ASYMPTOTIC ANALYSIS OF SOLID SPHERE SUBJECTED TO THERMAL SHOCK UNDER FRACTIONAL ORDER GENERALIZED THERMOELASTICITY

Based on fractional order generalized thermoelasticity, one dimensional problem of a solid sphere subjected a thermal shock is studied. The transient characteristics of thermal shock is considered to derive the approximate solutions of displacement, temperature and stresses by means of the Laplace transform technique and the asymptotic properties of Bessel functions. Numerical simulation has been conducted for an isotropic solid sphere with the boundary subjected to a thermal shock. The propagation of thermal wave and thermal elastic wave, and the distribution of each physical field in the different values of the fractional order parameter are obtained. The results show that the fractional parameter has a significant effect on propagation of two waves and distribution of each physical field, which can be regarded as an influence factor of the thermal relaxation time, and can change the effect of thermal shock by constraining the influence of the delay effects on thermal behaviors.