Sound insulation characteristics of functionally graded panels

An exact treatment based on the two-dimensional elasticity theory, is employed to investigate sound transmission through an arbitrarily thick isotropic functionally graded infinite plate subjected to an oblique plane acoustic incident wave. The mechanical properties of the graded plate are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the plate according to a power law distribution. The original inhomogeneous structure is approximated by a laminate model, for which the solution is expected to gradually approach the exact one as the number of layers increases. The T-matrix solution technique, which involves a system global transfer matrix formed as the product of the individual transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighboring layers along with the pertinent boundary conditions at the upper and lower interfaces of the plate with the surrounding acoustic fluid (air) are employed to solve for the unknown plane wave reflection and transmission coefficients. The analytical results are illustrated with numerical examples in which three frequently used metal-ceramic FGM panels with distinct compositional gradient profiles are subjected to plane incident waves at selected angles of incidence. Furthermore, a Gaussian weighting function for describing the directional distribution of incident energy is adopted for predicting the sound transmission loss along with the weighted sound reduction index, R. (as specified in ISO 717-1), of the FGM panels subjected to a perfectly diffuse sound field. Primary attention is focused on the effects of material compositional gradient profiles on the sound insulation characteristics of the panels. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.