Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder embedded in a finite prestrained compressible medium

Abstract

Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder contained in a finite prestrained infinite body is investigated within the scope of the piecewise-homogeneous body model by employing the three-dimensional linearized theory of elastic waves in a prestressed body. It is assumed that the materials of the cylinder and infinite body are compressible and that their elastic relations are described by a harmonic potential. Numerical results are presented and discussed for the case where the elastic constants of the cylinder are greater than those of the surrounding infinite body Keywords: axisymmetric wave propagation, finite prestrain, cylinder, wave dispersion 1. Introduction. An interesting and urgent problem concerned with nonlinear dynamic effects in elastic media is the elastodynamics of initially stressed bodies. It should be noted that initial stresses occur in structural elements during their manufacture and assembly, in the Earth's crust under the action of geostatic and geodynamic forces, in composite materials, etc.At present, the theory of elastodynamics utilized for initially stressed bodies is the linearized theory of elastodynamics for initially stressed bodies constructed using the linearization principle from the general nonlinear theory of elasticity or its simplified modifications. Under certain conditions, linearized equations make it possible to investigate all kinds of dynamic problems for initially stressed bodies. In this case, it is necessary to distinguish between so-called approximate and exact approaches. The approximate approaches are based on the Bernoulli, Kirchhoff-Love, and Timoshenko hypotheses and other methods of reducing three-dimensional (two-dimensional) problems to two-dimensional (one-dimensional) ones. It is evident that the approximate approaches simplify the mathematical solution procedure. In many cases, however, the results obtained by employing these approaches may not be acceptable in qualitative and quantitative sense. For example, the applied theories of rods, plates, and shells describe only a few propagating waves (modes). Moreover, within the framework of these approaches, the near-surface dynamic processes for initially stressed bodies cannot be described. Therefore, it is preferrable to use the exact approach, i.e., the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB) to solve dynamic problems for elastic bodies with initial stresses.Almost all investigations carried out by employing the TLTEWISB, (except [1-5, 17] and some references therein) refer to the influence of the initial stresses on the speed and dispersion of various types of waves (see, for example, [7-12, 16, 18] and the references therein and the reviews [6,13,14]). A systematic analysis of these investigations was given in the monographs [10][11][12][13]. It follows from these references that a considerable part refer to layered composite materials, and that concrete investigations on wave propagation in unidirectional f...

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Dispersion of guided waves in initially stressed layered plates

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