A mathematical analysis of an extended model describing sea ice-induced frequency lock-in for vertically sided offshore structures

• Published in: Nonlinear Dynamics
• Main Authors: Abramian, Andrei K. (author), Vakulenko, Sergei A. (author), van Horssen, W.T. (author)
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2021
• Subjects: Ice induced vibration; Lock-in; Moving contact; Negative friction; Quasi-mode; Sea ice
• Online Access: http://resolver.tudelft.nl/uuid:2b261e69-7cbb-48c5-a430-171d4967395b; https://doi.org/10.1007/s11071-021-07089-5

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”. Mathematical Physics