模态截断与简谐载荷响应的改进

利用矩阵级数展开和特征值的谱迭加原理 ,将截断模态对响应的贡献用已知模态和系统矩阵来精确表达 ,从而可以提高计算精度。本文在此基础上 ,利用特征值移位的方法使得其中载荷的频率可以高于被截断的固有模态的频率 ,给出了实用的移位值。数值例子表明本文改进方法是非常有效的

Modal Truncation and the Improved Response to Harmonic Excitation

Fast and accurately evaluating the contribution due to the truncated modes to the response of harmonic excitation is put forward by Z.X.Liu without using the truncated modes. By using the series ex pansion of a matrix function and the theory of spectral representation of a matr ix, the contribution due to the truncated modes to the response of a harmonic ex citation is expressed exactly and explicitly, with the available low-frequency modes and the system matrices. The objective of this paper is to extend the meth od by Z.X.Liu through eigenvalue shift so that the frequency of the harmonic ex citation can be larger than the natural frequency of the truncated modes, and th e practical shift value is put forward, therefore the method by Z.X.Liu is impr oved. Two numerical examples are given to demonstrate the validity and the effec tiveness of the present method.