热冲击下理想黏结三明治板的分数阶广义热弹性问题分析  

Analysis on fractional-order generalized thermoelastic problem for ideal adhesion sandwich plate under thermal shock

作　　者：徐业守 徐赵东[1] 何天虎[2] 陈锦祥[1] 张永胜[3] 胡健[3] 王康建[1] Xu Yeshou;Xu Zhaodong;He Tianhu;Chen Jinxiang;Zhang Yongsheng;Hu Jian;Wang Kangjian(Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing 210096 , China;School of Science, Lanzhou University of Technology, Lanzhou 730050 , China;Jiangsu Provincial Architectural Design and R esearch Institute Ltd. , Nanjing 210019 , China)

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,南京210096 [2]兰州理工大学理学院,兰州730050 [3]江苏省建筑设计研究院有限公司,南京210019

出　　处：《东南大学学报（自然科学版）》2017年第1期130-136,共7页Journal of Southeast University：Natural Science Edition

基　　金：国家杰出青年科学基金资助项目(51625803);国家自然科学基金资助项目(11572088);中青年科技创新领军人才资助项目;江苏省"333人才培养工程"资助项目

摘　　要：为了研究对称热冲击作用下三明治板的广义热弹动态响应,假定三明治板连接界面处为零阻抗理想黏结,材料特性参数随温度变化,采用分数阶广义热弹性理论,给出了层合板广义热弹耦合的控制方程.基于拉普拉斯变换及其数值反变换对控制方程进行求解,得到了无量纲温度、位移及应力的数值解.重点讨论了热传导系数、密度和比热容等材料参数在界面处的变化对热传递及结构响应的影响,同时考虑了分数阶参数及温度相关性参数的影响效应.计算结果表明,温度、位移和应力随界面处材料热传导系数、密度和比热容的减小而增加;分数阶参数对温度和应力的影响较大,对位移影响较小;温度、位移和应力的幅值随温度相关性参数的增大而减小.界面处材料热传导系数、密度和比热容的减小促进热沿板厚方向的传导,分数阶理论和材料的温度相关性对温度、位移和应力的分布影响显著.To investigate the generalized thermoelastic dynamic response of a sandwich plate subjected to symmetrical thermal shock,assuming that the value of thermal impedance at the interface is zero with ideal adhesion and the material properties change with the temperature,the governing equations of the layered plate with generalized thermoelasticity coupling are formulated based on the fractional order generalized thermoelasticity theory.The governing equations are solved based on Laplace transform and its numerical inversion,and the numerical values of the non-dimensional temperature,displacement,and stress are obtained.The effects of material parameters alteration including the thermal conductivity,density and heat capacity at the interface on the heat transfer and structure response are studied,and the effects of the fractional order parameter and temperature-dependent parameter are considered at the same time.The numerical results show that the values of temperature,displacement and stress increase with decreasing thermal conductivity,density and heat capacity at the interface.The fractional order parameter has a significant effect on temperature and stress,and a slight effect on displacement;the amplitudes of temperature,displacement,and stress decline with increasing temperature-dependent parameter.The decreases of thermal conductivity,density and heat capacity at the interface promote the heat transfer through the thickness direction of the plate,and the fractional-order theory and material temperature dependence have significant effects on the distributions of temperature,displacement,and stress are significant.

关 键 词：分数阶广义热弹性理论 对称层合板 温度相关性 拉普拉斯变换 

分 类 号：O343.6[理学—固体力学]