Strong fluid-structure coupling in a two-dimensional waveguide bounded by elastic plates

The typical model for compliant walls in a waveguide take them to be locally reacting. The corresponding boundary conditions for the transverse mode functions are Robin-type, which leads to an analysis that is a straightforward modification of the conventional analyses for rigid and pressure-release walls. The present investigation takes up the case where the walls are elastic plates, and the fluid loading is heavy. The consequence is strong coupling of the fluid and structural responses. The fact that the walls are not rigid obviates the possibility of a planar mode, so it is necessary to consider the transverse dependence of modes at any frequency. The analytically derived characteristic equation for the coupled response vividly displays the interaction of elastodynamics and acoustics. The eigenvalues are the transverse wavenumbers of the various modes at a specified frequency. They can be obtained through numerical methods, but implementing such a procedure to obtain dispersion curves of transverse wav...