Memory-dependent and fractional order analysis of the initially stressed piezo-thermoelastic medium

In the context of the triple-phase lag model, comparison studies are conducted between the memory-dependent derivative and fractional order derivative on the propagation of plane waves in a half-space of initially stressed transversely isotropic piezothermoelastic material. The coupled governing equations of the considered model involving relaxation time, time delay, fractional order parameter, and kernel function are selected according to specific problems and solved using the normal mode analysis technique and obtaining the analytical expression. The non-dimensional temperature, displacement, electrical displacements, and stresses at different values of the fractional order parameter and time delay factor are obtained graphically.

Automated summary

In the context of the triple-phase lag model, a comparison study is conducted on the propagation of plane waves in a half-space of initially stressed transversely isotropic piezothermoelastic material, using the memory-dependent derivative and fractional order derivative. The coupled governing equations of the model, involving relaxation time, time delay, fractional order parameter, and kernel function, are solved using normal mode analysis technique to obtain analytical expressions. Graphical results show the non-dimensional temperature, displacement, electrical displacements, and stresses at different values of the fractional order parameter and time delay factor.