On the extension of the mode-matching procedure for modeling a wave-bearing cavity

The present work highlights the scattering of fluid–structure coupled waves through a wave-bearing cavity in rigid waveguide. The cavity is filled with compressible fluid and comprises horizontal as well as vertical elastic boundaries. The mode-matching technique is extended by tailored-Galerkin and Galerkin procedures to incorporate the vibrational response of the vertical elastic components having different sets of edge conditions. It is found that in mode-matching tailored-Galerkin (MMTG) method, a unique general description of the displacement of vertical elastic component can deal with a variety of edge conditions, whereas the mode-matching Galerkin (MMG) technique relies upon the orthogonal basis a priori whose description varies by changing the edge conditions of vertical elastic components. Accordingly, for some sets of edge conditions the eigenvalues cannot be expressed explicitly and must be found numerically. The eigenmodes of the cavity region satisfy the generalized orthogonal conditions which ensure the point-wise convergence of MMTG and MMG approaches. Moreover, the truncated MMTG and MMG solutions reconstruct the matching conditions as well as satisfying the conserved power identity. It confirms the accuracy of performed algebra and retained solutions. From the numerical results it is found that by varying the conditions on the edges of bridging elastic components, the stopbands can be enhanced and shifted as well as broadened over the certain frequency regimes.