Hyperbolic Thermoelasticity Research Articles

Rayleigh waves in nonlocal orthotropic thermoelastic medium with diffusion

AbstractThis study examines Rayleigh wave propagation dynamics in a nonlocal orthotropic medium with thermoelastic diffusion, utilizing Eringen's nonlocal elasticity theory and the Lord–Shulman hyperbolic thermoelasticity model. Normal mode analysis is used to solve the problem, deriving the frequency equation for Rayleigh waves and analyzing specific cases. The elliptical path of surface particles and its eccentricity are calculated. Graphs illustrate the relationships of propagation speed, attenuation coefficient, penetration depth, and specific loss of Rayleigh waves concerning wave number for both thermally insulated and isothermal surfaces. The results reveal that the presence of nonlocal parameters and diffusion significantly increases the values of physical variables, especially with higher wave numbers, highlighting their considerable impact on the system's dynamics.

Thermoelastic diffusion based on a nonlocal three-phase-lag diffusion model with double porosity structure

This work aims to develop a new diffusion-elasticity-based model using Eringen’s nonlocal elasticity theory under the purview of the three-phase-lag (TPL) model of hyperbolic thermoelasticity. This problem is treated in the context of a double porosity structure in a homogeneous, isotropic thermoelastic medium. By considering the phase laggings of the diffusion flux vector and using nonlocal continuum mechanics, new constitutive and field equations are derived. The problem is solved by employing the normal mode analysis technique which gives the exact results of all the physical variables. To illustrate the theoretical results, different physical quantities are calculated numerically and presented graphically with respect to distance and time. The influences of different thermoelastic models like TPL (three-phase-lag model), GN-III (Green-naghdi model), DPL (dual-phase-lag model), LS (Lord-Shulman model), and CT (coupled thermoelasticity) on the physical quantities are shown graphically. Additionally, the effects of nonlocal parameters, double voids, and diffusion on the physical quantities are represented graphically. Some limiting and particular cases are also derived from the governing equations and those results have been compared with the existing results available in the literature. Some 3D surface curves are also presented to study the impact of diffusion, nonlocality, and double voids on various physical quantities.

Thermoelastic diffusion in nonlocal orthotropic medium with porosity

The present article investigates the linear theory of nonlocal thermoelasticity in homogeneous orthotropic porous medium with diffusion in the context of dual-phase-lag model. The focal point of the present study involves an examination of Fick’s mass diffusion law and the generalized Fourier’s law within the context of the dual-phase-lag model of hyperbolic thermoelasticity. The incorporation of voids, mass diffusion with phase lagging in the diffusion flux is the basis for establishing the void diffusion-elasticity models. Furthermore, the new dual-phase-lag diffusion model introduces the consideration of nonlocal effects in mass transfer. The resolution of the problem involves the utilization of normal mode analysis, employed for solving, and encompasses the application of thermal shock at the surface boundary. Numerical calculations of stress components, displacement components, voids, temperature, and concentration of the diffusive material are performed for various distances and time intervals.

On the hyperbolic thermoelasticity with several dissipation mechanisms

In this work, we study a two-dimensional problem involving a thermoelastic body with four dissipative mechanisms. The well-known theory proposed by Lord and Shulman is used. The existence and uniqueness of solution is proved by using theory of linear semigroups. Then, introducing some assumptions of the coupling coefficients, we prove that the energy decay is exponential. An extension to the theory provided by Green and Lindsay is briefly presented and to the three-dimensional case is also commented.

К 60-летию со дня рождения проф. Юрия Николаевича Радаева

10 февраля 2022 г. исполнилось 60 лет известному ученому в области механики деформируемого твердого тела и прикладной математики, педагогу, организатору науки и высшего образования в России Юрию Николаевичу Радаеву. В статье приведены основные библиографические данные Ю. Н. Радаева, в краткой форме представлены главные научные направления и результаты научной деятельности по фундаментальным проблемам математической теории пластичности, механике растущих тел и рассеянного накопления поврежденности, теории трещин, микрополярной упругости, связанной гиперболической термоупругости и термомеханике, общим математическим вопросам механики сплошных сред, механике сыпучих и гранулированных сред.

The propagation of plane waves in nonlocal visco-thermoelastic porous medium based on nonlocal strain gradient theory

The present paper deals with propagation of plane harmonic waves in nonlocal visco-thermoelastic porous medium based on the nonlocal strain gradient theory. For the first time, the assumptions of Green-Naghdi model type III of hyperbolic thermoelasticity with voids in conjunction with nonlocal strain gradient theory are taken into account in formulation of the problem. The constitutive relations and field equations for nonlocal thermoelastic materials with voids are presented. In addition to transverse waves, three longitudinal waves (elastic, thermal, volume fraction) can be observed. The fundamental solution to equations for steady oscillations is derived. The effects of nonlocal length scale parameter, voids, viscosity on phase velocities, attenuation coefficients and penetration depths of waves with diverse frequencies are comprehensively studied and graphically presented.

