The thermoelastic interactions in an infinite elastic medium with a cylindrical cavity are described in the context of the hyperbolic two-temperature generalized thermoelasticity theory (recently proposed by Youssef and El-Bary, 2018) in which heat conduction in deformable bodies depends upon the difference between the acceleration of conductive temperature and the acceleration of dynamic temperature. The boundary of the cavity is assumed to be stress-free and is subjected to a thermal shock. The problem is formulated to compare between classical generalized thermoelastic model and hyperbolic two-temperature thermoelastic model, on the basis of Lord-Shulman model and hyperbolic two-temperature Lord-Shulman model in a unified way. The Laplace transform method and decoupling of the coupled differential equations are used to solve the problem. Explicit expressions for displacement, stresses and temperature fields are approximated for small-time. Numerical values are displayed graphically for different models and comparison is presented for the illustration of the problem.

在双曲双温广义热弹性理论（Youssef and El-Bary最近提出，2018）的背景下描述了无限弹性介质中具有圆柱腔的热弹性相互作用，其中可变形体的热传导取决于导电温度的加速度和动态温度的加速度。腔的边界被假定为无应力，并且受到热冲击。在Lord-Shulman模型和双曲双温度Lord-Shulman模型的基础上，提出了该问题以比较经典广义热弹性模型和双曲双温度热弹模型。拉普拉斯变换方法和耦合微分方程的解耦用于解决该问题。位移，应力和温度场的显式表达式在短时间内近似。图形化地显示了不同模型的数值，并进行了比较以说明问题。