基于增量谐波平衡方法的Spar平台垂荡纵摇耦合内共振响应研究

PDF(1257 KB)

振动与冲击 ›› 2020, Vol. 39 ›› Issue (1) : 85-90.

论文

杜亚震，王文华，黄一

作者信息 +

Swing-pitch coupled internal resonance responses of Spar platform based on IHBM

DU Yazhen,WANG Wenhua,HUANG Yi

Author information +

文章历史 +

摘要

针对经典的Spar平台垂荡纵摇耦合运动问题，为解决传统小参数摄动方法和时间步进分析方法的不足，提出将增量谐波平衡方法（Incremental Harmonic Balance Method, IHBM）应用于研究其内共振响应特性。根据Floquet稳定性分析理论，对周期解的稳定性和分叉特性进行分析;在此基础上，通过将该方法与增量弧长法相结合，实现了快速、连续获得Spar平台垂荡纵摇耦合周期运动响应的目的;将IHBM计算结果与时域模拟和多尺度法计算结果进行对比，验证了该方法的准确性和高效性，该方法能够准确预测当波浪激励力频率满足一定条件，系统发生内共振时引起的纵摇不稳定运动现象。对于垂荡纵摇耦合产生的概周期运动，该方法结合Floquet理论能准确预测其发生的参数区间，从而为该周期运动的分析提供良好的基础。

Abstract

To overcome shortcomings of the classical perturbation method and the time integration method in analyzing swing-pitch coupled response motion of a Spar platform, the incremental harmonic balance method (IHBM) was proposed to study characteristics of the coupled responses. Floquet stability analysis theory was used to analyze the stability and bifurcation behavior of a periodic solution. Then, IHBM combined with the arc-length method was adopted to realize rapidly and continuously solving the Spar platform’s swing-pitch coupled periodic motion responses. The results using IHBM were compared with those using the time domain simulation and the multi-scale method to verify the correctness and high efficiency of IHBM. It was shown that IHBM can be used to predict pitch unstable phenomena induced by the system internal resonance; it can be combined with Floquet theory to predict parametric intervals of quasi-periodic motion induced by swing-pitch coupled motion to provide a good foundation for quasi-periodic motion analysis.

导出引用

杜亚震，王文华，黄一. 基于增量谐波平衡方法的Spar平台垂荡纵摇耦合内共振响应研究[J]. 振动与冲击, 2020, 39(1): 85-90

DU Yazhen,WANG Wenhua,HUANG Yi. Swing-pitch coupled internal resonance responses of Spar platform based on IHBM[J]. Journal of Vibration and Shock, 2020, 39(1): 85-90

参考文献

[1] 桑松, 石晓, 李长东, 等．深海SPAR平台垂荡-纵摇耦合运动Mathieu稳定性分析[J]. 中国海洋平台，2014, 29(4): 39-40．
SANG Song, SHI Xiao, LI Changdong, et al. Study on mathieu stability of heave-pitch coupled motions of Spar platform in deep sea[J]. China Offshore Platform, 2014, 29(4): 39-40．
[2] 赵晶瑞, 唐友刚, 冯丽梅，等．传统Spar平台垂荡主共振时非线性耦合响应的研究[J]. 应用力学学报，2010, 27(1): 20-27.
ZHAO Jingrui, TANG Yougang, FENG Limei, et al. An study on the nonlinear coupled responses of a classic Spar platform in the heave resonant waves[J]. Chinese Journal of Applied Mechanics, 2010, 27(1): 20-27．
[3] 赵晶瑞, 唐立志, 唐友刚,等. 传统Spar平台垂荡-纵摇耦合内共振响应[J]. 天津大学学报:自然科学与工程技术版，2009, 42(3): 201-207．
ZHAO Jingrui, TANG Lizhi, TANG Yougang, et al. Internal resonant responses of heave-pitch coupled motions of classic Spar platform[J]. Journal of Tianjin University(Science and Technology), 2009, 42(3): 201-207．
[4] Lei H, Liu L, Liu C, et al. The Nonlinear Bifurcation and Chaos of Coupled Heave and Pitch Motions of a Truss Spar Platform[J]. Journal of Ocean University of China,2015, 14(5):795-802.
[5] Shen W, Tang Y. Stochastic analysis of nonlinear coupled heave-pitch motion for the Truss Spar platform[J]. Journal of Marine Science and Application, 2011, 10(4): 471-477．
[6] Koo B J，Kim M H，Randall R E． Mathieu instability of a spar platform with mooring and risers[J]. Ocean Engineering, 2004, 31(17-18): 2175-2208．
[7] Bulian G. Nonlinear parametric rolling in regular waves—a general procedure for the analytical approximation of the GZ curve and its use in time domain simulations[J]. Ocean Engineering, 2005, 32(3):309-330.
[8] Lau S L, Cheung Y K．Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems [J]. Journal of Applied Mechanics, 1981, 48(4): 959-964．
[9] Raghothama A, Narayanan S．Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method [J]. Ocean Engineering, 2000, 27(10): 1087-1107．
[10] Lu W, Ge F, Wu X, et al. Nonlinear dynamics of a submerged floating moored structure by incremental harmonic balance method with FFT[J]. Marine Structures, 2013, 31(4): 63-81．
[11] 唐友刚，刘利琴，张素侠．海洋工程非线性动力学理论与方法[M]．北京：科学出版社，2016．
TANG Yougang, LIU Liqin, ZHANG Suxia. Theory and method of nonlinear dynamics of marine engineering[M]. Beijing: Science China Press,2016.
[12] Huang J L, Su R K L, Li W H, et al. Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances[J]. Journal of Sound & Vibration, 2011, 330(3):471-485.
[13] Cheung Y K. Application of the incremental harmonic balance method to cubic non-linearity systems[J]. Journal of Sound & Vibration, 1990, 140(2):273-286.
[14] Yong-Pyo H, Dong-Yeon L, Yong-Ho C, et al. An experimental study on the extreme motion responses of a spar platform in the heave resonant waves[C]//The Fifteenth International Offshore and Polar Engineering Conference. Seoul: 2005