Sound transmission prediction by 3 - D elasticity theory

theory, Applied Acoustics, Volume 70, Issue 5, May 2009, Pages 730-736, ISSN 0003-682X, http://dx.doi.org/10.1016/j.apacoust.2008.09.003. 1 Sound transmission prediction by 3-D elasticity theory Changzheng, Steven R. Nutt 1. Department of Chemical Engineering and Materials Science, University of Southern California, 3651 Watt Way, VHE 602, Los Angeles, CA 90089-0241, United States Abstract: The problem of sound transmission through layered panel structures is studied with the exact theory of three-dimensional (3-D) elasticity. The exact solution to the 3-D elasticity equations is obtained by the use of the Fourier spectral method. Based on this analytical solution, a transfer matrix is derived that relates the spectral displacements and stresses on the one surface of the panel to those on the opposite panel surface. The transfer matrix is then used to develop the analytical solutions for sound reflection and transmission coefficients. Explicit, concise expressions are obtained for the analytical solutions of the acoustic transmission and reflection coefficients under the general conditions of layered anisotropic panels. Examples are given for both single-layer and sandwich panels. Predictions on sound transmission from the 3-D elasticity theory are compared with available data from other methods, and the results are discussed.