分数阶热弹理论下一维六方准晶杆的动态响应  

Dynamic Response of a One-dimensional Hexagonal Quasicrystal Rod Based on Fractional-order Thermoelastic Theory

作　　者：李颖 刘官厅[1,2] LI Ying;LIU Guan-ting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第2期111-118,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12162027,11962026);内蒙古自治区高等学校科学技术自然科学重点资助项目(NJZZ22574);内蒙古自治区自然科学基金重点项目(2022ZD05);内蒙古师范大学研究生科研创新基金资助项目(CXJJS21120)。

摘　　要：基于分数阶热弹理论,对两端固定的有限长一维六方准晶杆受到移动热源作用时产生的动态响应进行研究。得到了该问题的控制方程,并利用拉普拉斯变换及其数值反演进行求解。对温度、位移、应力关于时间、热源速度、分数阶参数的扰动情况分别进行图像绘制。结果表明:时间与热源速度一定时,位移、温度、应力都会随着分数阶参数的增加而增加,但分数阶参数对位移产生的影响更小。The dynamic response of a finite quasicrystal rod fixed at both ends and subjected to a moving heat source is analyzed based on the fractional-order generalized thermoelastic theory in the paper. Firstly, the governing equations of the one-dimensional hexagonal quasicrystal rod are derived,and then its numerical solution is obtained by using the Laplace transform and its numerical inversion and the disturbance of temperature, displacement and stress to time, moving speed of heat source and fractional order parameters is plotted. It is found in the research that the stress, displacement and temperature increase with the increase of fractional order parameter when the speed of heat source and time keep constant and the existence of phason field leads to the great decrease of stress and displacement.

关 键 词：一维六方准晶杆 分数阶热弹理论 拉普拉斯变换 

分 类 号：O343[理学—固体力学]