On the condensation of thick symmetric multilayer panels including dilatational motion

Condensed models are used to describe the dynamic behaviour of a multilayer structure by means of an equivalent homogeneous layer defined by intrinsic properties. Existing condensed models mainly describe the bending, membrane and shearing motions of the multilayer plate and neglect its dilatational motion. As a result, the transmission loss across the multilayer may be underestimated if the layers are soft and thick. In this paper, a condensed model of physically symmetric multilayer is developed. The antisymmetric and symmetric motions of the structure are described separately by means of two equivalent admittances. These admittances depend on three intrinsic properties: a dynamic bending stiffness and two dynamic mass densities. The condensed model is validated comparing transmission loss computations with the Transfer Matrix Method for multilayers with elastic or poroelastic cores

On the accuracy limits of plate theories for vibro-acoustic predictions

Several vibro-acoustic models for either single wall or multi-layer constructions are based on classical plate and first order shear deformation theories. The equivalent or condensed plate models employ the thin plate model to extract the dynamic mechanical properties of the multi-layer system considering only flexural and shear motions for the structure under investigation. Since these plate models do not account for the compressional or symmetric motion of the structure, both thin and thick plate theories encounter limitations for mid to high frequency predictions depending on the structures considered. In this work, analytical expressions for the frequency limit of thin and thick plate theories are derived for an elastic layer of isotropic material from the analyses of wavenumbers and admittances. Additionally, refined expressions for coincidence and critical frequencies are presented. Validation of these frequency limits are made by comparing the transmission loss (TL) obtained from both plate theories with the TL computed through the theory of elasticity for a range of thin/thick and soft/stiff materials

A simple equivalent plate model for dynamic bending stiffness of three-layer sandwich panels with shearing core

Equivalent or condensed plate models are being used in various industries to reduce the computation time in finite element modelling. Out of the available equivalent plate models, the model developed by J.L.Guyader in 1978 exhibits high agreement with Lamb wave theory but it requires some time for implementation. Therefore, in this paper, a simple model is proposed to quickly compute the dynamic equivalent parameters of a three-layer sandwich panel. Although the model is formulated from only four parameters, which could be easily computed via the asymptotic and transition behaviours of the sandwich panel, it is shown to be able to capture the equivalent dynamic response for the entire frequency range