Multifrequency excitation of an inclined marine riser under internal resonances
Online Publication Date2019-07-26
Print Publication Date2020-01
Embargo End Date2020-07-26
Permanent link to this recordhttp://hdl.handle.net/10754/656500
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AbstractWe study the multifrequency excitation of an inclined marine riser under two-to-one and three-to-one internal resonances. The riser model accounts for the initial static deflection, self-weight, and mid-plane stretching nonlinearity. By tuning the initial applied tension and configuration angles of the riser, the ratio between its first and third natural frequencies approaches two. In another case, the ratio between its first and fifth natural frequencies approaches three. As recently revealed by experimental observations, a riser can experience multifrequency vortex-induced vibrations. Hence here, the excitation frequencies are tuned such that one frequency is near the first primary resonance, while the other frequency is near the second primary resonance. The multiple-timescale perturbation method is used to analyze the nonlinear motion of the riser considering the internal resonances. Frequency response results of the perturbation method are compared to a Galerkin solution, which show good agreement. The perturbation results in the two-to-one internal resonance case demonstrate that increasing the forcing amplitude at the second primary resonance suppresses the energy exchange due to internal resonance and reduces the likelihood of Hopf bifurcations, while an opposite trend is observed in the three-to-one internal resonance case. Then, the dynamic solutions of the modulation equations of the perturbation method are analyzed using the Floquet theory to examine the post-Hopf bifurcation response. The limit cycle responses in both internal resonance cases exhibit several period doubling bifurcations possibly leading to quasi-periodic and other complex motions, which can endanger the life of the riser.
CitationAlfosail, F. K., & Younis, M. I. (2019). Multifrequency excitation of an inclined marine riser under internal resonances. Nonlinear Dynamics. doi:10.1007/s11071-019-05136-w
SponsorsWe acknowledge the financial support of King Abdullah University of Science and Technology and Saudi Aramco.