A simplified numerical model for a plate backed by a thin foam layer in the low frequency range

Abstract This paper presents a simplified numerical model based on a hierarchical trigonometric functions set to predict the low frequency vibration behaviour of a plate backed by a thin foam layer. The base metal plate is excited in bending vibrations with a point load and can have various boundary conditions. The poro-elastic layer is modelled using the mixed displacement–pressure formulation of the Biot–Allard's theory. The base plate and the solid phase of the porous medium are described as an equivalent visco-elastic plate. The poro-elastic's fluid phase is coupled with the equivalent plate displacements. Comparisons with complete three-dimensional poro-elastic finite element solutions and experimental data are presented to define a domain of validation for the proposed simplified model.

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