弹性半空间热冲击问题的广义热弹性解  

Generalized Thermoelastic Solutions to the Problems of Thermal Shock on Elastic Half Space

作　　者：王颖泽[1] 王谦[1] 刘栋[1] 宋新南[1] 

机构地区：[1]江苏大学能源与动力工程学院,江苏镇江212013

出　　处：《应用数学和力学》2014年第6期640-651,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11102073);中国博士后科学基金(2012M511207);江苏高校优势学科建设项目(PAPD)~~

摘　　要：基于Laplace变换技术及其极限定理,推导了基于分数阶积分的不同广义热弹性理论模型下弹性半空间受热冲击作用的渐近解,该渐近解可以准确地揭示热量在弹性体内传播的波动特性,并可以捕捉到受热冲击作用在弹性波波前位置处产生的阶跃现象.通过对热冲击下弹性波的传播及热弹性响应的渐近求解及结果分析,比较了不同广义热弹性理论对于热冲击问题的预测能力,并揭示了热传输能力的不同对于热弹性行为的影响.Based on the Laplace transform technique and its limit theorem, the asymptotic solu- tions to the problems of thermal shock on elastic haft space were derived according to different generalized thermoelasticity models with the fractional order calculus introduced. The wave-like properties of heat propagation in elastic media were revealed accurately by these asymptotic so- lutions, and the jumps at the elastic wave fronts induced by thermal shock were also captured. The elastic wave propagation and the thermoelastic responses of displacement, temperature and stress fields were studied. The predictive abilities of the different generalized thermoelasticity models for thermal behaviors under thermal shock were compared, and the influence of the fractional order parameter on thermal behaviors was also be analyzed. The results show that, the molecular diffusion of heat has notable influence on the heat wave propagation, the re- spouse zones of related physical fields and the jump peak values of the temperature and stress fields, hut it has little effect on the thermoelastic wave propagation.

关 键 词：广义热弹性 分数阶积分 渐近解 热冲击 

分 类 号：O343.6[理学—固体力学]