Linear optimization method for layout of unconstrained damping materials with negligible effect on eigenmode

Abstract

Damping materials are sometimes employed to reduce vibrations. In vehicles, weight reduction and a high damping effect are required to reduce environmental impacts. Many studies have been conducted to determine an optimal topological layout with a high damping effect under a limited amount of damping material. However, many methods require finite element analysis to be performed several times owing to the nonlinearity of the objective function. In addition, if there exists a problem with the optimal shape, it is necessary to use a filter or change the penalty parameter and perform optimization again. Therefore, this study proposes a method to linearize optimization problems to reduce the number of finite element analysis procedures required, under the assumption that the layout of the damping material does not affect the eigenmode when the base structure is damped via unconstrained layer damping treatment. Several numerical examples are provided to demonstrate the effectiveness of proposed method. The verification results show that the optimal layout and loss factor of the proposed and conventional methods were similar for a large-scale finite element analysis model. Moreover, this study proposes an optimality evaluation method using the modal assurance criterion. As long as the assumption holds true, the proposed method can significantly improve the time efficiency when repeating optimization under different conditions.

Keywords

• topology optimization
• damping material
• loss factor
• modal strain energy method
• finite element method