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1
Content available Rayleigh wave propagation in isotropic sandy layer sliding over isotropic sandy semi-infinite medium with sliding contact
Madan Dinesh Kumar, Kumar Naveen, Rani Annu
International Journal of Applied Mechanics and Engineering
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2023
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Vol. 28, no. 1
58--70
EN
The present study aims to investigate Rayleigh wave propagation in an isotropic sandy layer overlying an isotropic sandy semi-infinite medium, with interface considered to be imperfect (slide contact and dislocation like model). Expressions for displacement components are obtained using the variable separation method. The dispersion frequency equation for the Rayleigh wave propagating in sandy media is derived using suitable boundary conditions. Particular cases, such as when the interface is in smooth contact and when sandy media are replaced by elastic media, are also discussed. Using MATLAB software, the effects of the imperfectness parameter (slide contact and dislocation like model) and sandy parameter on the Rayleigh waves’ phase velocity are investigated and compared with the already obtained results of the dislocation like model. The present study may find useful applications in geophysics, civil engineering and soil mechanics.
2
Content available Wave propagation in nonlocal orthotropic micropolar elastic solids
Tung D. X.
Archives of Mechanics
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2021
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Vol. 73, nr 3
237--251
EN
The presented paper is concerned with the propagation of Rayleigh waves in an orthotropic nonlocal micropolar elastic half-space. The main aim of the paper is to derive dispersion equations of Rayleigh wave as well as Stroh formalism for the orthotropic nonlocal micropolar medium. Based on the obtained dispersion equation, the effect of material, nonlocality parameter on the Rayleigh wave propagation is considered through some numerical examples.
3
Content available The effect of viscosity and heterogeneity on propagation of G-type waves
Gupta S., Smita
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 2
253--260
EN
Earthquakes yield motions of massive rock layers accompanied by vibrations which travel in waves. This paper analyses the possibility of G-type wave propagation along the plane surface at the interface of two different media which is assumed to be heterogeneous and viscoelastic. The upper layer is considered to be viscoelastic and the lower half space is considered to be an initially stressed heterogeneous half space. The dispersion equation, as well as the phase and group velocities, is obtained in closed form. The dispersion equation agrees with the classical Love type wave. The effects of the nonhomogeneity of the parameters and the initial stress on the phase and group velocities are expressed by means of a graph.
4
Content available remote Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media
Gupta S., Ahmed M., Pramanik A.
Acta Geophysica
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2017
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Vol. 65, no. 1
139--149
EN
The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.
5
Controllability of mixed Volterra–Fredholm type integrodifferential third order dispersion equations
Kumar M., Sukavanam N.
Journal of Applied Analysis
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2015
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Vol. 21, nr 1
1--7
EN
In this paper, we establish a result concerning the controllability of a mixed Volterra–Fredholm type integrodifferential third order dispersion equation. The result is obtained by using the theory of strongly continuous semigroups and the Banach fixed point theorem.
6
Content available Effects of warmness and spatial nonuniformity of plasma waveguide on periodic absolute parametric instability
Zaki N. G., Bekheit A. H.
Nukleonika
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2011
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Vol. 56, No. 4
305-309
EN
The periodic absolute parametric instability (API) of the low-frequency oscillations excited by a monochromatic pumping field of an arbitrary amplitude in a warm 1-D (one-dimensional) nonuniform magnetoactive plasma is investigated. The separation method can be used for solving the two-fluid plasma equations describing the system. By applying this method we were able to determine the frequencies and growth rates of unstable modes and the self-consistent electric field. Plasma electrons are considered to have a thermal velocity. Different solutions for the spatial equation can be obtained the following cases: A) API in a uniform plasma, B) API in a nonuniform plasma. The latter has been studied here for two cases: B.1) the exact harmonic oscillator and B.2) the bounded harmonic oscillator (a bounded plasma). An increment has been found in the build-up of the oscillations, and it has been shown that the spatial nonuniformity of the plasma exerts the stabilizing effect on the parametric instability. A reduced growth rate of API in the warm plasma, in comparison to the cold plasma, is reported. It has also been found that the warmness of the plasma has no effect on the solution of the space part of the problem (only through the separation constant).
7
Content available remote A note on solution of the dispersion equation for small-amplitude internal waves
Das D., Mandal B. N.
Archives of Mechanics
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2005
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Vol. 57, nr 6
493--501
EN
This note is concerned with establishing the nature of the roots of a dispersion equation, which arises in the study of small-amplitude internal waves in two immiscible superposed fluids, wherein the upper fluid has a free surface and the lower fluid has a rigid bottom. All roots of this dispersion equation are found by considering graphs of appropriate functions, and the fact that these are the only possible roots, has been established by Rouche's theorem of complex variable theory.
8
Surface waves in a heterogeneous layer over a liquid saturated poro-elastic solid half space
Pal P.
Acta Geophysica Polonica
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2000
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Vol. 48, nr 2
195-205
EN
Rayleigh waves in a heterogeneous layer over a saturated half space are investigated under plane strain conditions. The dispersion equation is derived using the methods for propagation of free waves in layered media. The effect of heterogeneity on phase velocity is studied by taking different numerical values of heterogeneity factor and the result is shown graphically.
9
Content available remote Istnienie i jednoznaczność rozwiązania problemu propagacji fali powierzchniowej w niejednorodnej izotropowej półprzestrzeni sprężystej
Klecha T.
Prace Instytutu Podstawowych Problemów Techniki PAN
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1998
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nr 11
3-11
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