基于快速Fourier变换法的广义特征值问题重根辨识方法

对具有重根的广义特征值问题,采用基于快速Fourier变换的方法进行求解,实现重根辨识.文章中采用多次单点初始激励的方式,仿真计算测点上的自由振动响应,对响应进行快速Fourier变换后得到频域数据.而后对频域数据分析,得到固有频率和多组测点振型数据.根据单频和重频处的振型特性,引入振型的余弦相似度为判别参数,辨识重根.数值算例表明,该方法可有效实现重根辨识,同时特征值的计算能达到较高精度.

A Method Based on Fast Fourier Transform for Generalized Eigenvalue Problems and Multiple Frequencies Identification

A method based on the fast Fourier transform was proposed to solve the generalized eigenvalue problems with multiple roots. This paper calculated dynamic responses on measure nodes with nonzero initial condition on one point. Both natural frequencies and mode shapes were extracted from data in the frequency domain. Responses under different initial conditions were calculated to get several sets of mode shape data. Taking cosine similarity of mode shapes as the discriminant parameter, multiple roots were identified. The numerical example shows that this method can identify the multiple roots efficiently and the result reaches a high accuracy.