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Journal ArticleDOI

Plane waves in nonlocal thermoelastic solid with voids

22 Jan 2019-Journal of Thermal Stresses (Taylor & Francis)-Vol. 42, Iss: 5, pp 580-606
TL;DR: In this paper, the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores was studied, and the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves.
Abstract: This work is concerned with the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds in the medium. All these waves are found to be dispersive in nature, but the coupled dilatational waves are attenuating, while transverse wave is nonattenuating. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter. While the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves. All the computed results obtained have been depicted graphically and explained.
Citations
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Journal ArticleDOI
TL;DR: In this article, the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green-Lindasy (MGL) theory of generalized thermelasticity with strain rate was studied.
Abstract: The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al (Meccanica 53:2543–2554, 2018) 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 of the 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 and the amplitude ratios for specific parameter choices Various graphs have been plotted to analyze the behavior of these quantities The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models

12 citations

Journal ArticleDOI
Baljeet Singh1
TL;DR: In this article, the propagation of surface waves in an isotropic and homogeneous nonlocal generalized thermoelastic solid half-space with voids was studied, and the dispersion relations for Rayleigh-t...
Abstract: The present paper deals with the propagation of surface waves in an isotropic and homogeneous nonlocal generalized thermoelastic solid half-space with voids. The dispersion relations for Rayleigh-t...

12 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibrations of a homogeneous isotropic nonlocal thermoelastic cylinder with void were investigated and the frequency equation for the continuation of vibrations for the mode numbers in the considered cylinder was deduced in closed form for traction free and isothermal/thermally insulated boundary conditions.
Abstract: The present work is devoted to the investigation of the free vibrations of a homogeneous isotropic nonlocal thermoelastic cylinder with void. Time-harmonic variations are used to reduce the governing partial differential equations to a system of ordinary differential equations. The frequency equation for the continuation of vibrations for the mode numbers in the considered cylinder is deduced in closed form for traction-free and isothermal/thermally insulated boundary conditions. To observe the free vibration, the frequency equation is further studied by using the numerical iteration method with the help of MATLAB software. The numerically simulated results from the analytical solutions are shown graphically for the natural frequency, thermoelastic damping and the frequency shift against mode numbers for the nonlocal as well as the local thermoelastic cylinders in the presence and absence of the void.

12 citations

Journal ArticleDOI

11 citations


Cites background from "Plane waves in nonlocal thermoelast..."

  • ...Recently, Sarkar and Tomar [22] reported plane waves in nonlocal thermoelastic solid with voids....

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  • ...Recently, Sarkar and Tomar [22] reported plane waves in nonlocal thermoelastic solid with voids using the LS model of thermoelasticity....

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Journal ArticleDOI
TL;DR: In this article, a new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address the reflection of thermo-elastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space.
Abstract: This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

10 citations

References
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Book
01 Jan 1962
TL;DR: In this article, the linearized theory of elasticity was introduced and the elasticity of a one-dimensional motion of an elastic continuum was modeled as an unbound elastic continuum.
Abstract: Preface Introduction 1 One-dimensional motion of an elastic continuum 2 The linearized theory of elasticity 3 Elastodynamic theory 4 Elastic waves in an unbound medium 5 Plane harmonic waves in elastic half-spaces 6 Harmonic waves in waveguides 7 Forced motions of a half-space 8 Transient waves in layers and rods 9 Diffraction of waves by a slit 10 Thermal and viscoelastic effects, and effects of anisotrophy and non-linearity Author Index Subject Index

4,133 citations


"Plane waves in nonlocal thermoelast..." refers background in this paper

  • ...(23)–(26) propagating in the positive direction of a unit vector n with speed c, we take the form of various potentials as [45,53,54] /; h; q;W f g 1⁄4 A/;Ah;Aq;B exp ik n r ct ð Þ ; (27) where A/; Ah and Aq are constant amplitudes, which may be complex, i 1⁄4 ffiffiffiffiffiffi 1 p is imaginary number, B is a vector constant, r ð1⁄4 x̂i þ ŷj þ zk̂Þ is the position vector and k is the wavenumber....

    [...]

Journal ArticleDOI
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations


"Plane waves in nonlocal thermoelast..." refers methods in this paper

  • ...These relations and equations are the same as those obtained in the Lord–Shulman theory [51,52] of thermoelasticity with one relaxation time....

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Journal ArticleDOI
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

2,287 citations


"Plane waves in nonlocal thermoelast..." refers background in this paper

  • ...The theory of classical coupled thermoelasticity (CCT) [1] is found to be penurious for many physically acceptable situations....

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  • ...Introduction The theory of classical coupled thermoelasticity (CCT) [1] is found to be penurious for many physically acceptable situations....

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Book
01 Jan 1957

1,987 citations


"Plane waves in nonlocal thermoelast..." refers background in this paper

  • ...(23)–(26) propagating in the positive direction of a unit vector n with speed c, we take the form of various potentials as [45,53,54] /; h; q;W f g 1⁄4 A/;Ah;Aq;B exp ik n r ct ð Þ ; (27) where A/; Ah and Aq are constant amplitudes, which may be complex, i 1⁄4 ffiffiffiffiffiffi 1 p is imaginary number, B is a vector constant, r ð1⁄4 x̂i þ ŷj þ zk̂Þ is the position vector and k is the wavenumber....

    [...]

Book
01 Jan 2002
TL;DR: Memory-dependent nonlocal nonlocal Electromagnetic Elastic Solids as mentioned in this paper have been shown to be memory-dependent on nonlocal elasticity and nonlocal linear elasticity, as well as nonlocal Linear Elasticity and Nonlocal Fluid Dynamics.
Abstract: 1. Motion and Deformation.- 2. Stress.- 3. Constitutive Axioms.- 4. Nonlocal Electromagnetic Theory.- 5. Constitutive Equations of Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 6. Nonlocal Linear Elasticity.- 7. Nonlocal Fluid Dynamics.- 8. Nonlocal Linear Electromagnetic Theory.- 9. Memory-Dependent Nonlocal Thermoelastic Solids.- 10. Memory-Dependent Nonlocal Fluids.- 11. Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 12. Memory-Dependent Nonlocal Electromagnetic Thermofluids.- 13. Nonlocal Microcontinua.- 14. Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids.- 15. Nonlocal Continuum Theory of Liquid Crystals.

1,967 citations