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.
Highlights
Sided, bottom-founded offshore structures occasionally experience sustained vibrations due to drifting ice sheets crushing against them
We introduce a mathematical model for a special type of ice-induced vibrations (IIV) 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
The main difficulty is that these partial differential equations (PDEs) and ordinary differential equations (ODEs) are coupled through boundary conditions for the ice rod deformations on a contact line between the ice rod and the oscillator
Summary
Sided, bottom-founded offshore structures occasionally experience sustained vibrations due to drifting ice sheets crushing against them. These models describe oscillators under an external-time dependent force, which simulates an action of the discrete events of ice failure These models exhibit a resonance effect as a possible source of large IIVs. Other IIV models treat the ice failure as a continuous process (see, for example [4]) and can be applied for large ice velocities. The problem is solved by means of an asymptotic approach and by using a mechanical model for the ice rod deformation during the interaction with the oscillator. The resulting equation for the IIV terms involves many parameters, but a crucial parameter is the ice velocity v The dynamics of such oscillator models can be studied by well-known methods (see, for example [11,12]).
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