海洋立管双模态动力学分岔分析  

Bifurcation Analysis of Dual-Mode Dynamics for Marine Risers

作　　者：孙云卿 吴志强[1] 章国齐 王远岑 SUN Yunqing;WU Zhiqiang;ZHANG Guoqi;WANG Yuancen(Department of Mechanics,Tianjin University,Tinajin 300350,P.R.China)

机构地区：[1]天津大学力学系,天津300350

出　　处：《应用数学和力学》2020年第5期480-490,共11页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划(973计划)(2014CB046805);国家自然科学基金(11672349,11372211)。

摘　　要：为研究剪切流作用下顶张力立管的涡激振动响应规律,将立管简化为Euler-Bernoulli梁模型,用van der Pol尾流振子描述流体的作用,建立了立管涡激振动的非线性动力学模型.基于二阶Galerkin模态离散所得常微分方程组,采用谐波平衡法、Poincaré映射方法和Lyapunov指数法分析系统响应特点.研究结果表明:随着流速的增加,系统响应在周期运动和概周期运动间多次转换,其中周期解区域对应系统的涡激共振区;谐波平衡法结果能够较准确地预测涡激共振区周期解的振幅和频率,以及非涡激共振区概周期解的主要频率成分.To study the vortex-induced vibration(VIV)of top tension risers(TTRs)under shear flow,the non-linear dynamic model of VIV for TTRs was constructed,in which the riser was simplified as an Euler-Bernoulli beam model and the van der Pol wake oscillator was used to describe the effect of fluid.Based on the 2 nd-order Galerkin modal discretization model,the harmonic balance method,the Poincarémapping method and the Lyapunov exponential method were used to reveal the system response characteristics.The results show that periodic responses and quasi-periodic responses occur alternately with the increase of the flow velocity,and the periodic response region corresponds to the vortex-induced resonance region.The approximate periodic solution obtained with the harmonic balance method can predict the amplitude and frequency of the periodic solution in the vortex-induced resonance region,and the main frequency components of the quasi-periodic solution in the non-vortex-induced resonance region.

关 键 词：涡激振动 尾流振子 谐波平衡法 POINCARÉ映射 Lyapunov指数法 多模态 

分 类 号：P756[天文地球—海洋科学] TE95[石油与天然气工程—石油机械设备]