Search Results (5)

This study has established and resolved a new mathematical model of a homogeneous, generalized, magnetothermoelastic half-space with a thermally loaded bounding surface, subjected to ramp-type heating and supported by a solid foundation where these types of mathematical models have been widely used in many sciences, such as geophysics and aerospace. The governing equations are formulated according to the Green–Lindsay theory of generalized thermoelasticity. This work’s uniqueness lies in the examination of Maxwell’s time-fractional equations via the definition of Caputo’s fractional derivative. The Laplace transform method has been used to obtain the solutions promptly. Inversions of the Laplace transform have been computed via Tzou’s iterative approach. The numerical findings are shown in graphs representing the distributions of the temperature increment, stress, strain, displacement, induced electric field, and induced magnetic field. The time-fractional parameter derived from Maxwell’s equations significantly influences all examined functions; however, it does not impact the temperature increase. The time-fractional parameter of Maxwell’s equations functions as a resistor to material deformation, particle motion, and the resulting magnetic field strength. Conversely, it acts as a catalyst for the stress and electric field intensity inside the material. The strength of the main magnetic field considerably influences the mechanical and electromagnetic functions; however, it has a lesser effect on the thermal function. Full article

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative thermoelasticity model. Thinner one-dimensional skin tissue is considered when its inner surface is free of traction and does not show any temperature increase. The skin tissue’s bounding surface has been heated by ramp-type heating. The classical thermoelastic theories are obtained from the present general formula. The governing equations of the present model are obtained. To move the system into a space state, the Laplace transform is used. The inverse of the Laplace transform is also used with Tzuo’s method to solve the problem. As a result, the field quantities are obtained numerically, and the results of the current model are graphically represented with a comparison to two different theories of thermoelasticity. The effects of various parameters on thermomechanical waves through the skin tissue are analyzed. The theory notes a vibrational behavior in heat transfer and a different effect on the parameters discussed in this article. Full article

A unified form of thermoelasticity theory that contains three familiar generalized thermoelasticity. The Lord–Shulman theory, Green–Lindsay theory, and the classical one can be outlined in this form. The field quantities of a rotating/non-rotating half-space with and without the effect of the decay parameter can be obtained due to the unified thermoelasticity theory. The present medium is subjected to a time-dependent thermal shock taking into account that the magnitude of the thermal shock wave is not totally fixed but decaying over time. A special case of a thermal shock waveform with constant magnitude may be considered. The field quantities such as temperature, displacements, and stresses of the present problem are analytically obtained. Some plots of these field variables are presented in two- and three-dimensional illustrations in the context of refined theories. Full article

The simple and refined Lord–Shulman theories, the simple and refined Green–Lindsay theories as well as the coupled thermoelasticity theory were all employed to investigate the deformation of a rotating thermoelastic half-space. The present medium is subjected to initial pressure, bounded by hydrostatic initial stress and rotation. A unified heat conduction equation is presented. The normal mode strategy is applied to get all analytical expressions of temperature, stresses, and displacements. Some outcomes are tabulated to validate the present refined theories with the simple and classical thermoelasticity theories. The effect of hydrostatic initial stress was investigated on all field quantities of the rotating thermoelastic half-space with and without initial pressure. Two- and three-dimensional plots are illustrated in the context of refined theories to discuss the behaviors of all variables through the coordinate axes. Some particular cases of special interest have been deduced from the present investigation. Full article

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive. Full article