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, 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
5 citations
TL;DR: In this article , the Laplace transform technique has been used to solve the system differential equations and to find an approximate analytical solution for the different physical fields of the nanobeam.
Abstract: Nanoelectromechanical systems (NEMS) have received great interest from researchers around the world since the advent of nanotechnology and nanoengineering. This can be attributed due to the unique characteristics of NEMS devices and their wide range of applications. Among these applications, nanobeams and nanotubes now have an important role in the design of a variety of NEMS engineering devices. In the current research, the thermoelastic vibration analysis of Euler-Bernoulli nanobeams has been investigated using the theory of non-local elasticity proposed by Eringen. Also to study the effect of temperature change, the generalized thermoelastic model with dual phase-lag (DPL) is applied. The studied nanobeam is subjected to an axial thermal excitation load and surrounded by a magnetic field of constant strength. The Laplace transform technique has been used to solve the system differential equations and to find an approximate analytical solution for the different physical fields of the nanobeam. The numerical results obtained for the studied variables have been graphically clarified and discussed analytically. The effects of various influencing factors such as magnetic field strength, temperature change, non-local parameter as well as ramp type parameter have been examined and studied in detail.
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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.
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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
"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....
[...]
...[33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc....
[...]