Propagation of Lamb waves in a pre-stained compressible elastic layer interaction with a layer of an ideal compressible fluid
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 78, Issue 2
Abstract
The problem of acoustic waves propagation in a pre-strained compressible elastic layer that interacts with a layer of ideal compressible fluid is considered. The study is carried out on the basis of the three-dimensional linearized equations of theory of elasticity finite deformations for elastic layer and of three-dimensional linearized Euler equations for ideal compressible fluid. The problem statement and the approach are based on the use of representations general solutions of the linearized equations for elastic and fluid layers. A dispersion equation is given which describes the propagation of Lamb waves in hydroelastic system within a wide frequency range. The characteristic equation is solved numerically and dispersion curves are constructed for a wide range of frequencies in the case of a thin fluid layer. The dependencies of phase velocities of Lamb modes on the thickness of elastic layer are given in absence of the interaction with the fluid. For hydroelastic waveguide the dependencies of phase velocities of Lamb waves on the thickness of elastic layer are presented. The dependencies of the relative change of the magnitudes of the phase velocities of Lamb modes on the thickness of the elastic layer are given. The influence of the initial deformation as well the thicknesses of the layers of the elastic body and fluid on the phase velocities of Lamb waves are analyzed. For hydroelastic system with increasing of the thickness elastic layer the velocity of first mode tends to the Stoneley wave velocity and velocity of second mode tends to the Rayleigh wave velocity is shown. The phase velocities of all higher modes tends to the velocity of shear waves in the elastic body. It is determined that the initial tension of the elastic layer leads to the increasing the phase velocities of first and second modes. It is determined that for all the modes, beginning with the third, there exist thicknesses the elastic layer and certain frequencies, at which the initial tension of the elastic layer has no effect on their phase velocities. It is shown, that in the case of a thin fluid layer, every mode, beginning with the fifth, has three such frequencies. It is found also that for certain frequency ranges the initial tension of the elastic layer can lead both to increasing and to decreasing of the phase velocities of Lamb modes.
Authors and Affiliations
Oleksandr Myhailovych Bahno,
Keywords
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