Rayleigh waves in porous nonlocal orthotropic thermoelastic layer lying over porous nonlocal orthotropic thermoelastic half space

ABSTRACT The present paper deals with the propagation of Rayleigh surface waves in a nonlocal thermoelastic orthotropic layer which is lying over a nonlocal thermoelastic orthotropic half space. The problem is considered in the context of Green-Naghdi type III model of hyperbolic thermoelasticity and Eringen’s nonlocal elasticity theory in the presence of voids. The problem is solved using eigenfunction expansion method. Frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

Rayleigh waves in porous orthotropic medium with phase lags

The present article deals with the propagation of Rayleigh surface waves in homogeneous orthotropic medium. This thermoelastic problem is studied under the purview of three-phase-lag model of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by eigenvalue approach. The frequency equations for different cases are derived. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. Phase velocity and attenuation coefficient decreases in the presence of voids. The present problem is the most general one as other problems can be obtained as special cases from it.

Surface waves in piezothermoelastic transversely isotropic layer lying over piezothermoelastic transversely isotropic half-space

In this article, the propagation of Rayleigh surface waves in a piezothermoelastic transversely isotropic layer lying over a piezothermoelastic transversely isotropic half-space is investigated in the context of the Green–Naghdi model type III of hyperbolic thermoelasticity. The secular equation of Rayleigh surface waves is derived, and different cases are discussed. Phase velocity, attenuation coefficient and specific loss of surface waves are computed and presented graphically with respect to frequency, and a comparison of different wave characteristics for classical and generalized thermoelastic models is presented in the figures.

Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space

The paper deals with Rayleigh wave propagation in a nonlocal thermoelastic layer, and the layer is lying over a nonlocal thermoelastic half-space. The problem is treated in the context of Eringen’s nonlocal thermoelasticity and Green–Naghdi model type III of hyperbolic thermoelasticity. The frequency equation of Rayleigh waves is derived, and different cases are also discussed. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss, and penetration depth is presented graphically.

Surface waves in porous nonlocal thermoelastic orthotropic medium

The present article deals with the propagation of Rayleigh surface waves in a homogeneous orthotropic medium based on Eringen’s nonlocal thermoelasticity. This thermoelastic problem is studied under the purview of Green–Naghdi model type III of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by an eigenvalue approach. The frequency equations for different cases are derived. The path of surface particles during Rayleigh wave propagation is found to be elliptical. In order to illustrate the analytical developments, the numerical solution is carried out and the computer-simulated results with respect to phase velocity, attenuation coefficient and specific loss are presented graphically.

Three-dimensional vibration analysis of porous cylindrical panel with a three-phase-lag model

The article deals with a three-dimensional analysis of free vibrations of a homogeneous isotropic, thermally conducting cylindrical panel with voids in the context of a three-phase-lag model of hyperbolic thermoelasticity. After expanding the displacement potentials, void volume fraction and temperature functions with orthogonal series, the equations of the considered vibration problem are reduced to five second-order-coupled ordinary differential equations whose formal solutions can be expressed by using Bessel functions with complex arguments. The corresponding results for the thermoelastic panel without voids and an elastic panel with and without voids have been deduced as special cases. To illustrate the analytical results, the numerical solutions of various relations and equations have been obtained to compare the frequency as a function of different cylindrical panel parameters in the case of different thermoelastic models. The computer-simulated results have been presented graphically to show the effect of voids and phase lag on the frequency.

Vibration analysis of transversely isotropic hollow cylinder considering three different theories using the matrix Frobenius method

Purpose The purpose of this paper is to deal with the three-dimensional analysis of free vibrations in a stress-free and rigidly fixed homogeneous transversely isotropic hollow cylinder in the context of three-phase-lag (TPL) model of hyperbolic thermoelasticity. Design/methodology/approach The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. Findings The natural frequency, dissipation factor and inverse quality factor in the stress-free and rigidly fixed hollow cylinder get significantly affected due to thermal vibrations and thermo-mechanical coupling. Originality/value The modified Bessel functions and matrix Frobenius method have been directly used to study the vibration model of a homogeneous, transversely isotropic hollow cylinder in the context of TPL model based on three-dimensional thermoelasticity.

