Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

Abd-alla, Abo-el-nour N.; Giorgio, Ivan; Galantucci, Luca; Hamdan, Abdelmonam M.; Vescovo, Dionisio Del

doi:10.1007/s00161-014-0400-7

Cited by 39 publications

(14 citation statements)

References 64 publications

(98 reference statements)

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“…The macroscopic physical properties tailored in the design of metamaterial may be, for instance, optical, electromagnetic, thermal, mechanical and any combination (and coupling) of many of them. For instance, the particular shape, geometry, size, orientation and arrangement of the microstructural elements affect, in some particular metamaterials, the propagation of waves in a not-often-observed manner, e.g., not allowing the propagation in some band gaps (see, e.g., [28][29][30][31]) even if such a property is not present in the material constituting the microstructural elements (see also [32][33][34][35] for others unusual wave propagation phenomena).…”

Section: Metamaterials and Their Modeling With Generalized Continuamentioning

confidence: 99%

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Turco

Dell’Isola

Cazzani

et al. 2016

Z. Angew. Math. Phys.

213

162

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Hencky (U ̈ber die angen ̈aherte L ̈osung von Stabilit ̈atsproblemen im Raum mittels der elastischen Gelenkkette. Ph.D. thesis, Engelmann, 1921) proposed a discrete model for elasticae by introducing rigid bars and rotational springs. Hencky (Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016) approach has been introduced to heuristically motivate the need of second gradient continua. Here, we present a novel numerical code implementing directly the discrete Hencky- type model which is robust enough to solve the problem of the determination of equilibrium configurations in the large deformation and displacement regimes. We apply this model to study some potentially applicable problems, and we compare its performances with those of the second gradient continuum model. The numerical evidence presented supports the conjecture that Hencky-type converges to second gradient model

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Section: Metamaterials and Their Modeling With Generalized Continuamentioning

confidence: 99%

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Turco

Dell’Isola

Cazzani

et al. 2016

Z. Angew. Math. Phys.

213

162

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“…Abd‐Alla et al. [17–19] studied the reflection of plane waves from electro‐magneto‐thermoelastic half‐space with a dual‐phase‐lag model. Biswas and Sarkar [20] derived the solution of the steady oscillations equations in a porous thermoelastic medium.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

Sarkar

Mondal²

2020

Z Angew Math Mech

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The present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

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“…Such information may be useful for experimental seismologists in correcting earthquake estimation [57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

Abd-alla

Alshaikh

Giorgio

et al. 2015

Mathematics and Mechanics of Solids

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In this paper, we built a mathematical model to study the influence of the initial stress on propagation of longitudinal waves in a hollow infinite circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of a tetragonal system material. The problem is described by the equations of elasticity, taking into account the effect of the initial stress and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with the z-axis directed along the axis of the cylinder. The displacement components will be obtained by founding the analytical solutions of the motion's equations. The frequency equations have been obtained in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries when the initial hydrostatic stress is compression or tension. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of an initial stress can differ significantly from those propagating in the absence of the initial stress. The results of this research are used in analyzing the relationship between magnetic field, the initial stress and the frequency equation and could lead to discussions for using the magnetic field and the initial stress in ultrasound imaging.

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Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

Cited by 39 publications

References 64 publications

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

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