An efficient tool for predicting the structural acoustic and vibration response of sandwich plates in light or heavy fluid

Abstract The vibroacoustics of a plate covered by a free or a constrained viscoelastic layer is analyzed in this article. A variational model, solved by the Rayleigh–Ritz method, is proposed for the case of a rectangular, baffled, simply supported multilayered plate immersed either in a light fluid or in a heavy fluid. In order to simplify the theoretical formulation, approximate assumptions are made regarding the calculation of the strain energy of the plate. These assumptions are inspired from Ungar's work on viscoelastically damped beam. They allow the equation of motion of the plate to be expressed in terms of one unknown displacement while most of the classical variational models use at least five unknown displacements. Hence, the size of the mass matrix and of the stiffness matrix are reduced and the computing time is decreased. The radiation of sound from the plate is rigorously calculated with the method of Sandman and Nelisse which makes high frequencies attainable without convergence problems. Theoretical validations of the proposed model are made using a well-known multilayered plate model. In addition, very precise experiment set up allows the measurement of the vibration response of two sandwich plates that reveal the precision of the proposed model and present the type of damping achievable with commercially available viscoelastic material.