Journal Article

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

Guo, Tieding, Su, Xiaoyang, Yuan, Quan, Kang, Houjun, Cong, Yunyue

2024

Overview

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. 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. The modes are subjected to perturbation parameters during discretization, and using norm error analysis on the stiffness matrix in different degrees of freedom (DOFs) systems confirms the model number of the continuum structure system. The results show that the DOF identified by the modal perturbation method is related to the perturbation parameter, and the smaller the perturbation parameter is, 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 traditional Galerkin method is connected to the modal perturbation, making traditional discretization a unique case for the modal perturbation method. This method can significantly reduce the modal truncation error, which is of great significance to the dynamic analysis of engineering applications.

• Publisher: Springer Netherlands,Springer Nature B.V
• Subject: Automotive Engineering / Boundary conditions / Cables / Classical Mechanics / Control / Degrees of freedom / Discretization / Dynamical Systems / Engineering / Error analysis / Galerkin method / Mechanical Engineering / Modal analysis / Noise control / Original Paper / Parameters / Perturbation methods / Perturbation theory / Stiffness matrix / Truncation errors / Vibration / Vibration analysis