Topology optimization of unconstrained damping treatments for plates

A finite element model for composite plates consisting of an elastic isotropic base layer covered with viscoelastic treatment is presented. The composite plate undergoes bending vibrations in the lateral direction. In contrast to many previous publications, the viscoelastic treatment is not constrained from the top in order to better simulate real cases. The objective is to find the optimum distribution of viscoelastic treatment which maximizes the modal damping ratio (MDR) for a certain volume of treatment. Topology optimization is performed with two strategies: optimizing the whole domain of viscoelastic treatment and optimizing a unit cell of the periodic treatment. Numerical examples show that the presented model is able to increase the MDR by an order of magnitude compared to plain treatments.