A mathematical analysis of an extended model describing sea ice-induced frequency lock-in for vertically sided offshore structures
A.K. Abramian (Russian Academy of Sciences (IPME RAS))
Sergei A. Vakulenko (Russian Academy of Sciences (IPME RAS))
W.T. Horssen (TU Delft - Mathematical Physics)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
This paper presents a mathematical analysis of an extended model describing a sea ice-induced frequency lock-in for vertically sided offshore structures. A simple Euler–Bernoulli beam as model for the offshore structure is used, and a moving boundary between an ice floe and the structure itself is introduced. A nonlinear equation for the beam dynamics is found by using an asymptotical approach and a Galerkin procedure. It is shown analytically that a frequency lock-in regime occurs during ice-induced vibrations (IIV), when the dominant ice force frequency is closed to a natural frequency of the structure. For beams, perturbed by small nonlinearities and a small damping, the concept of quasi-modes is introduced. A quasi-mode is a linear combination of the usual eigenmodes. The large time behaviour of solutions at the instability onset is determined by a single quasi-mode, which is maximally linearly unstable.The beam model analysis leads to the conclusion that an interaction between a moving ice floe and a structure can lead to a “negative friction” for particular values of the ice floe parameters. From the analysis presented in the paper it follows that the lock-in regime occurs when simultaneously two phenomena are present: a forcing resonance and a “negative friction”.