Generalized thermoviscoelastic model with memory dependent derivatives and multi-phase delay for an excited spherical cavity
A. Soleiman, Ahmed E. Abouelregal, Hijaz Ahmad, Phatiphat Thounthong
Abstract
Abstract In the current investigation, we present a generalized modified model of thermoviscoelasticty with memory-dependent derivatives and multi-phase-lag. The equations of the governing system are derived on the basis of the Kelvin-Voigt model and generalized thermoelasticity theory with multi-phase delay. For certain instances, in the presence and absence of memory-dependent derivatives, the proposed model is limited to other previous ones. The model is then adopted to investigate the problem of an isotropic medium with a spherical cavity heated uniformly by an energy source in the form of a non-Gaussian laser beam. Also, the inner surface of the cavity is restricted and exposed to constant heat flux. The system of differential equations was solved analytically by applying the Laplace transform technique before using an appropriate approximate numerical method to find the inverse transformations. To clarify the effects of the thermoviscoelastic parameters and memory dependent derivatives, we depicted our numerical calculations in figures. Finally, the results obtained are discussed in detail and also confirmed with those in the previous literature.