Hyperbolic thermoelasticity in gas medium

A numerical approach is used to investigate waves propagation due to laser radiation. A thin layer of gas medium is considered, and gas is modeled based on ideal gas concept. The aim of the research is to examine time relaxation constant’s influence on the coupled thermoelastic system. Heat flux relaxation according to Maxwell–Cattaneo law is studied. The spatial description is used in order to describe continuum fields. Density, temperature, heat flux and velocity are evaluated through the system of balance equations: mass, energy and momentum balances are taken in integral form. The high-speed thermal impact is modeled by defining the distribution of heat sources in the volume for the semitransparent medium with help of Bouguer law. The power of the laser pulse depends on time as the Dirac delta function or as the Heaviside function do. A number of problems with different time relaxation constant are considered, and the interaction between thermal and acoustic waves is examined. For numerical calculation, an explicit technique is applied.

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

AbstractA numerical solution for a coupled hyperbolic thermoelasticity problem of the Lord‐Shulman type is presented. An infinite layer with free boundaries that are kept at a constant temperature is irradiated by a short laser impulse. In this case the problem can be studied in the one‐dimensional formulation. An impact of the laser impulse on a medium is modeled by an internal heat source. The laser impulse intensity decays with a distance from an irradiated surface according to the Bouguer law. The layer is in an unperturbed state at the initial moment of time. The material properties of copper are taken to be the thermo‐mechanical properties of the layer.Two approaches for the boundary value problem are considered: the finite‐difference method (FDM) and the finite‐volume method (FVM). In the first case the system of two second‐order PDE is investigated, in the second case a system of integral balance equations and an integral thermal conductivity equation are composed. To integrate these equations both the explicit and implicit schemes are used. The obtained results are compared with each other and with an analytical solution. A numerical error is estimated for different time and space step sizes. The features inherent in various ways of integration of the coupled hyperbolic thermoelastic problem with the thermal excitation are found.

Quick and robust meshless analysis of cracked body with coupled generalized hyperbolic thermo-elasticity formulation

In this article, the MLPG method is applied to the generalized linear coupled thermoelectricity equations. Lord–Shulman modification with a relaxation time parameter is used in the hyperbolic heat conduction equations. A new linear test function which is zero on the boundaries of local test domains is introduced. The test function and its partial derivatives are determined by an exponential RBF approximation method. The approximation of test function and main variables are similar. For the construction of shape functions, neighbors of every point are determined based on the definition of the closest adjacent point pattern. Consequently, test function space becomes independent of trial function space. Direct interpolation method and penalty parameter are used to impose essential boundary conditions. The selection of appropriate parameters are demonstrated in two numerical examples. The small number of used points is the advantage of this method over the FEM that is shown in several examples. The accuracy of results is compared between the meshless method and different analytical and FE solutions. The effect of the relaxation time on SIF under thermal shock is discussed in a separate example. The comparison of meshless results with various examples shows that employed method is accurate and reliable.

Oldroyd fluids with hyperbolic heat conduction

Development of constitutive equations of Oldroyd fluids with hyperbolic heat conduction, directly from the free energy and dissipation functions, is the focus of this work. Two models from hyperbolic thermoelasticity of solids – theory with one thermal relaxation time and theory with two thermal relaxation times – provide a stepping-stone for this task. The setting for these models is offered, respectively, by the primitive thermodynamics of Edelen and the thermodynamic orthogonality of Ziegler, both cases involving an internal parameter: the inelastic strain. The identified free energy and dissipation functions show that, in the first case, the hyperbolic (telegraph-like) heat conduction is governed by the Maxwell-Cattaneo model involving one thermal relaxation time, whereas, in the second case, by the Fourier law and two thermal relaxation times in the constitutive laws for stress and entropy. In both cases, the thermal fields vanish from the mechanical equations as the Oldroyd fluid becomes incompressible, whereas the mechanical fields are present in the telegraph-type equations for temperature.

Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem

We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord–Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.

Structure and intrinsic properties of dispersion relation in hyperbolic thermoelasticity

ABSTRACTFor a system of field equations of hyperbolic thermoelasticity, we derive a propagation condition for a thermoelastic disturbance in a form of homogeneous plane wave in deformation and temperature. The corresponding dispersion relation is given in an explicit form, together with the dependence of characteristic coefficients on the principal invariants of the tensor of isothermal elasticity, heat conductivity, and thermoelasticity. Discussion of different types of homogeneous thermoelastic plane waves is given as well. Derived methodology is applied in the analysis of Green–Naghdi model.

Uniform stabilization of a quasilinear plate model in hyperbolic thermoelasticity

We study dynamic elastic deformations of a quasilinear plate model of Timoshenko's type under thermal effects, which are modeled by Cattaneo's law. We prove uniform exponential stabilization of the total energy as time approaches infinity. We show global wellposedeness of the model and build a convenient Lyapunov function, which allow us to conclude the main result of this work. Copyright © 2015 John Wiley & Sons, Ltd.