实心球体外表面受热冲击作用的广义热弹性分析

Research on Generalized Thermoelastic Problems of A Solid Sphere Subjected to Thermal Shock

基于L-S广义热弹性理论,对实心球体在外表面受均匀热冲击作用下的一维热弹性问题进行研究分析.利用热冲击的瞬时特性,借助Laplace正、反变换技术及贝塞尔函数的极限性质,对控制方程进行解析求解,得到了热冲击作用周期内温度场、位移场及正应力场的渐近解.通过计算得到了热冲击条件下各物理的分布规律以及非傅立叶效应和耦合效应对热弹性响应的影响规律.结果表明,在非傅立叶效应和耦合效应共同影响下,各物理场由波速不同的两组弹性波相互叠加而成,非傅立叶效应的存在削弱了热冲击的作用效果,而耦合效应则在影响热扰动在弹性体内传播的同时也在一定程度上减弱了延迟效应对热冲击的削弱效果.

One-dimensional thermal shock problem for a solid sphere subjected to a sudden heat was investigated by the L-S generalized theory of thermoelasticity. The transient behaviors of thermal shock was considered, some approximate small-time analytical solutions for the temperature, displacement and stress were obtained by means of the Laplace transform and the limit theorem of the Bessel functions. Numerical simulation was conducted, the distributions of each physical fields including temperature, displacement and stress and the influences of the Non-Fourier effect and coupling effect on the thermoelastic response were obtained. Results showed that each physical field was established by the interaction of two elastic waves with different speed, the thermal shock would be weaken by Non-Fourier effect, but this weaken effect could be restrained by coupling effect to some degree.