Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer
TL;DR: In this paper, a nonlocal theory of generalized thermoelastic materials with voids based on Eringen's nonlocal elasticity and Caputo fractional derivative is established.
Abstract: A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above...
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TL;DR: In this paper, a mathematical model for rotating thermal nanobeams is presented, which is based on Eringen's nonlocal elasticity theory, Euler-Bernoulli's assumptions, and generalized thermoelasticity with two different phase lags.
Abstract: In this study, a mathematical model for rotating thermal nanobeams is presented. A system of equations is derived that describes the thermoelastic behaviour of rotating nanoscale beams. The proposed model is based on Eringen’s nonlocal elasticity theory, Euler–Bernoulli's assumptions, and generalized thermoelasticity with two different phase lags. The nanoscale beam material is completely surrounded by an axial magnetic field and exposed to a time-dependent variable temperature field. The Laplace transform in the state-space approach is employed to solve the problem studied. Because of the difficulty in finding the inversion of the Laplace transforms, it was obtained numerically using one of the techniques based on the technique of the Fourier series expansion. The significance of different parameters such as the rotational angular velocity, nonlocal parameter, temperature change, and magnetic field on the nanobeam response has been investigated. Moreover, the results obtained are verified with the corresponding results from the literature.
17 citations
TL;DR: In this paper, a mathematical model of generalized thermoelasticity was proposed to investigate the transient phenomena due to the influence of magnitudes of the Caputo fractional derivative.
Abstract: Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magn...
17 citations
Cites background from "Nonlocal theory of thermoelastic ma..."
...Bachher and Sarkar [9] have solved an one-dimensional problem based on nonlocal theory of generalized thermoelasticity with voids and Caputo fractional derivative....
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TL;DR: In this article, the vibration of a functionally graded axisymmetric nonlocal thermoelastic hollow sphere with dual-phase-lag effect is addressed, where surfaces of the sphere are assumed to be thermally insulated or isothermal and stress free.
Abstract: The vibration of a functionally graded axisymmetric nonlocal thermoelastic hollow sphere with dual-phase-lag effect is addressed in this paper. Surfaces of the sphere are assumed to be thermally insulated or isothermal and stress free. According to a simple power law, the material is assumed to be graded in the radial direction. The linear theory of modified thermoelasticity with a dual phase lag based on Eringen’s nonlocal elasticity is employed to model this problem. The Matrix Frobenius method of continued power series is introduced to derive the analytical solutions. The phase velocity relations for the existence of various modes of vibrations in the designed hollow sphere are derived in compact forms. In order to explore the attributes of vibrations, the fixed-point numerical iteration technique is used to solve the secular equations. The numerical computations for the material crust in respect of the natural frequencies, thermoelastic damping and the frequency shifting are presented graphically using MATLAB software tools.
15 citations
TL;DR: In this paper, constitutive relations and field equations are developed for an isotropic linear micropolar thermoelastic material with voids within the context of Eringen's theory of nonlocal elasticity.
Abstract: Constitutive relations and field equations are developed for an isotropic linear micropolar thermoelastic material with voids within the context of Eringen’s theory of nonlocal elasticity. It is fo...
15 citations
TL;DR: In this article, free vibrations of nonhomogenous (functionally graded material (FGM)) axisymmetric nonlocal thermoelastic hollow sphere has been taken into consideration for investigation.
Abstract: Free vibrations of non-homogenous (functionally graded material (FGM)) axisymmetric nonlocal thermoelastic hollow sphere has been taken into consideration for investigation The material of nonlocal thermoelastic sphere is supposed to be graded using power law in radial direction The solution of continued power series is employed to resolve the differential equations and to investigate the analytical solutions for field functions ie temperature, stress and displacement The analytical results have been authenticated using numerical computations with computer based software like MATLAB The numerical results have been shown graphically for the comparison of frequency shift and thermoelastic damping for local and nonlocal elastic materials Deduction of results has been validated with the already published literature
14 citations
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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
"Nonlocal theory of thermoelastic ma..." refers methods in this paper
...Laplace transform [45] together with an eigenvalue approach [33,46] technique is employed to obtain the closed form solutions in the transform domain....
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TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
2,201 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
681 citations
"Nonlocal theory of thermoelastic ma..." refers background in this paper
...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
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...Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
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TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.
Abstract: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.
482 citations
"Nonlocal theory of thermoelastic ma..." refers background in this paper
...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....
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...[33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc....
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