An analytical study of sound transmission through unbounded panels of functionally gradedmaterials

Abstract

The problem of sound transmission and reflection from unbounded panels of functionally graded materials is studied using an analytical approach. By means of matrix manipulation and Fourier component analysis, the three-dimensional (3-D) governing equations of elastodynamics are converted into a system of ordinary differential equations with variable coefficients in the frequency and wavenumber domain. Integration of the ordinary differential equation system across the panel thickness leads to a closed-form solution for the transfer matrix. Analytical expressions are then obtained for sound reflection and transmission coefficients for panels of functionally graded materials. The present model is used to predict sound transmission losses for various panel examples. The results compare well with published data from other methods, thereby validating the accuracy of the formulation developed in this study.