motion of the structure are first transformed into the form of state equations,and non-stationary random excitations are discretized into random vectors at a series of time points.The state equations derived are then solved by means of a high precision direct integration method,which yields an explicit linear expression of the structure responses by the random vectors at different time points.Based on the above explicit expression,mean values and variances of the structure responses at different time points are obtained through the calculation rules of the first order moments and the second order moments.On the other hand,Monte-Carlo numerical simulation can be conducted by use of the explicit derived expression,which not only provides mean values and variances of the random responses,but also gives the evolutionary probability density function of the non-stationary responses.Numerical examples show that the proposed methods have high accuracy and efficiency and have no restrictions on the forms of the random excitations.