深海立管涡激振动双稳态现象
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摘要
为研究深海立管的涡激振动现象,本文在其流固耦合非线性动力学模型中考虑了流体阻尼的平方非线性特性以及结构惯性耦合。基于一阶Galerkin模态离散方程,通过特征值计算分析了流速对系统稳定性的影响,通过Poincaré映射方法分析了流速对响应非线性特征(频率、幅值)的影响。结果表明:涡激振动锁频区范围,可用无阻尼情况下的耦合颤振区来估计;锁频区左右两侧均存在双稳态现象,左侧为概周期运动与锁频运动共存,右侧为锁频运动与小幅周期运动共存。小流速下,响应中同时存在结构模态和涡激模态,锁频时响应表现为结构模态,而大流速时响应只含有涡激模态。
In order to study the vortex-induced vibration of deep-sea riser,the square nonlinearity of fluid damping and the inertial coupling of the structure are considered in the fluid-solid nonlinear coupling dynamic model.Based on the first order Galerkin modal discrete equation,the influence of flow velocity on the stability of the system is analyzed by eigenvalue calculation.The influence of flow velocity on the response nonlinear feature(frequency and amplitude) is analyzed by Poincaré mapping method.The results show that coupled flutter region can be used to estimate the range of frequency-locked region of vortex induced vibration;On both sides of the frequency-locked region,there are two types of bistable phenomena:the coexistence of quasi-periodic motion and locking movement on the left side,the coexistence of small amplitude periodic motion and locking movement on the right side.There are structural modal and vortex modes simultaneously under small flow velocity,and the response is expressed as structural modal.At large flow velocity,the response only contains vortex induced modal.
In order to study the vortex-induced vibration of deep-sea riser,the square nonlinearity of fluid damping and the inertial coupling of the structure are considered in the fluid-solid nonlinear coupling dynamic model.Based on the first order Galerkin modal discrete equation,the influence of flow velocity on the stability of the system is analyzed by eigenvalue calculation.The influence of flow velocity on the response nonlinear feature(frequency and amplitude) is analyzed by Poincaré mapping method.The results show that coupled flutter region can be used to estimate the range of frequency-locked region of vortex induced vibration;On both sides of the frequency-locked region,there are two types of bistable phenomena:the coexistence of quasi-periodic motion and locking movement on the left side,the coexistence of small amplitude periodic motion and locking movement on the right side.There are structural modal and vortex modes simultaneously under small flow velocity,and the response is expressed as structural modal.At large flow velocity,the response only contains vortex induced modal.
引文
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[14]张杰.深海立管参激-涡激联合振动与疲劳特性研究[D].天津:天津大学,2014.Zhang Jie.Vortex-induced vibration and fatigue analysis of deepwater risers considering parametric excitations[D].Tianjin:Tianjin University,2014.(in Chinese)
[15] Purath B T.Numerical simulation of the truss spar ‘Horn Mountain’ using couple[J].Texas A&M University,2005.
[16] Lienhard J H.Synopsis of lift,drag,and vortex frequency data for rigid circular cylinders[M].Technical Extension Service,Washington State University,1966.
[17] Gao Y,Zong Z,Sun L.Numerical prediction of fatigue damage in steel catenary riser due to vortex-induced vibration[J].Journal of Hydrodynamics,Ser.B,2011,23(2):154-163.
[18] de Langre E.Frequency lock-in is caused by coupled-mode flutter[J].Journal of Fluids and Structures,2006,22(6-7):783-791.
[2] Feng C C.The Measurement of vortex-induced effects on flow past stationary and oscillating circular D-section cylinders[J].University of British Columbia,1968.
[3] Brika D,Laneville,et al.Vortex-induced vibrations of a long flexible circular cylinder[J].Journal of Fluid Mechanics,1993.
[4] Khalak A,Williamson C H K.Dynamics of a hydroelastic cylinder with very low mass and damping[J].Journal of Fluids&Structures,1996,10(5):455-472.
[5] Khalak A,Williamson C H K,Khalak A,et al.Fluid forces and dynamics of a hydroelastic structure with very low mass and damping[J].Journal of Fluids&Structures,1997,11(8):973-982.
[6] Khalak A,Williamson C H K,Khalak A,et al.Motions,forces and mode transitions in vortex-induced vibrations at low mass-damping[J].Journal of Fluids&Structures,1999,13(7-8):813-851.
[7] Hartlen R T,Currie I G,Hartlen R T,et al.Lift-oscillator model of vortex-induced vibration[J].Journal of the Engineering Mechanics Division,1970,96(5):577-591.
[8] Bishop R E D,Hassan A Y.The lift and drag forces on a circular cylinder in a flowing fluid[J].Royal Society of London Proceedings,1964,277(1368):32-50.
[9] Iwan W D.The vortex-induced oscillation of non-uniform structural systems[J].Journal of Sound&Vibration,1981,79(2):291-301.
[10] Iwan W D,Blevins R D.A model for vortex induced oscillation of structures[J].Journal of Applied Mechanics,1974,41(3):581.
[11] Facchinetti M L,Langre E D,Biolley F.Vortex shedding modeling using diffusive Van Der Pol oscillators[J].Comptes Rendus Mecanique,2002,330(7):451-456.
[12] Facchinetti M L,de Langre E,Biolley F.Coupling of structure and wake oscillators in vortex-induced vibrations[J].Journal of Fluids and Structures,2004,19(2):123-140.
[13]陈威霖,及春宁.单圆柱涡激振动中的振幅不连续和相位切换现象研究[J].水动力学研究与进展（A辑）,2016,4:441-448.Chen Weilin,Ji Chunning.Vibration amplitude discontinuity and phase jump of vortex-induced vibration of an isolated circular cylinder[J].Chinese Journal of Hydrodynamics(Part A),2016,4:441-448.(in Chinese)
[14]张杰.深海立管参激-涡激联合振动与疲劳特性研究[D].天津:天津大学,2014.Zhang Jie.Vortex-induced vibration and fatigue analysis of deepwater risers considering parametric excitations[D].Tianjin:Tianjin University,2014.(in Chinese)
[15] Purath B T.Numerical simulation of the truss spar ‘Horn Mountain’ using couple[J].Texas A&M University,2005.
[16] Lienhard J H.Synopsis of lift,drag,and vortex frequency data for rigid circular cylinders[M].Technical Extension Service,Washington State University,1966.
[17] Gao Y,Zong Z,Sun L.Numerical prediction of fatigue damage in steel catenary riser due to vortex-induced vibration[J].Journal of Hydrodynamics,Ser.B,2011,23(2):154-163.
[18] de Langre E.Frequency lock-in is caused by coupled-mode flutter[J].Journal of Fluids and Structures,2006,22(6-7):783-791.