A method for designing desired eigenmode through changing internal force between subsystems

Abstract

Vibration related to several performances such as durability and noise performance is the one of the important performances on automotive product. The technique of reshaping eigenmode is a practical way to improve the performance on the product design phase. However, it is difficult to design desired mode shapes efficiently because the mode shapes are determined by the balance between mass and stiffness distribution on a whole structure. In this paper, a method for designing desired eigenmodes through changing internal forces between subsystems is proposed. Firstly, according to frequency based substructuring, the dynamic stiffness matrix of a whole structure could be divided into the matrices of subsystems and internal forces occurred from coupling components. Then, on a specified eigenfrequency as a design target, it can be derived that the mode shapes are controllable by changing to desired internal forces. Secondly, desired internal forces are calculated through designing spring constants between subsystems based on the kernel compliance analysis method which can analyze vibration when several subsystems are coupled on multiple degrees of freedom. Furthermore, when desired internal forces are calculated, a method to change a component of the internal force vector one by one is also proposed. This method can visualize the range which can be designed all spring constants as positive values in advance and can avoid selecting negative spring constants. Finally, this proposed method is applied to a numerical case study to reduce vibration responses with allocating modal strain energy to subsystems through reshaping an eigenmode.

Keywords

• structural modification
• modal analysis
• substructuring
• eigenmode
• vibration coupling