Application of the matrix element method: A mode-matching approach for wave-bearing cavities in complex media

The present study employs an analytical scheme useful for investigating the reflection, transmission, and absorption of fluid–structure coupled waves in a dissipative device with flexible boundaries. The method is based on contour integration, which avoids the cumbersome root-finding processes for complex dispersion relations, thereby eliminating the error of missing roots. The procedure involves applying the mode matching technique along with the generalized orthogonality relation to transform the differential system into linear algebraic systems. The matrix elements involve unknown wavenumbers in the finite chamber with wave-bearing boundaries and porous material filling the cavity region, separated from air by a screen. Due to the absorbing properties of the medium, the wavenumbers are complex, and the matrix elements are reformulated using contour integration without needing explicit information about the wavenumbers. It is found that by changing the properties of absorbent material and membrane parameters the attenuation behavior can be optimized.