| 多频参激—涡激联合作用下顶张力立管分岔分析 |
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| 引用本文： | 张昕涛,赵珧冰,蔡绍辉,陈林聪.多频参激—涡激联合作用下顶张力立管分岔分析[J].海洋工程,2023,41(5):16-24. |
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| 作者姓名： | 张昕涛 赵珧冰 蔡绍辉 陈林聪 |
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| 作者单位： | 1. 华侨大学 土木工程学院，福建 厦门 361021；2. 福建省智慧基础设施与监测重点实验室，福建 厦门 |
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| 基金项目： | 国家自然科学基金面上资助项目（12272139）；福建省自然科学基金面上资助项目（2022J01290）；福夏泉国家自主创新示范区协同创新平台项目（3502ZCQXT2022002） |
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| 摘 要： | 复杂海洋环境中，顶张力立管顶部平台受到不同分量叠加的波浪作用，导致其轴向张力与多个频率相关，系统产生多频参激与涡激的联合振动，其动力学行为变得更为复杂，尤其是分岔和混沌等非线性振动特性有待进一步分析。首先，基于欧拉—伯努利梁理论，引入范德波尔尾流振子，建立和推导受多频参激—涡激联合作用下立管的动力学模型及其运动微分方程；接着，利用伽辽金法得到离散后的常微分方程组，采用多尺度法得到系统共振响应的调谐方程；最后，通过数值算例探究系统在多源和多频载荷联合作用下的共振响应。结果表明：对于多频参数激励，其中一个参数激励幅值在立管振动中起主导作用，而另一个会引起分岔的位置、数量和性质发生改变；随质量—阻尼参数增大，系统共振响应幅值整体先增大后减小，各分岔点出现的位置整体先向泄涡频率较大处移动，随后向泄涡频率较小处移动；质量—阻尼参数的变化还可能诱使系统发生倍周期分岔和混沌现象，危害结构安全。此外，采用直接数值积分求解微分方程组，验证近似分析结果，两者吻合较好。
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| 关 键 词： | 顶张力立管 涡激振动 多频参激振动 分岔与混沌 |
| 收稿时间： | 2022/10/6 0:00:00 |
| 修稿时间： | 2022/12/20 0:00:00 |
Bifurcation analysis of top tension riser under multi-frequency parametric and vortex excitations simultaneously |
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| ZHANG Xintao,ZHAO Yaobing,CAI Shaohui,Chen Lincong.Bifurcation analysis of top tension riser under multi-frequency parametric and vortex excitations simultaneously[J].Ocean Engineering,2023,41(5):16-24. |
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| Authors: | ZHANG Xintao ZHAO Yaobing CAI Shaohui Chen Lincong |
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| Abstract: | Considering the complex marine environment, the floating platform of the top tension riser is excited by the waves superposed by multi-frequency components. As a result, the riser tension is related to the multi-frequency, causing the riser to undergo multi-frequency parametric and vortex-induced vibrations simultaneously. The dynamic behaviors of the riser become more complex, especially the non-linear vibration characteristics, e. g. , bifurcations and chaos, whose phenomena should be further analyzed. Firstly, based on the Euler-Bernoulli beam theory, introducing the van der Pol wake oscillator, a dynamic model and differential equations of the riser are established and derived under the combining effects of multi-frequency parametric and vortex-induced vibrations. Then, the ordinary differential equations are obtained using the Galerkin method, and the system modulation equations are obtained using the multi-scale method. Finally, some numerical examples are presented to explore the resonance response of the system subjected to multi-type and multi-frequency external excitations. Numerical results show that: considering multi-frequency parametric excitations, one of the parametric excitation amplitudes plays a dominant role in the riser vibrations, while another will cause some variations of bifurcation position, number and properties. As the mass-damping parameter increases, the overall amplitude of the system resonance response increases and then decreases, and the locations of the bifurcation points generally move towards the higher vortex release frequency and then towards the lower vortex release frequency; the changes in the mass-damping parameter may also induce period-doubling bifurcations and chaos motions, this may jeopardize structural safety. In addition, direct numerical integration is used to solve differential equations. The approximate analysis and numerical integration results agree well. |
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