Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

Singh, Abhishek Kumar; Das, Amrita; Lakshman, Anirban; Chattopadhyay, Amares

doi:10.1515/acgeo-2016-0060

Cited by 11 publications

(4 citation statements)

References 26 publications

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“…Assume that the plate thickness is measured along the 𝑥 3 axis, with the plate's mid-plane lying on the 𝑥 1 𝑥 2 plane. The stress-strain relation for MEE fluid-saturated medium can be written as [50][51][52][53][54][55][56][57][58][59][60][61],…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Assume that the plate thickness is measured along the

x_3

axis, with the plate's mid‐plane lying on the

x_1x_2

plane. The stress–strain relation for MEE fluid‐saturated medium can be written as [50–61],

\begin{matrix} (}, \begin{matrix} σ_{11} = S_{11} ε_{11} + S_{12} ε_{22} + S_{13} ε_{33} - e_{31} E_{3} - q_{31} H_{3} + M_{1} ζ, \\ σ_{22} = S_{12} ε_{11} + S_{11} ε_{22} + S_{13} ε_{33} - e_{31} E_{3} - q_{31} H_{3} + M_{1} ζ, \\ σ_{33} = S_{13} ε_{11} + S_{13} ε_{22} + S_{33} ε_{33} - e_{33} E_{3} - q_{33} H_{3} + M_{3} ζ, \\ σ_{23} = S_{44} ε_{23}, \\ σ_{13} = S_{44} ε_{13}, \\ σ_{12} = false(S_{11} goodbreak- S_{12} false) ε_{12}, \\ D_{3} = e_{31} false(ε_{11} goodbreak+ ε_{22...} \end{matrix}) \end{matrix}

…”

Section: Mathematical Modelmentioning

confidence: 99%

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Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Som,

Manna

2024

Z Angew Math Mech

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This study investigates the localized wave propagation at the free edge of a thin semi‐infinite Magneto‐Electro‐Elastic (MEE) plate. The plate is supported by a two‐parameters elastic foundation. Biot's porosity theory is considered to formulate the porosity in the model, and the pore structure is saturated with an incompressible fluid. The Kirchhoff–Love plate theory determines the plate displacement field. A non‐homogeneity in the material parameters is considered, which varies with the spatial coordinate along the thickness direction of the plate. In order to illustrate the impacts of the surface elements on bending wave propagation, the model incorporates the surface elasticity theory. The short circuit boundary conditions are implemented to derive the general form of the potential function connected with the electric and magnetic fields, respectively. The dispersion relation for bending edge wave on a MEE fluid‐saturated porous plate is obtained by considering a sinusoidal waveform, which propagates along the free edge of the plate. A numerical method named Finite Difference (FD) scheme is employed to analyze the stability of the numerical scheme and also extract the expression of the velocity profiles of the bending edge wave in the absence of the pore structure. The impacts of the various parameters included in the considered model are examined using a numerical example, from which conclusions regarding their sensitivity are derived.

show abstract

Section: Mathematical Modelmentioning

confidence: 99%

“…Assume that the plate thickness is measured along the

x_3

axis, with the plate's mid‐plane lying on the

x_1x_2

plane. The stress–strain relation for MEE fluid‐saturated medium can be written as [50–61],

\begin{matrix} (}, \begin{matrix} σ_{11} = S_{11} ε_{11} + S_{12} ε_{22} + S_{13} ε_{33} - e_{31} E_{3} - q_{31} H_{3} + M_{1} ζ, \\ σ_{22} = S_{12} ε_{11} + S_{11} ε_{22} + S_{13} ε_{33} - e_{31} E_{3} - q_{31} H_{3} + M_{1} ζ, \\ σ_{33} = S_{13} ε_{11} + S_{13} ε_{22} + S_{33} ε_{33} - e_{33} E_{3} - q_{33} H_{3} + M_{3} ζ, \\ σ_{23} = S_{44} ε_{23}, \\ σ_{13} = S_{44} ε_{13}, \\ σ_{12} = false(S_{11} goodbreak- S_{12} false) ε_{12}, \\ D_{3} = e_{31} false(ε_{11} goodbreak+ ε_{22...} \end{matrix}) \end{matrix}

…”

Section: Mathematical Modelmentioning

confidence: 99%

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Som,

Manna

2024

Z Angew Math Mech

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“…After that, Samal and Chattaraj 3 researched the propagation of surface in fibre‐reinforced anisotropic layer saturated between two flexible media. Singh et al 4,5 proposed two different model to study the propagation of SH‐wave in fibre‐reinforced materials with corrugated boundaries. The influence of point source on the propagation of a Love‐type wave in a piezoelectric composite structure has been investigated by Singh et al 6,7 To obtain the analytical formulations for vectorial group and ray velocities in anisotropic layers with monoclinic symmetry, Ilyashenko and Kuznetsov 8 constructed the dispersion relation for SH waves in stratified anisotropic plates with arbitrary elastic anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Analysis the dispersive nature of Love wave in fibre‐reinforced composite materials plate: A Green's function approach

Kumar

Kumhar

Kundu

et al. 2022

Math Methods in App Sciences

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The research article mainly focuses on investigating the dispersive behaviour of Love waves influenced by an impulsive point source in a fibre-reinforced magnetoelastic (FRME) plate placed on functionally graded fibre-reinforced visco-elastic (FGFRVE) semi-infinite stratum. The materials of the considered structure have been assumed under the influence of magnetic field and functionally graded. The functionally graded in the lower semi-infinite space is caused by consideration of quadratic variation in the shear moduli and mass density. Maxwell's equation and generalised Ohm's law have been employed to calculate the Laurentz force in the fibre-reinforced magnetoelastic (FRME) plate.For solving the coupled field equations, three-dimensional Green's function and Fourier transform are applied; consequently, the closed-form of the Love wave's dispersion relation is obtained. The obtained dispersion curve is plotted and compared in the numerical results and discussions by taking the different magnitude of materials quantities such as reinforcement parameter, magnetoelastic coupling parameter, functionally graded parameter, and visco-elastic parameter.In some particular cases, the deduced dispersion equation is found to be identical to the classical Love wave equation for uniform homogeneous isotropic cases, indicating that the assumed structures are valid. The obtained results from the entire study can be utilised to better understand the dispersive nature of Love wave propagation in the considered systems containing fibre-reinforced, magnetoelastic, viscoelastic, and point sources.

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“…Chatterjee et al (2015) studied the propagation of shear waves in visco-elastic heterogeneous layer overlying on initially stressed half space. Effect of reinforcement on halfspace is discussed (Singh et al, 2016). Tong et al (2016) investigated wave propagation EC 37,9 characteristics in fluid saturated porous materials in the framework of nonlocal Biot's theory.…”

Section: Introductionmentioning

confidence: 99%

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

Ala

Gurijala

Perati

2020

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Purpose The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained. Design/methodology/approach Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied. Findings Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results. Originality/value Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

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Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

Cited by 11 publications

References 26 publications

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

Analysis the dispersive nature of Love wave in fibre‐reinforced composite materials plate: A Green's function approach

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

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