摘要
基于分数导数和弹性力学理论,将油气井管杆模型简化为黏弹性圆柱管,建立了轴对称情况下不可压缩黏弹性圆柱管的运动控制方程,由不可压缩性假定直接得到了位移解形式,利用Laplace变换求解得到了油气井管杆环向位移和应力的解析解.数值算例分析结果表明:分数导数的阶数、模型常数比和管杆内外半径比对油气井管杆径向位移有较大的影响,且径向位移随频率变曲线存在峰值,分数导数的阶数和模型常数比越大,则峰值越小,峰值对应的频率越大,而内外半径比的影响则相反;分数导数的阶数、模型常数比和管杆内外半径比对油气井管杆对环向应力和竖向应力有较大的影响,而对径向应力的影响校对较小.
Based on the theory of fractional derivative and elastic mechanics theory,the model of oil and gas wells tube is simplified into a viscoelastic cylindrical tube.The motion control equation of the incompressible viscoelastic cylindrical tube under axial symmetry is established.The displacement solution is directly obtained from the incompressibility assumption.The Laplace transformation is used to solve the circumferential displacement and stress,and analytical solution of the oil and gas wells tube is obtained.The numerical results show that the order of fractional derivative,the ratio of model constant and the ratio of inner radius to outer radius of oil and gas wells tube have great influence on the radial displacement of oil and gas wells tube,and the curve of radial displacement varying with frequency has a peak value.The larger the order of fractional derivative and the ratio of model constant,the smaller the peak value,the larger the frequency corresponding to the peak value,while the influence of the ratio of inner radius and outer radius of oil and gas wells tube is opposite.The order of fractional derivative,the ratio of model constant and the ratio of inner radius to outer radius of oil and gas wells tube have great influence on circumferential stress and vertical stress,but little influence on radial stress.
作者
闫启方
高云飞
张维维
刘林超
YAN Qifang;GAO Yunfei;ZHANG Weiwei;LIU Linchao(College of Architecture and Civil Engineering,Xinyang Normal University,Xinyang 464000,China)
出处
《信阳师范学院学报（自然科学版）》
CAS
北大核心
2020年第3期480-486,共7页
Journal of Xinyang Normal University(Natural Science Edition)
基金
国家自然科学基金项目(U1504505)
河南省科技计划项目(182102310878)
河南省高等学校重点科研项目(19B560008)
信阳师范学院南湖学者奖励计划青年项目(201506)。
关键词
黏弹性
不可压缩
油气井管杆
力学响应
viscoelasticity
incompressible
oil and gas wells tube
mechanical response
