Abstract Summary
An elastic layer submerged into a compressible fluid is considered. The results of the low-frequency asymptotic analysis are discussed. The adapted scaling corresponds to the so-called fluid-borne bending type wave. The approximate equations for the leading, first, second and third order are derived. The first order approximation corresponds to the traditional formulation for a thin Kirchhoff plate submerged into an incompressible fluid. It is remarkable that the plate inertia can be neglected at leading (zero) order. Higher-order corrections appear at second and third orders. In particular, the transverse shear deformation has to be taken into consideration at second order along with asymptotic corrections in impenetrability conditions. At the same time, the fluid compressibility has to be incorporated only at the third order. The associated approximate dispersion relations are also demonstrated. Numerical comparisons with the ‘exact’ dispersion relation are also presented.
