Dynamic analysis of plates with thick unconstrained layer damping

Abstract

In this work the dynamic behaviour of free layer damping plates with thick unconstrained viscoelastic layer is analysed. With this aim, the Kirchhoff–Love thin plate formulation is adapted to take shear stiffness into account by using a frequency dependent equivalent flexural stiffness.To check the validity of the proposed formulation, it is implemented in a finite element model and compared to both the Oberst model and a reference 3D solid model in terms of eigenvalues and dynamic response across a wide range of boundary conditions – clamped in all edges, free, simply supported at edges, clamped in a single edge and simply supported at corners. In all the cases the material of the viscoelastic layer presents fractional damping, its modulus thus being complex and frequency dependent.The results show that the proposed model is in good agreement with the 3D model and that it provides better accuracy than the Oberst model, specially as the thickness of the damping layer, and consequently the effect of the shear, increases. Hence, the need of developing a 3D solid model can be avoided as well as the storage and computation time problems it arises, that are specially critical in industrial practical applications.