分数阶热弹性理论下中空粘弹性圆柱热弹耦合动力响应

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (22) : 152-159.

论文

郭颖1，熊春宝2，虞跨海1，梁斌1

作者信息 +

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

GUO Ying1,XIONG Chunbao2,YU Kuahai1,LIANG Bin1

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文章历史 +

摘要

基于Ezzat型分数阶广义热弹性理论，引入Kelvin-Voigt粘弹性模型建立了粘弹性中空圆柱热弹耦合动力模型，探讨了粘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，并分析了粘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：粘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。
关键词：分数阶广义热弹性；Kelvin-Voigt粘弹性；Laplace变换；热冲击

Abstract

Based on Ezzat’s fractional order thermoelastic theory, the Kelvin-Voigt viscoelastic model was introduced to establish the thermoelastic coupling dynamic model of viscoelastic hollow cylinder, and the dynamic response of a viscoelastic hollow cylinder subjected to a thermal shock on outer surface is investigated. The inner and outer surfaces of the hollow cylinder are constrained to some extent. The governing equations of the problem based on the fractional order thermoelastic theory are formulated and solved by means of Laplace transform and its numerical inversion. The non-dimensional temperature, displacement, radial stress and hoop stress are thusly obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of the viscoelastic relaxation time and fractional coefficient on the variations of the physical variables considered. The results show that the viscoelastic relaxation time has an 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.
Key words: Fractional order thermoelastic; Kelvin-Voigt viscoelastic; Laplace transform; Thermal shock

导出引用

郭颖1，熊春宝2，虞跨海1，梁斌1. 分数阶热弹性理论下中空粘弹性圆柱热弹耦合动力响应[J]. 振动与冲击, 2022, 41(22): 152-159

GUO Ying1,XIONG Chunbao2,YU Kuahai1,LIANG Bin1. Thermoelastic coupled dynamic response of a hollow viscoelastic cylinder based on the fractional order thermoelastic theory[J]. Journal of Vibration and Shock, 2022, 41(22): 152-159

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