Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Chattopadhyay, Amares; Gupta, Shishir; Kumari, Pato; Sharma, V. K.

doi:10.2478/s11600-011-0059-4

Cited by 44 publications

(17 citation statements)

References 20 publications

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“…Now, the purpose is to find the expression for scalar potentialˆ1.x/. Equation (11) suggests that the special solution of it is given bŷ…”

Section: Dispersion Relationmentioning

confidence: 99%

“…Some other advances in the concerned field include Chattopadhyay et al. , which studied the propagation behavior of SH‐wave in anisotropic as well as heterogeneous layers viz. irregular magnetoelastic monoclinic layer, viscoelastic layer, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…where 13 D C 44 @w 1 @x C e 15 @ 1 @x , 23 D C 44 @w 1 @y C e 15 @ 1 @y , D 1 D e 15 @w 1 @x " 11 @ 1 @x , D 2 D e 15 @w 1 @y " 11 @ 1 @y , 11 D 0, 22 D 0, 33 D 0, 12 D 0 and D 3 D 0.…”

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confidence: 99%

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Green's function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source

Singh

Das

Mistri

et al. 2017

Math. Meth. Appl. Sci.

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Green's function technique serves as a powerful tool to find the particle displacements due to SH‐wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH‐wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT‐5H ceramics, Barium titanate (BaTiO3) ceramics, Silicon dioxide (SiO2) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe2O4), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well‐known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.

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“…Now, the purpose is to find the expression for scalar potentialˆ1.x/. Equation (11) suggests that the special solution of it is given bŷ…”

Section: Dispersion Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Green's function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source

Singh

Das

Mistri

et al. 2017

Math. Meth. Appl. Sci.

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“…Chattopadhyay and Singh (2011) investigates the possibility of SH-wave propagation due to a point source in a magnetoelastic monoclinic layer overlying a monoclinic half-space with the aid of Green’s function. Some more disquisition on this ground may be referred from Chattopadhyay et al (2012) and Chattopadhyay and Kar (1981). In recent years, the urge of development of materials for specific functions, their practical applications and research on them has become the cornerstone of modern material science.…”

Section: Introductionmentioning

confidence: 99%

On point source influencing Love-type wave propagation in a functionally graded piezoelectric composite structure: A Green’s function approach

Singh

Das

Ray

et al. 2018

Journal of Intelligent Material Systems and Structures

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Green’s function plays an important role in solving the problems concerning point action or impulse responsible for wave motions in materials. Prime objective of the this article is to investigate the propagation behaviour of Love-type wave influenced by a point source in a composite structure comprising a functionally graded piezoelectric material layer lying over a functionally graded fibre-reinforced material half-space. Green’s function technique is adopted in order to obtain the dispersion equation, which is further reduced to the classical Love wave equation as a particular case of the problem. The effect of increasing thickness of functionally graded piezoelectric material layer on the circular frequency and wave number is unravelled and depicted graphically. Moreover, influence of heterogeneity, piezoelectricity and dielectric constant associated with functionally graded piezoelectric material layer and effect of heterogeneity parameter and corresponding magnification factor concerned with functional gradedness of functionally graded fibre-reinforced material half-space have been reported through numerical computation and graphical delineation. For sake of computation, numerical data of PZT-5H ceramics for the functionally graded piezoelectric material layer and carbon-fibre epoxy-resin for functionally graded fibre-reinforced material half-space have been considered. Comparative study is performed to elucidate the effect of presence and absence of reinforcement in functionally graded half-space on the phase velocity of Love-type wave propagating in composite structure.

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“…Ghorai et al [11] considered the Love waves in a fluidsaturated porous layer under a rigid boundary and lying over an elastic half-space under gravity. Chattopadhyay et al [12] concluded the effect of point source and heterogeneity on the propagation of SH waves in a viscoelastic layer over a viscoelastic half-space. Gupta et al [13] established the possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

Vaishnav

Kundu

Gupta

et al. 2016

Mathematical Problems in Engineering

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Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

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Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Cited by 44 publications

References 20 publications

Green's function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source

Green's function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source

On point source influencing Love-type wave propagation in a functionally graded piezoelectric composite structure: A Green’s function approach

Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

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