Abstract
A generalized transmission and reflection matrix (GTRM) method for determining the acoustic response of multilayered media is developed in this paper. The principle of the method is to decipher the wave vectors by constructing generalized T/R matrices and recursive formulas. The generalized T/R matrices are introduced to account for the contributions of multiple reflection and transmission in a global manner. Three types of interface T/R matrices are developed to accommodate the coupling between any type of physical medium. This method is not only stable for high-frequency and large thickness cases by excluding the growing terms but also explicitly exhibits the physical mechanism of wave propagation. Acoustic response in both frequency and time domains can be solved by the method. Moreover, the method has a simple framework, and it is easy to be implemented in numerical tools. The method is successfully validated by several typical acoustic problems, including poroelastic medium immersed in fluid, aluminum-glass-aluminum immersed in fluid, and poroelastic sediment sandwiched between water and bedrock. In fact, the present method can be extended to any physical problem of a multilayered structure. When the wave frequency is high or the layered media is greatly thick or the material combination is highly complex, the advantage of the GTRM method is more conspicuous.
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