Optimal design of unconstrained damping material on a thin panel by using topology optimization

Damping material is usually applied on the steel panel of a vehicle to reduce vibration level. On the other hand, the weight reduction is also required to improve fuel consumption. Therefore, modal loss factors induced by damping material on the steel panel of a vehicle body structure need to be maximized with a given volume. In this paper we propose a practical design method to maximize modal loss factors by optimizing the material distribution of damping material under a prescribed volume constraint. The modal loss factor of an eigensmode can be written as the ratio of the strain energy stored in the damping material over the total strain energy in the system under consideration. In the proposed method, we assume the eigenvectors are almost the same as the eigenvectors when damping material is removed. The modal loss factor can then be expressed by using a corresponding eigenvalue where the mass density of the damping material is ignored whereas the stiffness is taken into account. Several numerical examples are provided to show the optimal distributions of the damping material by using a flat panel. Damping material is distributed in the domain where the strain energy is stored, which agrees well with our experiences. Moreover, by applying a sensitivity filter that utilizes a weighted average of design sensitivities over local area, damping material can be distributed collectively in a single domain to meet practical requirements for manufacturing,