Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Abstract

Modal analysis is a widely applied method to study the vibration phenomenon of continuum structures, but there is no clear method to solve the modal truncation problem at present. In order to determine the contribution of different modes to the whole system, a new mode truncation method based on perturbation theory is proposed in this paper. In the process of discretization, perturbation parameters are introduced into the modes, and the modal number in the continuum structure system is confirmed according to the norm error of stiffness matrix in different degrees of freedom (DOFs) systems. The results show that the DOF identified by the modal perturbation method is related to the perturbation parameters, and the smaller the perturbation parameters are, the fewer modes need to be considered. When the perturbation parameter is large enough, the response of the system can only be accurately explained by truncation to higher-order modes. Finally, the perturbation parameter is fixed to 1, and the modal perturbation is connected with the traditional Galerkin method, which means that the traditional discretization is a special case of the modal perturbation method, and the number of modes can still be determined by the induced norm. This method can significantly reduce the modal truncation error, which is of great significance to the dynamic analysis of engineering applications.