Influence of Prestresses on Quasi-Lamb Modes in Hydroelastic Waveguides
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International Applied Mechanics, Vol. 56, No. 1, January, 2020
INFLUENCE OF PRESTRESSES ON QUASI-LAMB MODES IN HYDROELASTIC WAVEGUIDES
A. N. Guz and A. M. Bagno
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. Keywords: compressible elastic layer, compressible elastic half-space, half-space of compressible ideal fluid, layer of compressible ideal fluid, initial stresses, quasi-Lamb waves Introduction. The laws of propagation of surface acoustic waves are widely used in seismology, seismic prospecting, hydroacoustics, and ultrasonic nondestructive methods [1, 16, 17, 21, 22, 27–31, 33–35]. The wide practical use of surface waves necessitates a better description of the properties of real elastic materials. Such factors include prestresses. Induced purposefully or remaining after the manufacturing process, such prestresses have a strong effect on wave processes. Relevant problems and results obtained with allowance for prestresses are discussed in [3, 4, 6–8, 10–12, 14, 15, 18, 19, 23–26, 32]. To study the propagation of quasi-Lamb waves in hydroelastic waveguides consisting of a liquid half-space and an elastic layer or an elastic half-space and a liquid layer, we will use prestressed body model and compressible ideal fluid model and the three-dimensional linearized Euler equations for the fluid, which is assumed to be at rest, and the three-dimensional linearized equations of finite deformations for the elastic body. We will use a problem formulation and a method that are based on the general solutions of the equations of motion of a compressible ideal fluid and a prestressed compressible elastic body proposed in [3–9, 18–20]. 1. Problem Statement. Basic Equations. We will consider such dynamic processes in the hydroelastic system that the additional strai
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