基于分数阶热弹性理论的圆形隧洞热弹性耦合动力响应

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摘要基于分数阶热弹性理论，研究了热/力源作用下无限大土体中圆形隧洞的热弹性耦合瞬态动力响应。建立了圆形隧洞内壁面受到随时间变化的热、力冲击作用下周围土体的控制方程，利用Laplace变换得到了土体的无量纲温度增量、径向位移、径向应力和环向应力等的解析表达式。在此基础上，利用Laplace逆变换Crump数值反演法得到了土体在时间域的动力响应。数值分析了分数阶参数对热/力源条件下土体的温度、径向位移、径向应力和环向应力的影响。研究表明：热源作用下分数阶参数对径向位移的影响较小，对温度增量、径向应力和环向应力影响较大。而在热力共同作用下，分数阶参数对土体的温度增量影响显著，而对径向位移、径向应力和环向应力的影响较小。随着剪切模量的增加，位移的峰值逐渐减小.

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	闻敏杰1
	2
	徐金明2
	熊厚仁2

关键词 ：圆形隧洞, 分数阶, 广义热弹性理论, 动力响应, Laplace变换

Abstract：Based on the generalized fractional order thermo-elasticity theory, coupled dynamic response of a cylindrical tunnel in an infinite soil under the action of heat/power source was investigated with the analytical method.The governing dynamic equations of the surrounding soil under time-varying thermal or force impact on inner wall surface of the circular tunnel were established.The analytical expressions for dimensionless temperature increment, radial displacement, radial stress and circumferential stress of soil body were obtained using Laplace transformation.Then, dynamic responses of soil body in time domain were obtained with Laplace Inverse Transformation and Crump numerical inversion method.Effects of fractional order parameters on soil body’s temperature, radial displacement, radial stress and circumferential stress under heat/power source were analysed numerically.It was shown that fractional order parameters have less influence on soil radial displacement, but have larger influence on soil temperature increment, radial stress and circumferential stress under action of heat source; fractional order parameters have significant influence on soil temperature increment, but have less influence on soil radial displacement, radial stress and circumferential stress under the joint action of heat and power sources; with increase in shear modulus, displacement peak values gradually decrease.

Key words： cylindrical tunnel fractional order generalized thermo-elasticity theory dynamic response Laplace transformation

收稿日期: 2018-10-18 出版日期: 2020-10-28

引用本文:

闻敏杰1，2，徐金明2，熊厚仁2. 基于分数阶热弹性理论的圆形隧洞热弹性耦合动力响应[J]. 振动与冲击, 2020, 39(21): 89-94.
WEN Minjie1,2, XU Jinming2, XIONG Houren2. Coupled dynamic response of a cylindrical tunnel based on fractional order thermo-elasticity theory. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(21): 89-94.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I21/89

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