The present research deals with the propagation of Rayleigh wave in transversely isotropic magneto-thermoelastic homogeneous medium in the presence of mass diffusion and three-phase-lag heat transfer. The wave characteristics such as phase velocity, attenuation coefficients, specific loss, and penetration depths are computed numerically and depicted graphically. The normal stress, tangential stress components, temperature change, and mass concentration are computed and drawn graphically. The effects of three-phase-lag heat transfer, GN type-III, and LS theory of heat transfer are depicted on the various quantities. Some particular cases are also deduced from the present investigation.

The current research deals with the analysis of reflection and refraction of plane wave at the imperfect boundary of two dissimilar transversely isotropic piezo-thermoelastic (PT) solid half-spaces with diffusion and two temperature. The formulation is applied in a 2-D model under the purview of three-phase lag (TPL) memory dependent derivative (MDD) heat transfer and TPL MDD diffusion. For the incident QL or QTS wave, there exist four coupled quasi reflected waves: RQL (reflected quasi-longitudinal), RQMD (reflected quasi-mass diffusion), RQT (reflected quasi thermal) and RQTS (reflected quasi-transverse) and four transmitted waves: TQL (transmitted quasi-longitudinal), TQMD (transmitted quasi-mass diffusion), TQT (transmitted quasi thermal) and TQTS (transmitted quasi-transverse) waves propagating with different speeds in two solid half-spaces. The expressions for the amplitude ratios and energy ratios are calculated for the reflected and refracted waves. Calculations for normal force stiffness, transverse force stiffness, thermal contact conductance and welded boundaries are also done as particular cases. Some special cases are also discussed. MATLAB software is used for the numerical and graphical analysis and to show the effect of two-temperature on the amplitude ratios of different reflected and refracted waves for incident QL and QTS waves.

The present study focuses on recent research on thermoelasticity theories as well as their associated reformed models related to the micro-/nano-beams/nano-bars. Our goal is to present an overview of the use and limitations of existing relevant theories. The properties of these theories were analyzed by many researchers in a variety of fields as well as different problems, providing insight into their characteristics. In this review, we discuss theory, techniques, formulation, as well as limitations for solving equations for micro-/nano-beams/nano-bars. In light of the fact that this review may be a useful tool for researchers who work in sensitive industries such as MEMS/NEMS/Resonators/Sensors.

The aim of the present investigation is to examine the memory-dependent derivatives (MDD) in 2D transversely isotropic homogeneous magneto thermoelastic medium with two temperatures. The problem is solved using Laplace transforms and Fourier transform technique. In order to estimate the nature of the displacements, stresses and temperature distributions in the physical domain, an efficient approximate numerical inverse Fourier and Laplace transform technique is adopted. The distribution of displacements, temperature and stresses in the homogeneous medium in the context of generalized thermoelasticity using LS (Lord-Shulman) theory is discussed and obtained in analytical form. The effect of memory-dependent derivatives is represented graphically.