The dispersion of the axisymmetric waves propagating in the pre-strained highly elastic plate under bi-lateral contact with a fluid

Abstract

The paper is concerned with the study of axisymmetric waves in an initially axisymmetric, finitely strained plate of highly compressible elastic material immersed in a fluid whose flow is confined by rigid walls. The fluid is modeled as compressible and inviscid and its flow is described by the linearized Euler equations. The motion of the plate is described by the so-called three-dimensional linearized equations and relations of elastic wave theory in initially stressed bodies. The dispersion equation in question is obtained and solved numerically. Concrete numerical results are obtained for the cases where the material of the plate is chosen as Soft-rubber and as Lucite, and water is chosen as the fluid. Based on these results, the influence of the initial axisymmetric finite strains in the plate on the dispersion curves at different fluid depths is analyzed. In particular, it is found that bilateral contact of the plate with the fluid leads to the appearance of asymmetric and symmetric quasi-Scholte waves, and that the propagation velocity of these waves increases (decreases) with the initial stretching (compression) of the plate.