Abstract
The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.
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References
Bhaskara Rao, D. S. and Panneer Selvam, R., 2016. Response analysis of tension-based tension leg platform under irregular waves, China Ocean Eng., 30(4), 604–614.
Bulian, G., 2006. Nonlinear parametric rolling in regular waves: An approximate analytical solution for the response curve in the region of first parametric resonance, J. Ship Res., 50(3), 239–249.
Bulian, G., Francescutto, A., Umeda, N. and Hashimoto, H., 2008. Qualitative and quantitative characteristics of parametric ship rolling in random waves in the light of physical model experiments, Ocean Eng., 35(17–18), 1661–1675.
Chang, B.C., 2008. On the parametric rolling of ships using a numerical simulation method, Ocean Eng., 35(5–6), 447–457.
Dunwoody, A.B., 1989a. Roll of a ship in Astern seas–Metacentric height spectra, J. Ship Res., 33(3), 221–228.
Dunwoody, A.B., 1989b. Roll of a ship in Astern seas–Response to GM fluctuations, J. Ship Res., 33(4), 284–290.
Fossen, T.I. and Nijmeijer, H., 2011. Parametric Resonance in Dynamical Systems, Springer.
France, W.N., Levadou, M., Treakle, T.W., Paulling, J.R., Michel, R.K. and Moore, C., 2003. An investigation of head-sea parametric rolling and its influence on container lashing systems, Marine Technology and Sname News, 40(1), 1–19.
Francescutto, A., 2001. An experimental investigation of parametric rolling in head waves, J. Offshore Mech. Arct., 123(2), 65–69.
Galeazzi, R., Blanke, M. and Poulsen, N.K., 2013. Early detection of parametric roll resonance on container ships, IEEE Transactions on Control Systems Technology, 21(2), 489–503.
Ginsberg, S., 1998. Lawsuits Rock APL’s Boat, San Fransisco Business Times.
Haslum, H.A. and Faltinsen, O.M., 1999. Alternative shape of Spar platforms for use in hostile areas, Proceedings of Offshore Technology Conference, Houston, Texas, OTC-10953.
Hong, Y.P., Lee, D.Y., Choi, Y.H., Hong, S.K. and Kim, S.E., 2005. An experimental study on the extreme motion responses of a Spar platform in the heave resonant waves, Proceedings of the 15th International Offshore and Polar Engineering Conference, ISOPE-2005, Seoul, Korea.
Liu, L.Q., Zhou, H. and Tang, Y.G., 2015. Coupling response of heave and moonpool water motion of a truss spar platform in random waves, China Ocean Eng., 29(2), 169–182.
Neves, M.A.S. and Rodríguez, C.A., 2007. Influence of non-linearities on the limits of stability of ships rolling in head seas, Ocean Eng., 34(11–12), 1618–1630.
Neves, M.A.S., Sphaier, S.H., Mattoso, B.M., Rodríguez, C.A., Santos, A.L., Vileti, V.L. and Torres, F.G.S., 2008. On the occurrence of mathieu instabilities of vertical cylinders, Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2008), Estoril, Portugal, Vol. 1, 619–627.
Paulling, J.R., 1961. The transverse stability of a ship in a longitudinal seaway, J. Ship Res., 4(1), 37–49.
Pedersen, P., 1980. Stability of the solutions to Mathieu-Hill equations with damping, Ingenieur-Archiv, 49(1), 15–29.
Pettersen, E. and Machado-Damhaug, U.E., 2007. Parametric motion responses for deep draft production units, Proceedings of the 17th International Offshore and Polar Engineering Conference (ISOPE 2007), Lisbon, Portugal, 144–151.
Radhakrishnan, S., Datla, R. and Hires, R.I., 2007. Theoretical and experimental analysis of tethered buoy instability in gravity waves, Ocean Eng., 34(2), 261–274.
Rho, J.B., Choi, H.S., Shin, H.S. and Park, I.K., 2005. A study on Mathieu-type instability of conventional spar platform in regular waves, Int. J. Offshore Polar, 15(2), 104–108.
Spyrou, K.J. and Thompson, J.M.T., 2000. The nonlinear dynamics of ship motions: a field overview and some recent developments, Phil. Trans. R. Soc. Lond. A, 358(1771), 1735–1760.
Spyrou, K.J., 2000. Designing against parametric instability in following seas, Ocean Eng., 27(6), 625–653.
Spyrou, K.J., Tigkas, I., Scanferla, G., Pallikaropoulos, N. and Themelis, N., 2008. Prediction potential of the parametric rolling behaviour of a post-panamax containership, Ocean Eng., 35(11–12), 1235–1244.
Tao, L. and Cai, S., 2004. Heave motion suppression of a Spar with a heave plate, Ocean Eng., 31(5–6), 669–692.
Wang, T. and Zou, J., 2006. Hydrodynamics in deepwater TLP tendon design, J. Hydrodyn., 18(3), 386–393.
Witz, J.A., 1995. Parametric excitation of crane loads in moderate sea states, Ocean Eng., 22(4), 411–420.
Yang, H.Z. and Xiao, F., 2014. Instability analyses of a top-tensioned riser under combined vortex and multi-frequency parametric excitations, Ocean Eng., 81, 12–28.
Yang, H.Z. and Xu, P.J., 2015. Effect of hull geometry on parametric resonances of spar in irregular waves, Ocean Eng., 99, 14–22.
Zhang, L.B., Zou, J. and Huang, E.W., 2002. Mathieu instability evaluation for DDCV/SPAR and TLP tendon design, Proceedings of the 11th Offshore Symposium, Society of Naval Architect and Marine Engineer (SNAME), Houston, 41–49.
Zhao, J., Tang, Y. and Shen, W., 2010. A study on the combination resonance response of a classic Spar platform, J. Vib. Control, 16(14), 2083–2107.
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Foundation item: This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51379005 and 51009093).
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Yang, Hz., Xu, Pj. Parametric Resonance Analyses for Spar Platform in Irregular Waves. China Ocean Eng 32, 236–244 (2018). https://doi.org/10.1007/s13344-018-0025-x
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DOI: https://doi.org/10.1007/s13344-018-0025-x