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Licensed Unlicensed Requires Authentication Published by De Gruyter September 24, 2019

Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

Lin Zhao , Weihao Meng , Zhongqiang Zheng EMAIL logo and Zongyu Chang

Abstract

Tethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

MSC 2010: 37Nxx; 65Pxx; 70Kxx; 74Hxx

Acknowledgment

The authors are grateful for the support of National Natural Science Foundation of China (51809245), New Century Talents Program of Ministry of Education of China, the Fundamental Research Funds for Central Universities and Open Program of Key laboratory of Mechanism Theory and Equipment Design of Ministry of Education.

References

[1] A. A. Tjavaras, Q. Zhu, Y. Liu, et al., The mechanics of highly-extensible cables[J], J. Sound Vib. 213(4) (1998), 709–737.10.1006/jsvi.1998.1526Search in Google Scholar

[2] Q. Zhu, Y. Liu, A. A. Tjavaras, et al., Mechanics of nonlinear short-wave generation by a moored near-surface buoy[J], J. Fluid Mech. 381 (1999), 305–335.10.1017/S0022112098003826Search in Google Scholar

[3] J. M. T. Thompson, A. R. Bokaian and R. Ghaffari, Subharmonic and chaotic motions of compliant offshore structures and articulated mooring towers[J], J. Energy Resour. Technol. 106(2) (1984), 191–198.10.1115/1.3231037Search in Google Scholar

[4] H. S. Choi and J. Y. K. Lou, Nonlinear behaviour of an articulated offshore loading platform[J], Appl. Ocean Res. 13(2) (1991), 63–74.10.1016/S0141-1187(05)80063-XSearch in Google Scholar

[5] A. Raghothama and S. Narayanan, Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method[J], Ocean Eng. 27(10) (2000), 1087–1107.10.1016/S0029-8018(99)00025-6Search in Google Scholar

[6] S. Radhakrishnan, R. Datla and R. I. Hires, Theoretical and experimental analysis of tethered buoy instability in gravity waves[J], Ocean Eng. 34(2) (2007), 261–274.10.1016/j.oceaneng.2006.01.010Search in Google Scholar

[7] J. Wang, H. Li, P. Li, et al., Nonlinear coupled analysis of a single point mooring system[J], J. Ocean Univ. China 6(3) (2007), 310.10.1007/s11802-007-0310-4Search in Google Scholar

[8] Z. Y. Chang, C. M. Xu and H. J. Li, Nonlinear dynamic behavior of moored buoy excited by free surface waves [J], China Ocean Eng. 23(3) (2009), 585–592.Search in Google Scholar

[9] O. Gottlieb and S. C. S. Yim, Nonlinear oscillations, bifurcations and chaos in a multi-point mooring system with a geometric nonlinearity [J], Appl. Ocean Res. 14(4) (1992), 241–257.10.1016/0141-1187(92)90029-JSearch in Google Scholar

[10] A. Umar and T. K. Datta, Nonlinear response of a moored buoy [J], Ocean Eng. 30 (2003), 1625–1646.10.1016/S0029-8018(02)00144-0Search in Google Scholar

[11] A. Umar, T. K. Datta and S. Ahmad, Complex dynamics of slack mooring system under wave and wind excitations [J], Open Oceanogr. J. 4(1) (2010), 9–31.10.2174/1874252101004010009Search in Google Scholar

[12] K. Ellermann, E. Kreuzer and M. Markiewicz, Nonlinear dynamics of floating cranes [J], Nonlinear Dyn. 27 (2002), 107–183.10.1023/A:1014256405213Search in Google Scholar

[13] K. Ellermann, Dynamics of a moored barge under periodic and randomly disturbed excitation [J], Ocean Eng. 32 (2005), 1420–1430.10.1016/j.oceaneng.2004.11.004Search in Google Scholar

[14] Z. Wang, T. McCarthy and M. N. Sheikh, Taut-slack algorithm for analyzing the geometric nonlinearity of cable structures [C], 21st International offshore and polar engineering conference, United States, ISOPE-2011, (2011), 188–194.Search in Google Scholar

[15] V. J. Kurian, M. A. Yassir, C. Y. Ng and I. S. Harahap, Nonlinear dynamic analysis of multi-component mooring lines incorporating line-seabed interaction[J], Res. J. Appl. Sci. Eng. Technol. 6(8) (2013), 1428–1445.10.19026/rjaset.6.3967Search in Google Scholar

[16] Z. F. Qi, L. J. Jia, Y. F. Qin, et al., Dynamic modeling and simulating analysis of submersible buoy system[C], Appl. Mech. Mater. Trans Tech Publications 475 (2014), 1391–1396.10.4028/www.scientific.net/AMM.475-476.1391Search in Google Scholar

[17] Q. Huang and G. Pan, Research on 3-D motion simulation of mooring buoy system under the effect of wave[C], International Conference on Intelligent Robotics and Applications, pp. 136–147, Springer, Cham, 2015.10.1007/978-3-319-22879-2_13Search in Google Scholar

[18] Z. Chang, Y. Tang, H. Li, et al., Analysis for the deployment of single-point mooring buoy system based on multi-body dynamics method[J], China Ocean Eng. 26(3) (2012), 495–506.10.1007/s13344-012-0037-xSearch in Google Scholar

[19] X. Zhu and S. Y. Wan, Dynamic analysis of a floating spherical buoy fastened by mooring cables[J], Ocean Eng. 121 (2016), 462–471.10.1016/j.oceaneng.2016.06.009Search in Google Scholar

[20] Z. Ballard and B. P. Mann, Two-dimensional nonlinear analysis of an untethered spherical buoy due to wave loading[J], J. Comput. Nonlinear Dyn. 8(4) (2013), 041019.10.1115/1.4024887Search in Google Scholar

[21] R. G. Dean and R. A. Dalrymple, Water wave mechanics for engineers and scientists[M], Singapore: world scientific publishing Co Inc, 2 (1991).10.1142/1232Search in Google Scholar

[22] J. H. Michell, The highest waves in water [J], London Edinburgh Dublin Philos. Mag. J. Sci. 36(222) (1893), 430–437.10.1080/14786449308620499Search in Google Scholar

[23] M. Cencini, F. Cecconi and A. Vulpiani, Chaos: from simple models to complex systems[M], World Sci. 17(2009), 111–124.10.1142/7351Search in Google Scholar

Received: 2018-01-10
Accepted: 2019-06-19
Published Online: 2019-09-24
Published in Print: 2020-02-25

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