In-plane surface wave in a classical elastic half-space covered by a surface layer with microstructure

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

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Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space

Mechanics Research Communications ◽

10.1016/j.mechrescom.2018.07.006 ◽

2018 ◽

Vol 92 ◽

pp. 49-53 ◽

Cited By ~ 2

Author(s):

L.A. Khajiyeva ◽

D.A. Prikazchikov ◽

L.A. Prikazchikova

Keyword(s):

Surface Wave ◽

Half Space ◽

Elastic Half Space ◽

Elliptic Model

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Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

Journal of Vibration and Control ◽

10.1177/1077546320909972 ◽

2020 ◽

Vol 26 (21-22) ◽

pp. 1980-1987

Author(s):

Baljeet Singh ◽

Baljinder Kaur

Keyword(s):

Surface Wave ◽

Boundary Conditions ◽

Rayleigh Wave ◽

Surface Waves ◽

Half Space ◽

Rotation Rate ◽

Secular Equation ◽

Elastic Half Space ◽

Impedance Boundary ◽

Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

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Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

Acta Mechanica et Automatica ◽

10.2478/ama-2021-0005 ◽

2021 ◽

Vol 15 (1) ◽

pp. 30-36

Author(s):

Askar Kudaibergenov ◽

Askat Kudaibergenov ◽

Danila Prikazchikov

Keyword(s):

Surface Wave ◽

Half Space ◽

Moving Load ◽

Elastic Half Space ◽

Elementary Functions ◽

Material Models ◽

Line Load ◽

Transient Regimes ◽

Surface Wave Field ◽

Asymptotic Formulation

Abstract The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

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Reduced model for the surface dynamics of a generally anisotropic elastic half-space

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0590 ◽

2020 ◽

Vol 476 (2234) ◽

pp. 20190590 ◽

Cited By ~ 4

Author(s):

Yibin Fu ◽

Julius Kaplunov ◽

Danila Prikazchikov

Keyword(s):

Surface Wave ◽

Half Space ◽

Travelling Waves ◽

Moving Load ◽

Multiple Scale ◽

Elastic Half Space ◽

Surface Dynamics ◽

Near Surface ◽

Surface Resonance ◽

Anisotropic Elastic

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v − v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

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An Efficient Semi-Analytical Method to Compute Displacements and Stresses in an Elastic Half-Space with a Hemispherical Pit

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m544 ◽

2015 ◽

Vol 7 (3) ◽

pp. 295-322 ◽

Cited By ~ 2

Author(s):

Valeria Boccardo ◽

Eduardo Godoy ◽

Mario Durán

Keyword(s):

Analytical Solution ◽

Boundary Conditions ◽

Half Space ◽

Plane Surface ◽

Elastic Half Space ◽

Numerical Results ◽

Quadratic Functional ◽

Infinite Plane ◽

Equilibrium Equations ◽

Finite Element Software

AbstractThis paper presents an efficient method to calculate the displacement and stress fields in an isotropic elastic half-space having a hemispherical pit and being subject to gravity. The method is semi-analytical and takes advantage of the axisymmetry of the problem. The Boussinesq potentials are used to obtain an analytical solution in series form, which satisfies the equilibrium equations of elastostatics, traction-free boundary conditions on the infinite plane surface and decaying conditions at infinity. The boundary conditions on the free surface of the pit are then imposed numerically, by minimising a quadratic functional of surface elastic energy. The minimisation yields a symmetric and positive definite linear system of equations for the coefficients of the series, whose particular block structure allows its solution in an efficient and robust way. The convergence of the series is verified and the obtained semi-analytical solution is then evaluated, providing numerical results. The method is validated by comparing the semi-analytical solution with the numerical results obtained using a commercial finite element software.

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The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

Bulletin of the Seismological Society of America ◽

10.1785/bssa0520010027 ◽

1962 ◽

Vol 52 (1) ◽

pp. 27-36

Author(s):

J. T. Cherry

Keyword(s):

Surface Wave ◽

Half Space ◽

Rayleigh Waves ◽

Poisson’S Ratio ◽

Horizontal Stress ◽

Elastic Half Space ◽

The Body ◽

Body Waves ◽

Poisson's Ratio ◽

A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

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