In this paper the linear theory of the thermoelasticity has been employed to study the effect the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the magnetic field , rotation, initial stress and gravity. The medium under consideration is traction free, homogeneous, isotropic, as well as with three-phase-lag. The normal mode analysis is used to solve the resulting non-dimensional coupled equations. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained similarly, the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by different theories Lord-Shulman theory (L-S), the Green-Naghdi theory of type III (G-N III) and the three-phase-lag model in the absence and presence of a magnetic field, rotation, initial stress and gravity. The results indicate that the effect of rotation, magnetic field, initial stress and gravity field are very pronounced.

Effect of rotation and gravity on the reflection of P-waves from thermo-magneto-microstretch medium in the context of three phase lag model with initial stress

The time nonlocal generalization of the classical Fourier law with the “Long-tail” power kernel can be interpreted in terms of fractional calculus and leads to the time fractional heat conduction e...

Fractional heat conduction in a thin hollow circular disk and associated thermal deflection

To explore the dynamic responses of generalized thermoelastic problems with nonlocal effect in microtemporal scale, a finite length thermoelastic rod subjected to a moving heat source is modeled and investigated in generalized thermoelasticity. The rod is fixed at both ends and its material properties are temperature-dependent. The corresponding governing equations are first given and then reduced into one-dimensional ones with temperature-dependent properties assumed to be functions of reference temperature. Subsequently, the equations after normalization are solved together with the initial conditions and the boundary conditions by means of Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. In calculation, the effects of the velocity of the heat source, the temperature-dependent properties and the nonlocal parameter on the distributions of the considered variables are emphatically ...

Investigation on the dynamic responses of a generalized thermoelastic problem with variable properties and nonlocal effect

Fiber-reinforced materials have widespread applications, which prompt the study of the effect of fiber reinforcement. Research studies have indicated that thermal conductivity cannot be considered as a constant, which is closely related to temperature change. Based on those studies, we investigate the fiber-reinforced generalized thermoelasticity problem under thermal stress, with the consideration of the effect of temperature-dependent variable thermal conductivity. The problem is assessed according to the L-S theory. A fiber-reinforced anisotropic half-space is selected as the research model, and a region of its surface is subjected to a transient thermal shock. The time-domain finite element method is applied to analyze the nonlinear problem and derives the governing equations. The nondimensional displacement, stress, and temperature of the material are obtained and illustrated graphically. The numerical results reveal that the variable conductivity significantly influences the distribution of the field quantities under the fiber-reinforced effect. And also, the boundary point of thermal shock is the most affected. The obtained results in this paper can be applied to design the fiber-reinforced anisotropic composites under thermal load to satisfy some particular engineering requirements.

/pdf/effect-of-variable-thermal-conductivity-on-the-generalized-4y8pfnfga3.pdf

Effect of Variable Thermal Conductivity on the Generalized Thermoelasticity Problems in a Fiber-Reinforced Anisotropic Half-Space


 Effective classical representations of heterogeneous systems fail to have an effect on the overall response of components on the spatial scale of heterogeneity. This effect may be critical if the effective continuum subjects' scale differs from the material's microstructure scale and then leads to size-dependent effects and other deviations from conventional theories. This paper is concerned with the thermoelastic behavior of rotating nanoscale beams subjected to thermal loading under mechanical thermal loads based on the non-local strain gradient theory (NSGT). Also, a new mathematical model and governing equations were constructed within the framework of the extended thermoelastic theory with phase delay (DPL) and the Euler-Bernoulli beam theory. In contrast to many problems, it was taken into account that the thermal conductivity and specific heat of the material are variable and linearly dependent on temperature change. A specific operator has been entered to convert the nonlinear heat equation into a linear one. Using the Laplace transform method, the considered problem is solved and the expressions of the studied field variables are obtained. The numerical findings demonstrate that a variety of variables, such as temperature change, Coriolis force due to rotation, angular velocity, material properties, and nonlocal length scale parameters, have a significant influence on the mechanical and thermal waves.


Thermal vibration in rotating nanobeams with temperature-dependent due to exposure to laser irradiation

A one-dimensional generalized magnetothermoelastic problem of a thermoelastic rod with finite length is investigated in the context of the fractional order thermoelasticity. The rod with variable properties, which are temperature-dependent, is fixed at both ends and placed in an initial magnetic field, and the rod is subjected to a moving heat source along the axial direction. The governing equations of the problem in the fractional order thermoelasticity are formulated and solved by means of Laplace transform in tandem with its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress in the rod are obtained and illustrated graphically. The effects of the temperature-dependent properties, the velocity of the moving heat source, the fractional order parameter, and so forth on the considered variables are concerned and discussed in detail, and the results show that they significantly influence the variations of the considered variables.

/pdf/effect-of-variable-properties-and-moving-heat-source-on-1mgl0kjy1y.pdf

Guo Ying

Papers

Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity