阻尼振动系统复特征解的摄动分析

 当振动系统的质量矩阵和刚度矩阵作小修改时,不重复求解大型广义特征问题,在初始的模态坐标变换基础上,用矩阵摄动法给出修改系统的振动频率和振型;然后利用修改系统的振动频率与比例阻尼参数求出修改系统的阻尼比。工程算例表明,这种方法计算简单,具有较高的精度。

PERTURBATION ANALYSIS OF THE COMPLEX EIGENSOLUTIONS FOR DAMPED VIBRATION SYSTEM

A perturbation method for analyzing the vibration frequencies, damping ratios and modes of damped vibration system, whose matrices have small changes, is presented in this paper. When the mass and stiffness matrices of the original syatem vary slightly, the eigensolutions can be obtained without solving a large generalized eigenvalue problem again. The vibration frequencies and modes of the updated system can be derived by matrix perturbation method based on the original vibraton mode coordinate transformation. The damping ratios of the updatea system can also be given by using the vibration frequencies of the updated system and proportional damping parameters. The results of the engineering computational examples show that the presented method having simple computational and high accuracy properties is an available perturbation method.