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A model for elastic half space under a visco-elastic layer in generalized thermoelasticity

CONTINUUM MECHANICS AND THERMODYNAMICS 2025年第2期37卷 1-12页

作者： Khader, S. E. Marrouf, A. A. Khedr, M. Egyptian Atom Energy Author Math & Theoret Phys Dept Cairo Egypt Univ Alexandria Fac Sci Dept Phys Alexandria Egypt

We consider a model of two layers for two cases. In the first case, a viscoelastic upper layer over an elastic half-space. In the second case, an elastic upper layer over a viscoelastic half-space. The upper layer's surface is taken to be traction-free and is subjected to a constant thermal shock. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. Laplace transform techniques are used. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions. This work may be useful in the design of materials used in thermal insulation, vibration reduction, and applications in microelectronics.

关键词： Different materials Half space generalized thermoelasticity Laplace transform Visco-elastic

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Dynamic response of a 1D semi-infinite piezoelectric rod with fractional order generalized thermoelasticity

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NUMERICAL HEAT TRANSFER PART A-APPLICATIONS 2025年第5期86卷 1370-1381页

作者： Zhu, Haitao Tang, Lichen Liu, Chang Shanghai Nucl Engn Res & Design Inst Shanghai Peoples R China Shanghai Nucl Engn Res & Design Inst Shanghai 200233 Peoples R China

In this work, the problem of a 1D semi-infinite piezoelectric rod in the context of fractional generalized thermoelasticity is considered. The rod with one end fixed is subjected to a moving heat source. The physical quantities are analytically given by the eigenvalue approach with the Laplace transform and the distribution of displacement, temperature, and stress can be obtained through the numerical inverse of Laplace transform. Numerical results show that the fractional order parameter has a great effect on all physical quantities, and it is necessary to take the fractional order thermoelasticity into account when dealing with the thermoelastic problems of piezoelectric materials.

关键词： Eigenvalue approach fractional order parameter generalized thermoelasticity laplace transform piezoelectric rod

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generalized thermoelasticity of an infinite body with a cylindrical cavity and variable material properties

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JOURNAL OF THERMAL STRESSES 2005年第5期28卷 521-532页

作者： Youssef, HM Univ Alexandria Fac Educ Dept Math Alexandria Egypt

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.

关键词： thermoelasticity generalized thermoelasticity material properties

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generalized thermoelasticity of beams under partial thermal shock

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APPLIED MATHEMATICAL MODELLING 2020年第0期79卷 402-413页

作者： Sakha, M. Eslami, M. R. Amirkabir Univ Technol Mech Engn Dept Tehran Iran

In this paper, the generalized thermoelastic response of a beam subjected to a partial lateral thermal shock is analysed. The beam is made of homogeneous and isotropic material and is assumed to follow the Hooke law for its constitutive material. The displacement gradient is small and the linear form of strain-displacement relations is used for the beam. The equations of motion and the boundary conditions of the beam are derived based on Hamilton's principle. According to the first and second laws of thermodynamics, a non-Fourier constitutive equation is employed to derive the energy equation of the beam. The non-Fourier effects lead to the constitutive equation of the hyperbolic type and thus the thermal and mechanical waves can be observed. The propagation of waves in the beam are simulated by finite element model and the wave reflections for different types of boundary conditions are studied. The relaxation time is considered as a significant parameter and results show that energy absorption of the structure and the wave propagation speed depend upon this parameter. (C) 2019 Elsevier Inc. All rights reserved.

关键词： generalized thermoelasticity Partial thermal shock Mechanical waves Thermal waves Finite element method Legendre expansion

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generalized thermoelasticity of Thermal-Shock Problem in a Non-homogeneous Isotropic Hollow Cylinder with Energy Dissipation

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 2012年第5期33卷 913-923页

作者： Othman, Mohamed I. A. Abbas, Ibrahim A. Zagazig Univ Dept Math Fac Sci Zagazig Egypt King Abdulaziz Univ Fac Sci & Arts Khulais Dept Math Jeddah 21413 Saudi Arabia Sohag Univ Dept Math Fac Sci Sohag Egypt

A solution of a thermal-shock problem of generalized thermoelasticity of a non-homogeneous isotropic hollow cylinder using a finite-element method is developed. The formulation is applied to the generalized thermoelasticity based on the Green and Naghdi (GN) theory of type II and type III by an appropriate choice of parameters. The problem has been solved numerically using a finite-element method. Numerical results for the distributions of displacement, temperature, radial stress, and hoop stress are represented graphically. The results indicate that the effects of non-homogeneity are very pronounced. The effects of non-homogeneity are presented with the two types of the Green and Naghdi theory.

关键词： Energy dissipation Finite-element method generalized thermoelasticity Isotropic Non-homogeneous

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generalized thermoelasticity for an Isotropic Solid Sphere Indual-Phase-Lag of Heat Transfer with Surface Heat Flux

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INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE & MECHANICS 2011年第2期12卷 96-105页

作者： Abouelregal, Ahmed E. King Khaled Univ Fac Sci Dept Math Abha Saudi Arabia

The dual-phase-lag heat transfer model is applied for an isotropic solid sphere. The solution of the problem is carried out when the boundary of the sphere is maintained at constant heat flux and the displacement of the surface is constrained. The analytical solutions of the displacement, temperature, and stresses are determined. Laplace transform technique is used to obtain the solution. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. Numerical values of displacement, temperature, and stresses are computed for a particular material and presented graphically. A comparison with other thermoelasticity theories also has been studied.

关键词： generalized thermoelasticity solid sphere dual-phase-lag heat flux numerical Laplace transform

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State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

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Applied Mathematics and Mechanics(English Edition) 2013年第1期34卷 63-74页

作者： H.M.YOUSSEF Department of Mathematical Faculty of EducationAlexandria UniversityAlexandria 21527Egypt

In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.

关键词： generalized thermoelasticity energy dissipation two-temperature heat source

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State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2007年第5期44卷 1550-1562页

作者： Youssef, H. M. Al-Lehaibi, Eman A. Umm Alk Qura Univ Fac Engn Dept Math Mecca 5555 Saudi Arabia Fac Educ Dept Sci Jeddah Saudi Arabia

In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory [Youssef, H., 2005a. The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26(4), 4827;Youssef, H., 2005b. Theory of two-temperature generalized thermoelasticity, IMA J. Appl. Math., 1-8]. The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and traction free. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature parameter. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： thermoelasticity generalized thermoelasticity two-temperature state space

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A generalized thermoelasticity Problem for a Half-Space with Heat Sources and Body Forces

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 2010年第3期31卷 648-662页

作者： El-Maghraby, Nasser Mohamed Arab Acad Sci & Technol Dept Basic & Appl Sci Alexandria Egypt

In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a linear theory of a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane is considered. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

关键词： Body forces Exponential Fourier transform generalized thermoelasticity Half space Heat sources Laplace transform

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A Thick Plate Problem Under the Action of a Body Force in generalized thermoelasticity

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 2010年第11-12期31卷 2323-2336页

作者： Abdel-Halim, A. A. AAST Basic & Appl Sci Dept Coll Engn & Technol Alexandria Egypt

The two-dimensional problem for a thick plate is considered within the context of the theory of generalized thermoelasticity with one relaxation time under the action of a body force. The upper surface of the plate is subjected to a known temperature distribution, while its lower one is laid on a thermally insulated rigid foundation. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. The distributions of the considered physical variables are obtained and represented graphically.

关键词： Body forces Exponential Fourier transform generalized thermoelasticity Laplace transform Thermal relaxation times Thick plate

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