Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids
TL;DR: In this paper, the analysis of free vibrations of a thermoelastic hollow sphere with voids is investigated under dual-phase-lag generalized thermo-elasticity and Erigen's nonlocal elasticity.
Abstract: The analysis of free vibrations of a thermoelastic hollow sphere with voids is investigated under dual-phase-lag generalized thermoelasticity and Erigen’s nonlocal elasticity. By implementing the s...
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TL;DR: In this paper, photo-thermoelastic waves throughout the photothermal process for a semiconducting half-space have been investigated in contrast to many scientists who ignore the coupling effects between plasma and thermo-elasticity.
Abstract: For engineers and physicists, it is important to investigate the excitement of thermoelastic vibrations by photothermal effects since they are used in many fields. For this purpose, the photo-thermoelastic waves throughout the photothermal process for a semiconducting half-space have been investigated in this work. In contrast to many scientists who ignore the coupling effects between plasma and thermoelasticity, the influences of thermoelastic, carrier recombination and electronic elastic deformations on the semiconductor solids have been studied here. One of the thermoelastic theories which is appropriate for the limited speeds of heat waves has been considered. To solve the non-dimensional system resulting from generalized thermal elasticity theory without dissipating energy, coupled plasma, elastic wave and thermal wave equations, the normal mode technique has been applied. The amplitude expression for the field variables have been derived and graphically displayed. The numerical results have been verified and the influence of various factors has been also studied. In addition, several special cases of interest have been deduced. The analysis showed that the effective parameters have important effects on the physical fields by applying the presented model.
10 citations
01 May 2022
TL;DR: In this paper , the nonlocal elasticity together with electro−magneto thermal dual phase lag (DPL) model to a transversely isotropic generalized thermoelastic hollow sphere with voids is addressed in radial direction.
Abstract: The nonlocal elasticity together with electro‐magneto thermal dual‐phase‐lag (DPL) model to a transversely isotropic generalized thermoelastic hollow sphere with voids is addressed in radial direction. The governing equations and stress–strain‐displacement relations have been resolved by applying time harmonics technique. The elimination technique is employed to resolve the homogeneous equations to find the unknowns. The unknowns such as dilatation, displacement, voids volume fraction, temperature change, and radial/de‐hoop stresses have been calculated analytically. In order to discover the vibration analysis, the numerical Iteration method has been applied to thermally insulated/isothermal boundary conditions. For computation purpose the software like MATLAB tool has been used. The real parts of generated data obtained from the frequency equations have also been shown graphically to frequency shift and natural frequencies. The effects of DPL model of the theory of generalized transversely isotropic thermoelasticity with voids have been represented with and without the effects of magnetic field for nonlocal/local elastic materials and validated with existing literature.
7 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, 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 article , a nonlocal model with one thermal relaxation time is presented to investigate the propagation of waves in a thermoelastic semi-infinite medium, and the effects of nonlocal parameters, ramp type heating, and thermal relaxation times on the wave propagation distribution of physical fields for mediums are graphically displayed and analyzed.
Abstract: A novel nonlocal model with one thermal relaxation time is presented to investigate the propagation of waves in a thermoelastic semi-infinite medium. We used Eringen’s theory of the nonlocal continuum to develop these models. Analytical solutions in all physical quantities are provided by using Laplace transforms and eigenvalue techniques. All physical quantities are presented as symmetric and asymmetric tensors. The temperature, the displacement, and the stress variations in semi-infinite materials have been calculated. The effects of nonlocal parameters, ramp type heating, and the thermal relaxation times on the wave propagation distribution of physical fields for mediums are graphically displayed and analyzed.
2 citations
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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
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
TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.
1,788 citations
TL;DR: In this article, a universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion, wave, phonon-electron interactions, and pure phonon scattering.
Abstract: A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave (macroscopic in space but microscopic in time), phonon-electron interactions (microscopic in both space and time), and pure phonon scattering The model is generalized from the dual-phase-lag concept accounting for the laging behavior in the high-rate response While the phase lag of the heat flux captures the small-scale response in time, the phase lag of the temperature gradient captures the small-scale response in space The universal form of the energy equation facilitates identifications of the physical parameters governing the transition from one mechanism (such as diffusion or wave) to another (the phonon-electron interaction)
1,435 citations
TL;DR: In this paper, a review of contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermodynamic properties is presented, and a glance is made at the new theory which includes the so-called dual-phase-lag effects.
Abstract: This review article is a continuation of a previous article by the author, Thermoelasticity with second sound: A review, which appeared in this journal in March, 1986 (Appl Mech Rev 39(3) 355-376). Here, attention is focused on papers published during the past 10-12 years. Contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermoelasticity theory are reviewed. The recently developed theory of thermoelasticity without energy dissipation is described, and its characteristic features highlighted. A glance is made at the new thermoelasticity theory which includes the so-called dual-phase-lag effects. There are 338 references.
1,019 citations