Energy distribution analysis for low damping systems consisting of multiple subsystems based on the kernel Compliance Analysis (kCA) method extended with the Autonne-Takagi factorization

Abstract

In the development of mechanical structures, it has been required for a long time to establish a modular design method of resonance by controlling the vibration coupling among subsystems. From the analytical perspective of coupled vibration among modules, the kernel compliance analysis (kCA) method exists. The kCA method has the advantage of being able to analyze vibration coupling when modules, which will be called subsystems below, are connected with multiple degrees of freedom. However, the kCA method is not directly applicable to damped systems. This is because the kernel compliance matrix, which is the core of the kCA method, of the damped system is a complex symmetric matrix. To avoid the difficulty, in this paper, the Autonne-Takagi factorization is employed instead of the general eigenvalue decomposition to decompose the complex symmetric matrix. Furthermore, the old-type frequency-based substructuring was introduced so that vibration coupling analysis can be performed among multi-subsystems. With these extensions of the kCA, a method to analyze the energy distribution ratio between subsystems was derived. By using the analysis results, it is possible to shift the resonance frequency and determine the appropriate placement of damping materials.

Keywords

• vibration coupling
• modular design
• modal analysis
• substructuring
• autonne-takagi factorization
• component-based tpa