复阻尼结构动力方程的增维精细积分法

为了避开求解复阻尼结构强迫激励动力学方程的积分运算,引入增维精细积分方法。根据复阻尼系统复化对偶原则,将动力学方程和激励波对偶复化为实部和虚部的形式,推导出增维矩阵的精细积分求解过程。结果表明,由于不用求解迭代矩阵H的逆矩阵,避免了矩阵奇异带来的计算解的不稳定性。在计算矩阵仅增加一维的情况下,化积分运算为代数运算,扩大了精细积分法的应用范围。通过对比增维精细积分法和频域法计算结果,二者结果保持较高的一致性。

Magnified dimension precise integration method for the dynamic equations of complex damped structures

In order to avoid the integral operation of the forced excitation dynamics equation of complex damped structures,a magnified precise integration method was introduced. According to the dual principle of complex damping system,the dual dynamic equations and the dual excitation waves were divided into real and imaginary parts,and the solving process by using the precise integration of the augmented matrix was derived. The results show that because the inverse matrix of the iteration matrix H doesn’t need to be solved,the instability of the computational solution caused by the singularity of matrix is avoided. In the calculation of the matrix,only a one-dimensional integral calculation is increased and the integral operation is transformed into algebraic operations,so,the scope of application of the precise integration method can be expanded. The comparison between the results calculated by using the augmented precise integration method and the frequency domain method shows they are in good consistency.