分数阶理论下实心球体受热冲击作用的渐进分析

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

基于分数阶广义热弹性理论,针对实心球体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析.利用热冲击的瞬时特征,借助于Laplace正、反变换技术及柱函数的渐进性质,推导了热冲击作用周期内位移场、温度场和应力场的渐进表达式.通过计算,得到了不同传热能力下受热冲击作用时热波、热弹性的传播规律以及位移场、温度场及应力场的分布规律.结果表明:分数阶参数取值的不同,热波、热弹性波的传播以及各物理场的分布均有所不同,分数阶参数可视为延迟时间的影响因子,通过改变延迟效应对热弹性行为的影响来改变热冲击的作用效果.

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.