Dispersion relations of waves in a rod embedded in an elastic medium

Parnes, R.

doi:10.1016/0022-460x(81)90291-1

Cited by 8 publications

(11 citation statements)

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“…At the same time, it was noted in [15] that the results obtained can lead to the determination of the parameters of the system consisting of a cylinder (rod) and an embedded elastic medium under which a resonant response due to forced ground motion occur. Consequently, in the particular case where the initial strains are absent in the constituents of the considered system, the problem investigated in the present paper is a generalization of that investigated in [15], because in the present paper there is no restriction on the radial displacement of the cylinder and the equation of motion of the cylinder is also written for the radial and longitudinal displacements. We will turn again to [15] when we will discuss the numerical results.…”

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“…Note that the geometrical model used in the present paper was also used in [15] and some others listed therein in which the wave dispersion problem in the rod-embedded medium system was investigated. However, in [15] the cylinder (rod) was assumed to be radially rigid and the equation of motion of the cylinder was written for the longitudinal displacement only, but the equation of motion for the surrounding medium was stated by the exact equations of the linear theory of elastodynamics.…”

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confidence: 99%

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confidence: 99%

“…However, in [15] the cylinder (rod) was assumed to be radially rigid and the equation of motion of the cylinder was written for the longitudinal displacement only, but the equation of motion for the surrounding medium was stated by the exact equations of the linear theory of elastodynamics. At the same time, it was noted in [15] that the results obtained can lead to the determination of the parameters of the system consisting of a cylinder (rod) and an embedded elastic medium under which a resonant response due to forced ground motion occur. Consequently, in the particular case where the initial strains are absent in the constituents of the considered system, the problem investigated in the present paper is a generalization of that investigated in [15], because in the present paper there is no restriction on the radial displacement of the cylinder and the equation of motion of the cylinder is also written for the radial and longitudinal displacements.…”

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

Akbarov

Guliev²

2009

Int Appl Mech

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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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confidence: 99%

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