Finite element frequency-domain acoustic analysis of open-cell plastic foams

Abstract

A numerical method using an impulsive excitation to excite and collect the acoustic frequency response functions of corrugated open-cell plastic foams is presented in this study. In the study, the Biot's poroelasticity equations are first phrased in terms of solid and fluid displacements and then transformed into the Laplace domain. With the use of the general quadrilateral or triangular elements, the stiffness matrixes for the foams in the Laplace domain are then derived by the Galerkin-type finite element method. After solving and obtaining the dynamic stiffness transfer functions for the foams that are excited by an impulsive pressure on their upper surface, the Laplace transformed stiffness transfer functions are then transformed into frequency domain called dynamic stiffness functions, which can be further used in calculating the acoustic properties of foams. For validations, the proposed Laplace transformed finite element method (LTFEM) is first used to predict the acoustic properties of a planar and rigidly backed open-cell plastic foam with infinite width and permeable upper surface. Thereafter, the influences of the thickness, the width-to-thickness ratio, and the roller as well as fixed side edge restraints on the planar foams’ acoustic properties are examined. Furthermore, the use of LTFEM to predict the acoustic properties of corrugated foams are demonstrated and discussed. Without the use of the additional acoustic field that is required in the earlier studies, results predicted in the present study are in good agreement with either the exact solutions or the experimental data.