特性参数与温度相关的非局部广义热弹问题的动态响应

摘要

基于 Green-Lindsay广义热弹性理论和 Eringen的非局部弹性理论,研究了材料特性参数与温度相关、受热冲击和应力冲击作用的半无限大体的一维非局部热弹动态响应问题.借助于拉普拉斯积分变换及其数值反变换,经数值求解,得到了无量纲温度、位移、应力的分布规律,并用图形进行表示.分别研究了温度相关的材料特性参数、分数阶参数及非局部效应参数对温度、位移和应力的影响效应,结果表明:温度相关的材料特性参数对各物理量的影响显著;分数阶系数对温度影响较大,对位移和应力影响不大;非局部效应参数对位移和应力有显著影响,对温度影响较小.%Based on Green-Lindsay’s generalized thermoelasticity theory and Eringen’s nonlocal elasticity theory,the problem of dynamic response of a semiinfinite obj ect with temperature-dependent material characteristic parameters to one-dimensional nonlocal thermoelasticity is investigated when the obj ect is subj ected to with temperature-dependent properties and thermal shock and stress shock.By means of La-place integral transform and its numerical inversion,the distributions of the non-dimensional temperature, displacement and stress are obtained with numerical solution and illustrated graphically.The effect of the temperature-dependent material characteristic parameters,fractional-order parameter,and nonlocal effect parameter on temperature,displacement and stress is investigated,respectively.The result shows that the temperature-dependent material characteristic parameters will have an obvious influence on every physical quantities,the influence of fractional-order coefficient on the temperature will be greater,but a little on the displacement and stress,and the nonlocal effect parameter will have a remarkable influence on the dis-placement and stress,but less on the temperature.