Finite thermal wave propagation in a half space due to variable thermal loading (original) (raw)
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Applied Mathematics
The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. 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. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux q and a phase-lag of temperature gradient on displacement, temperature, stress.
On the wave propagation in the time differential dual-phase-lag thermoelastic model
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015
We study the propagation of plane time harmonic waves in the infinite space filled by a time differential dual-phase-lag thermoelastic material. There are six possible basic waves travelling with distinct speeds, out of which, two are shear waves, and the remaining four are dilatational waves. The shear waves are found to be uncoupled, undamped in time and travels independently with the speed that is unaffected by the thermal effects. All the other possible four dilatational waves are found to be coupled, damped in time and dispersive due to the presence of thermal properties of the material. In fact, there is a damped in time longitudinal quasi-elastic wave whose amplitude decreases exponentially to zero when the time is going to infinity. There is also a quasi-thermal mode, like the classical purely thermal disturbance, which is a standing wave decaying exponentially to zero when the time goes to infinity. Furthermore, there are two possible longitudinal quasi-thermal waves that a...
Three-dimensional thermal shock problem of generalized thermoelastic half-space
Applied Mathematical Modelling, 2010
A three-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain and displacement distributions are represented graphically.
Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating
2006
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 a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. Laplace and Fourier transform 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 ramp-type heating. The inverse Fourier transforms are obtained analytically while 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 ramping parameter of heating with different theories of thermoelasticity.
On the Wave Propagation in the Thermoelasticity Theory with Two Temperatures
Journal of Elasticity, 2020
This paper considers the thermoelastic theory with two temperatures that involves higher gradients of thermal and mechanical effects. The wave propagation question is addressed within the class of waves of assigned wavelength. Considering harmonic in time wave solutions, it is found that the transverse waves are undamped in time and nondispersive, and they are not altered by the thermal effects. Conversely, the longitudinal waves are dispersive and damped in time; the dispersion relation is established like a cubic equation and the effects of conductive temperature are explicitly presented. Rayleigh surface waves are also studied and an explicit secular equation is derived by using wave solutions damped in time. Illustrative examples are numerically analyzed and graphically depicted. The results achieved are meaningful because they are able to bring information about the propagation of waves with assigned length and, moreover, they are in agreement with the results regarding the wave speed of travelling discontinuities. Also the structure of the wave solutions provides information upon asymptotic stability.
Computational Methods in Science and Technology, 2016
The present work seeks to investigate the propagation of magneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space in contact with vacuum. Normal load has been applied on the boundary of the existing media that is supposed to be permeated by a primary uniform magnetic field. We employ both the parabolic type (dual phase-lag magneto-thermoelasticity of type I (MTDPL-I)) and hyperbolic type (dual phase-lag magneto-thermoelasticity of type II (MTDPL-II)) dual phase-lag heat conduction models to account for the interactions among the magnetic, elastic and thermal fields. The integral transform technique is applied to solve the present problem and the analytical results of both cases have been obtained separately. A detailed analysis of results has been made in order to understand the nature of waves propagating inside the medium and the effects of the phase-lag parameters. The effect of the presence of magnetic field has been highlighted. Numerical results have also been obtained to analyze the effect of magnetic field on the behavior of the solution more clearly and a detailed analysis of the results predicted by two models has been presented. It has been noted that in some cases there are significant differences in the solution obtained in the contexts of MTDPL-I and MTDPL-II theory of magneto-thermoelasticity.
Wave propagation in temperature rate dependent thermoelasticity with two temperatures
The present investigation is concerned with two problems. (i) Reflection and transmission of thermoelastic waves between two thermoelastic half-spaces with two temperature at an imperfect interface; and (ii) Propagation of Rayleigh waves at the free surface of thermoelastic solid with two temperature. In problem (i) the amplitude ratios for reflection and transmission coefficients are obtained and deduced for normal force stiffness, transverse force stiffness, thermal contact conductance and perfect bonding. The numerical results obtained have been illustrated graphically to understand the behavior of amplitude ratios versus angle of incidence of longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. It is found that the amplitude ratios of various reflected and transmitted waves are affected by the stiffness and two temperature effects. In problem (ii) the phase velocity and attenuation coefficient are obtained and presented graphically to depict the effect of two temperatures. Some special cases of interest have been deduced from the two problems also.
Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source
Acta Mechanica, 2010
The present work is concerned with the wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source under the theory of thermoelasticity with three phase-lags (Roychoudhari in J Therm Stress 30:231-238, 2007). For the solution of the problem, we employ a potential function approach together with Laplace and Hankel transform method. Analytical expressions for the distributions of different fields like temperature, displacement and stresses inside the medium are derived by inverting Laplace transforms in an approximate manner for small values of time. The problem is illustrated by computing numerical values of the field variables for a particular material. The theoretical as well as numerical results are compared with the corresponding results for other theories of thermoelasticity reported earlier.