分数阶热弹性理论下中空黏弹性圆柱热弹耦合动力响应  

Thermoelastic coupled dynamic response of a hollow viscoelastic cylinder based on the fractional order thermoelastic theory

作　　者：郭颖 熊春宝[2] 虞跨海 梁斌 GUO Ying;XIONG Chunbao;YU Kuahai;LIANG Bin(School of Civil Engineering,Henan University of Science and Technology,Luoyang 471023,China;School of Civil Engineering,Tianjin University,Tianjin 300072,China)

机构地区：[1]河南科技大学土木工程学院,河南洛阳471023 [2]天津大学建筑工程学院,天津300072

出　　处：《振动与冲击》2022年第22期152-159,201,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(51975187);河南省高等学校重点科研项目(22A130004)。

摘　　要：基于Ezzat型分数阶广义热弹性理论,引入Kelvin-Voigt黏弹性模型建立了黏弹性中空圆柱热弹耦合动力模型,探讨了黏弹性中空圆柱热弹耦合问题。中空圆柱体内外表面均有一定约束,且在其外表面处施加热冲击作用。给出Ezzat型分数阶双相滞后广义热弹性理论下问题的控制方程,结合Laplace变换和数值反变换技术对控制方程进行求解,最终得到中空圆柱中无量纲位移、温度、径向应力和环向应力的分布规律,并分析了黏弹性松弛时间因子和分数阶系数对各物理量的影响。结果表明:黏弹性松弛时间因子对于无量纲温度外的所有物理量均有明显影响,但对径向应力和环向应力的影响更为明显;分数阶系数对于所有物理量均有明显影响,在曲线峰值或谷值处影响最显著。Based on the Ezzat’s fractional order thermoelastic theory, the Kelvin-Voigt viscoelastic model was introduced to establish the thermoelastic coupled dynamic model of a hollow viscoelastic cylinder, and the dynamic response of the cylinder subjected to a thermal shock on its outer surface was investigated, while the inner and outer surfaces of the hollow cylinder were constrained to some extent. The governing equations of the problem based on the fractional order thermoelastic theory were formulated and solved by means of the Laplace transform and numerical inversion technology. The non-dimensional temperature, displacement, radial stress and hoop stress were obtained and illustrated graphically. In the numerical anaysis, emphasis was focused on investigating the effects of the viscoelastic relaxation time and fractional coefficient on the variation of the physical variables considered. The results show that the viscoelastic relaxation time has obvious effect on all physical variables except the non-dimension temperature and the fractional coefficient has obvious influence on all physical variables, especially at the peak or valley of the curve.

关 键 词：分数阶广义热弹性 Kelvin-Voigt黏弹性 LAPLACE变换 热冲击 

分 类 号：TU473.4[建筑科学—结构工程]