Memory-dependent magneto-thermoelasticity for perfectly conducting two-dimensional elastic solids with thermal shock

Recently,Yu et al.(2014)proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative.The magneto-thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory.Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations.The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress.The effects of the kernel function,time-delay parameter,magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically.The results show that these parameters has significant influence on the variations of the considered variables.

Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.

The Reflection of Magneto-Thermoelastic P and SV Waves at a Solid Half Space Using Dual-Phase-Lag Model

The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magnetothermoelastic solid.The ratios of reflection coefficients to that of incident coefficients are obtained for P-and SV-wave cases.The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries.The reflection coefficients are depending on the angle of incidence,magnetic field,phase lags and other material constants.Results show that the sum of energy ratios is unity at the interface.The results are discussed and depicted graphically.