基于分数阶理论的两端固定杆热弹动力响应
Thermoelastic Dynamic Response of Rods Fixed at Both Ends based on Fractional Order Theory
郭颖 1杜翠 2马建军3
作者信息
- 1. 河南科技大学土木建筑学院,河南洛阳 471023;河南科技大学机电工程学院,河南洛阳 471023
- 2. 河南科技大学土木建筑学院,河南洛阳 471023;成都信息工程大学软件工程学院,四川成都 610000
- 3. 河南科技大学土木建筑学院,河南洛阳 471023
- 折叠
摘要
基于Ezzat型分数阶广义热弹性理论和Green-Lindsay广义热弹性理论,借助拉普拉斯积分变换及其数值反变换法研究了移动热源作用下两端固定的温度相关性杆一维热弹动力响应问题,得到了无量纲位移、应力和温度沿x方向的分布情况.分别研究了分数阶参数α、2个不同的热松弛时间因子τ0和τ1、温度相关性参数v以及移动热源传播速度v对无量纲位移、应力和温度的影响,结果表明:分数阶参数α对所考虑的无量纲物理量均有明显影响;热松弛时间因子τ0对无量纲温度外的其他2个物理量影响显著,热松弛时间因子τ1仅对无量纲温度的影响最为显著;随着温度相关性参数v和移动热源传播速度v增大,各物理量呈逐渐减小的状态.
Abstract
Based on Ezzat's fractional order generalized thermoelastic theory and Green-Lindsay generalized thermoelastic theory,the one-dimensional thermoelastic dynamic response issue of temperature-dependent rods fixed at both ends under the action of moving heat sources was studied by means of Laplace integral transform and its numerical inverse transform.The distribution of non-dimension displacement,stress and temperature along the x-direction was obtained.The effects of fractional order coefficient α,two different thermal relaxation time factors r0 and τ1,temperature correlation parameter v and moving heat source propagation velocity v on non-dimension displacement,stress and temperature were studied,respectively.The results show that fractional order coefficient α has obvious effects on the non-dimension physical quantities considered.The thermal relaxation time factor τ0 has significant influence on the other two physical quantities except non-dimension temperature,and the thermal relaxation time factor τ1 only has the most significant influence on non-dimension temperature.With the increase of temperature correlation parameter v and moving heat source propagation velocity v,every physical variables gradually decreases.
关键词
Ezzat型分数阶广义热弹性理论/Green-Lindsay广义热弹性理论/温度相关性/杆Key words
Ezzat s fractional order generalized thermoelastic theory/Green-Lindsay generalized thermoelastic theory/temperature-dependent/rod引用本文复制引用
基金项目
国家自然科学基金(11502072)
河南省自然科学基金(222300420153)
2022河洛青年托举项目(2022HLTJZC10)
河南省科技攻关项目(212102310055)
出版年
2024
国家科技期刊平台
NSTL
万方数据