分数阶广义热弹性理论下中空柱热弹性分析

Thermo-elastic analysis of hollow cylinder by theory of fractional order generalized thermo-elasticity

基于Laplace变换及特征值法,推导并给出了分数阶广义热弹性理论下中空柱内表面作用有热冲击情况的解析解,通过Laplace数值逆变换法求解得到了位移场、温度场、应力场的分布规律。结果表明:特征值法能准确给出Laplace域内方程组的解;分数阶参数对温度场和应力场有较大影响,对位移场影响较小。作为广义热弹性理论的一种推广,在处理热传导问题时,通过分数阶广义热弹性理论进行研究更科学、全面。

In this article,the problem of a thermo-elastic hollow cylinder in the context of fractional order generalized thermo-elasticity is considered.The inner surface of the cylinder is subjected to a thermal shock.The solutions are analytically obtained by Laplace transform and eigenvalue approach and the distributions of displacement,temperature and stress through the numerical inversion of Laplace transform are obtained.Results obtained show that the eigenvalue approach can give accurate solutions of equations in Laplace domain.The fractional order has a small effect on the displacement distribution while it has a great effect on the distribution of the other field quantities.As a generalization of the generalized thermo-elasticity,it is more scientific and comprehensive to take the fractional order generalized thermo-elasticity into consideration when the heat conduction problems are needed to be solved.