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Memory dependent triple-phase-lag thermo-elasticity in thermo-diffusive medium

Yadav Anand Kumar, Singh Aarti, Jurczak Paweł

International Journal of Applied Mechanics and Engineering

2023

Vol. 28, no. 4

137--162

The objective of the paper is to look at the propagation and reflection of plane waves in a thermo-diffusion isotropic medium. The reflection of plane waves in a thermo-diffusion medium was investigated in this study with reference to triple phase lag thermo-elasticity. The memory dependent derivative (MDD) is applied for this investigation. The fundamental equations are framed and solved for a particular plane. The four plane waves that are propagating across the medium are, shown namely: longitudinal displacement, P-wave, thermal diffusion T-wave, mass diffusion MD-wave and shear vertical SV-wave. These four plane wave velocities are listed for a specific medium, illustrating the impact of the diffusion coefficient and are graphically represented. Expressions for the reflection coefficient for the incidence plane wave are produced from research on the reflection of plane waves from the stress-free surface. It should be noted that these ratios are graphically represented and shown when diffusion and memory dependent derivative (MDD) factors are in play. The new model is relevant to many different fields, including semiconductors, earth- engineering, and electronics, among others, where thermo-diffusion elasticity is significant. Diffusion is a technique that can be applied to the production of integrated circuits, MOS transistors, doped polysilicon gates for the base and emitter in transistors, as well as for efficient oil extraction from oil reserves. Wave propagation in a thermos-diffusion elastic media provides crucial information about the presence of fresh and enhanced waves in a variety of technical and geophysical contexts. For experimental seismologists, developers of new materials, and researchers, this model might be useful in revising earthquake estimates.

Memory response on generalized thermoelastic medium in context of dual phase lag thermoelasticity with non-local effect

Tiwari R., Saeed A. M., Kumar R., Kumar A., Singhal A.

Archives of Mechanics

2022

Vol. 74, nr 2-3

69--88

Theory of non-local continuum is contemporary appraised and is found to be supplementary coherent to capture the impacts of each and every point of the material at its single point. The conviction of memory dependent derivative is also newly appraised and is observed to be more intuitionistic for predicting the realistic character of the real-world obstacles. Attractiveness of the belief of a memory dependent derivative lies in its unique properties such as its significant constituents – a kernel function and time-delay are freely selected according to the requirement of a problem. The present study comprises a new meticulous thermoelastic heat conduction model for the homogeneous, isotropic, thermoelastic half space medium concerning memory effects and non-local effects. Governing equations are constructed on the basis of the newly appraised non-local generalized theory of thermoelasticity with two phase lags in the frame of a memory dependent derivative. Exact analytical solutions of the physical fields such as dimensionless temperature, displacement as well as thermal stress are evaluated by using a suitable technique of the Laplace transform. Quantitative results are determined in a time-domain for different values of time by taking the numerical inversion of the Laplace transform. Noteworthy role of the constituents of the memory dependent derivative such as kernel function as well as time-delay factor has been scrutinized on the crucial field variables of the medium through computational outcomes. Moreover, the impact of non-local parameter is examined on the variations of field quantities through the quantitative results.