Analyzing coupled wave dynamics in elastic waveguides with height variations: Modeling and insights

This study employs a combined mode matching technique and Galerkin approach to analyze fluid–structure coupled wave interactions a an elastic plate bounded waveguide containing height variation. The dynamical response of plate coupled with the acoustics govern higher order derivative involving boundary value problem. The associated eigenfunctions are non-orthogonal and the system underlies non-Sturm–Liouville system. The Galerkin approach is adopted to model the vibrational response of an elastic plate, while the continuity conditions at the fluid–structure interface are applied to get linear algebraic systems which are truncated and solved numerically. Results confirm power conservation, with reflected and transmitted powers summing to unity across all frequencies. For structure-borne modes, transmission dominates at lower frequencies but fluctuates near cut-on frequencies, while reflection dominates fluid-borne modes due to impedance mismatch. The model's accuracy is validated by adherence to power conservation and agreement with the tailored-Galerkin method, establishing a reliable framework for analyzing wave energy propagation in coupled systems.