The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The ...The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading (the thermal shock and the ramp-type heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.展开更多
文摘The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading (the thermal shock and the ramp-type heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.