Asymptotic models for a fluid-loaded elastic layer #

Sheeru Shamsi, Julius Kaplunov, Ludmila Prikazchikova

14:10 Tuesday in 2Q48.

Part of the Self-propulsion and fluid-body interactions session.

Abstract #

The classical problem for an elastic layer immersed into a compressible fluid is revisited starting from the general asymptotic perspective. The results of the low-frequency analysis are discussed. The adapted scaling corresponds to the so-called fluid-borne bending wave. Approximate equations are derived at various orders, up to the third one. The first order approximation corresponds to the traditional formulation for a thin Kirchhoff plate submerged into an incompressible fluid. It is worth noting that the plate inertia can be neglected at leading (zero) order. Various higher-order corrections to the aforementioned setup based on Kirchhoff theory appear at second and third orders. Specifically, the transverse shear deformation has to be taken into consideration at second order along with an appropriate asymptotic correction in the impenetrability condition, whereas the plate rotatory inertia and the fluid compressibility have to be incorporated only at the third order. Finally, the associated approximate dispersion relations are compared with the straightforward asymptotic expansion of the ‘exact’ dispersion relation.