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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

AbstractThis 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.

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Citations
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01 Jan 2016
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Abstract: Thank you very much for downloading thermoelastic models of continua. As you may know, people have search numerous times for their chosen readings like this thermoelastic models of continua, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their laptop. thermoelastic models of continua is available in our digital library an online access to it is set as public so you can download it instantly. Our digital library spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the thermoelastic models of continua is universally compatible with any devices to read.

51 citations

Journal ArticleDOI
Abstract: The main idea of the present work is to extend Eringen’s theory of nonlocal elasticity to generalized thermoelasticity with dual-phase-lag and voids. Then we study the propagation of time harmonic ...

50 citations


Cites background or methods or result from "Plane waves in nonlocal thermoelast..."

  • ...reduces to the classical transverse wave speed, a result recently obtained by Sarkar and Tomar [14] in the relevant medium when r 61⁄4 1....

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  • ...Within the framework of Eringen’s theory of nonlocal elasticity [1], the constitutive relations for thermoelastic solid with voids are given by [12,14] 1 e2r2 ð Þsij 1⁄4 sij 1⁄4 2leij þ kekk þ b/ ch ð Þdij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / n/ bekk þmh; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk þ ahþm/; (4)...

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  • ...(28) gives the coupled longitudinal wave velocities for Lord-Shulman thermoelastic model [19] which are recently obtained by Sarkar and Tomar [14]....

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  • ...For this purpose, we have borrowed the values of relevant material parameters from Sarkar and Tomar [14] and Sing et al....

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  • ...This shows that x 1⁄4 xc acts as a cutoff frequency for the existing transverse wave, a conclusion in accordance with that earlier mentioned by Sarkar and Tomar [14]....

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Journal ArticleDOI
Abstract: The present article deals with the investigation of the propagation of thermoelastic plane harmonic waves in a nonlocal thermoelastic medium. The Green and Naghdi theory II (without energy ...

19 citations


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

  • ...Khurana and Tomar [12] extended the theory of nonlocal elasticity to nonlocal theory of microstretch elasticity and then they investigated wave propagation in nonlocal microstretch solid....

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  • ...Recently, Sarkar and Tomar [20] studied plane waves in nonlocal thermoelastic solid with voids and thermal relaxation time and Mondal et al....

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  • ...Recently, Sarkar and Tomar [20] studied plane waves in nonlocal thermoelastic solid with voids and thermal relaxation time and Mondal et al. [21] reported waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity....

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Journal ArticleDOI
Abstract: The generalized thermoelasticity theory based upon the Green and Naghdi model II of thermoelasticity as well as the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves which are dispersive in nature and associated with attenuation. In addition to the coupled waves, there also exists one independent vertically shear type wave which is dispersive but without any attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear type wave is found to to be associated with a critical frequency, while the coupled longitudinal waves may have critical frequencies under constraints. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on the phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients as well as the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.

19 citations


References
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Book
01 Jan 1962
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

4,124 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....

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Journal ArticleDOI
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.

2,848 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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Book
01 Jan 1957

1,930 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
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.

1,929 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 2002
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.

1,821 citations