Influence of Prestresses on Quasi-Lamb Modes in Hydroelastic Waveguides

Abstract

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer that interacts with a half-space of a compressible ideal fluid and in a prestrained compressible elastic half-space that interacts with a layer of an ideal compressible fluid is studied. Use is made of the three-dimensional linearized equations of the theory of elasticity of finite deformations for the compressible elastic solid and the three-dimensional linearized Euler equations for the compressible ideal fluid. A problem statement and an approach based on the general solutions of the linearized equations for elastic solid and fluid are used. The dispersion equations that describe the propagation of quasi-Lamb waves in hydroelastic systems over a wide frequency range are derived. The effect of the initial stresses and the thicknesses of the elastic layer and liquid layer on the phase velocities of quasi-Lamb modes is analyzed. A criterion of the existence of quasi-Lamb waves in hydroelastic waveguides is proposed. The developed approach and the obtained results make it possible to establish the limits of applicability of the models of wave processes based on different theories of small initial deformations, as well on the classical theory of elasticity. The numerical results are presented in the form of graphs and are analyzed.