Thermo-viscoelastic properties in a non-simple three-dimensional material based on fractional derivative Kelvin–Voigt model

• Published in: Indian journal of physics Vol. 96; no. 2; pp. 399 - 410
• Main Author: Abouelregal, Ahmed E.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.02.2022; Springer Nature B.V
• Subjects: Astrophysics and Astroparticles; Conduction heating; Conductive heat transfer; Fourier transforms; Inverse method; Mathematical models; Order parameters; Original Paper; Physics; Physics and Astronomy; Thermoelasticity; Time dependence; Viscoelasticity; Fractional Kelvin; Two-temperature; Voigt model; Three-phase lags; Fractional thermoelasticity
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-020-01979-x

This paper provides a connection between the theories of thermoelasticity with fractional order, two-temperature, Kelvin – Voigt viscoelasticity and heat conduction with three-phase lags. The proposed model is used to study the thermoelastic vibrations in a homogeneous isotropic three-dimensional solid whose surface is traction free and subject to a time-dependent thermal loading. The problem has been addressed using Laplace and double Fourier transform methods to remove the time variable as well as two space variables. To obtain the numerical results of the investigated fields in the physical domain, we applied a numerical inverse method. We have also concluded some special cases of interest from this work. Furthermore, the results are displayed graphically to illustrate the influence of viscosity, phase lags, two-temperature and fractional-order parameters on all physical fields.