Plane waves in nonlocal thermoelastic solid with voids
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.
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TL;DR: In this paper, the free vibrations of transversely isotropic nonlocal electro-magneto thermoelastic hollow cylinder with voids are addressed in the preview of generalized thermelasticity, and the governing equations and the constitutive relations are transformed into coupled ordinary differential equations by applying time harmonic variations.
Abstract: The free vibrations of transversely isotropic nonlocal electro-magneto thermoelastic hollow cylinder with voids are addressed in the preview of generalized thermoelasticity. The governing equations and the constitutive relations are transformed into coupled ordinary differential equations by applying time harmonic variations. The boundary conditions of the outer and the inner surfaces of the hollow cylinder are considered to be traction free, no change in voids volume fraction and thermally insulated/isothermal temperature field. The analytical results for frequency equations are presented and validated with existing literature. To explore the free vibration analysis from the considered boundary conditions, the numerical iteration method has been generated to create data by using MATLAB software tools. The obtained analytical results are represented graphically with the assistance of numerical computations and simulations in absence/presence of magnetic field for nonlocal/local thermoelastic materials. To verify the elastic nonlocal effects in different models of thermoelasticity, the field functions are represented graphically with and without magnetic field effects. The study may find applications in the field of seismology for drilling and mining in the earth's crust appliances, lightweight armors, geophysics, acoustics, and oil prospecting etc.
5 citations
TL;DR: In this paper , the free vibrations of transversely isotropic nonlocal electro-magneto thermoelastic hollow cylinder with voids are addressed in the preview of generalized thermelasticity.
Abstract: The free vibrations of transversely isotropic nonlocal electro-magneto thermoelastic hollow cylinder with voids are addressed in the preview of generalized thermoelasticity. The governing equations and the constitutive relations are transformed into coupled ordinary differential equations by applying time harmonic variations. The boundary conditions of the outer and the inner surfaces of the hollow cylinder are considered to be traction free, no change in voids volume fraction and thermally insulated/isothermal temperature field. The analytical results for frequency equations are presented and validated with existing literature. To explore the free vibration analysis from the considered boundary conditions, the numerical iteration method has been generated to create data by using MATLAB software tools. The obtained analytical results are represented graphically with the assistance of numerical computations and simulations in absence/presence of magnetic field for nonlocal/local thermoelastic materials. To verify the elastic nonlocal effects in different models of thermoelasticity, the field functions are represented graphically with and without magnetic field effects. The study may find applications in the field of seismology for drilling and mining in the earth's crust appliances, lightweight armors, geophysics, acoustics, and oil prospecting etc.
5 citations
26 Aug 2020
TL;DR: In this article, the propagation of plane wave in an infinite isotropic nonlocal couple stress thermoelastic solid has been investigated and the effect of non-locality has also been observed and shown graphically.
Abstract: This work is concerned with the propagation of plane wave in an infinite isotropic nonlocal couple stress thermoelastic solid. Two problems have been evaluated by making incidence of (i) a longitudinal displacement wave and (ii) a set of coupled transverse waves. All these waves are dispersive in nature. Reflection phenomenon of an incident coupled longitudinal wave from stress free boundary surface of a nonlocal thermoelastic solid has also been studied. The dispersion curves of various waves of Magnesium crystal are calculated numerically and shown graphically. The effect of nonlocality has also been observed and shown graphically.
5 citations
TL;DR: In this article, an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids is presented.
Abstract: The current work is an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids. The analysis is made on the reflection phenomena in context of three-phase-lag thermo-elastic model. It is observed that, four-coupled longitudinal waves and an independent shear vertical wave exist in the medium which is dispersive in nature. It is seen that longitudinal waves are damped, and shear wave is un-damped when angular frequency is less than the cut-off frequency. The voids, thermal and non-local parameter affect the dilatational waves whereas shear wave is only depending upon non-local parameter. It is found that reflection coefficients are affected by nonlocal and fractional order parameters. Reflection coefficients are calculated analytically and computed numerically for a material, silicon and discussed graphically in details. The results for local (classical) theory are obtained as a special case. The study may be useful in semiconductor nanostructure, geology and seismology in addition to semiconductor nanostructure devices.
5 citations
TL;DR: In this article , a nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach.
Abstract: In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters.
5 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....
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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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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 2002TL;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