Optimal design of constrained plate damping layers using continuum finite elements

The aim of this paper is to determine the optimal shape of a viscoelastic damping layer within a constrained layer plate that is undergoing harmonic excitation at its midpoint. The optimization objective is to minimize the peak displacement of the plate at the first resonant frequency. The material loss factor is monitored as well to determine the improvement in performance between an initial, uniform layer shape and the optimized shape. A fine mesh validation model is also created to verify the optimized shape. As manufacturing costs would be reduced for a uniform shape, the optimized shape is used as a guide to create a new, uniform damping layer, which is compared with the previous results. Several geometries and boundary conditions are examined. The ABAQUS finite element code is used to model the structures. Elasticity theory based continuum elements are used so that all stress effects are taken into account in the models. The optimization code uses a Sequential Quadratic Programming algorithm. Results show significant improvement in the loss factor for optimized shapes. For most models, the optimal shape tends towards being a thin, uniform damping layer, which indicates shearing effects dominate in producing the optimal shape. In one case, however, it appears that some normal stress effects also have some influence.