广义特征值问题的快速傅里叶变换法

摘要

For generalized eigenvalue problems,a method based on the fast Fourier transform (FFT) was developed.In the proposed method,the dynamical structural response was viewed as a signal containing 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 can compute all eigenvalues without the matrix inversion.A numerical example manifests the correctness of the proposed method.%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。该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。数值算例验证了该方法的正确性。