On a simple oscillator problem describing ice-induced vibrations of an offshore structure

Abstract

In this paper, a new simple oscillator model is considered describing ice-induced vibrations of upstanding, water-surrounded, and bottom-founded offshore structures. Existing models are extended by taking into account deformations of an ice floe and a moving contact interaction between an ice rod, which is cut out from the floe, and the oscillator which represents the offshore structure. Special attention is paid to a type of ice-induced vibrations of structures, known as frequency lock-in, and characterized by having the dominant frequency of the ice forces near a natural frequency of the structure. A new asymptotical approach is proposed that allows one to include ice floe deformations and to obtain a nonlinear equation for the simple oscillator vibrations. The instability onset, induced by resonance effects for the oscillator and generated by the ice rod structure interaction, is studied in detail.

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

“…As suggested in [2,12] the ice floe is considered as a system of ice rods. Considering only one rod follows from the theory introduced in [35].…”

“…The boundary conditions at x = q(t) (moving boundary) also can be found in many other problems (see for instance [3,10,30,39]) where, oscillations in axially moving cables are considered. The following equation describes the dynamics of the ice rod, which is defined on the semi-infinite domain I t = {x : q(t) < x < ∞} (see [2,35]),…”

“…The ice rod displacement is studied in detail in [2]. We repeat here the main formulas needed for the analysis of (32-33).…”

“…The second theory explains the initiation of the steady regimes by negative damping occurring during an ice structure interaction [5,23]. Based on experiments and field observations some new coupled models for IIV were developed [1,2,9,12,14,16,21,25,33]. In these models the structure is usually described as a one or a two degree of freedom oscillator with a linear or nonlinear structure rigidity.…”

Effect of Maneuvering on Ice-Induced Loading on Ship Hull: Dedicated Full-Scale Tests in the Baltic Sea

“…A lot of effort has been afforded to determine the frequency of ice-induced loads for offshore structures as resonating frequency could cause severe damage to the structure (e.g., [7]). However, the speed of the ship affects the frequency of ice-induced loads.…”