A new analytical approach for the modeling of sound propagation in a stratified medium

Abstract

• An analytical method is proposed to describe sound propagation in stratified mediums. • The proposed method is easy to implement. • Both the acoustical indicators and field variables are found analytically. • The proposed method combines the advantages of other, existing methods in a single one. • The proposed method is verified by analyzing three different examples. In this article, the operator decoupling technique, which has been used in Green's function solution methods of partial differential equations, is adapted to provide a solution methodology for sound propagation in a stratified medium that does not require modification for different media. The developed technique can be employed to solve wave equations in different media including Biot equations, so it can be used for the analytical study of sound propagation in a stratified medium. The method is named the operator decoupling method (ODM) and as an example of implementing it, the normal sound propagation in a laterally infinite porous layer, which is analyzed by one-dimensional Biot equations, is explored. Then, a simple expression for the surface impedance is derived by satisfying the boundary conditions in a different manner. In addition, by using the operator decoupling method, the oblique incidence of a sound wave to a laterally infinite porous layer whose governing equations are two-dimensional Biot equations are investigated. Additionally, the analytical study of the oblique sound incidence to a laterally infinite medium with four layers is completed. Finally, the advantages of the method are compared with the other analytical solution methods. The operator decoupling method encompasses the capabilities of the other methods in a single method. Furthermore, it is easy to implement, and readily gives a detailed description of sound propagation in stratified media.