广义特征值问题的快速傅里叶变换法

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (22) : 67-71.

论文

广义特征值问题的快速傅里叶变换法

吴锋，徐小明，钟万勰

作者信息 +

The Fast Fourier Transform Method for The Generalized Eigenvalue Problem

Wu Feng, Xu Xiaoming, Zhong Wanxie

Author information +

文章历史 +

摘要

本文针对广义特征值问题提出离散傅里叶变换法。该方法把结构的动力响应看作是一种信号，利用快速傅里叶变换进行分析，从而得到结构的振动频率。本文方法避免对刚度矩阵求逆，可同时计算出所有的特征值，是一种直接方法。数值算例验证了本文方法的正确性。

Abstract

For the generalized eigenvalue problem, a method based on the fast Fourier transform (FFT) is developed. In the proposed method, the dynamical structural response is viewed as a signal which contains all information about the vibrational frequencies. Using FFT to the signal, the vibrational frequencies can be obtained. The method is a kind of direct solution method which could compute all eigenvalues without the matrix inversion. The numerical example manifests the correction of the proposed method.

导出引用

吴锋;徐小明;钟万勰. 广义特征值问题的快速傅里叶变换法[J]. 振动与冲击, 2014, 33(22): 67-71

Wu Feng;Xu Xiaoming;Zhong Wanxie. The Fast Fourier Transform Method for The Generalized Eigenvalue Problem[J]. Journal of Vibration and Shock, 2014, 33(22): 67-71