NONLINEAR ICE ROD-STRUCTURE VIBRATIONS

Abstract eng:
In this paper, we introduce a new nonlinear model for the moving ice rod-structure interaction. Nonlinear vibrations of that system is a complicated process, which involves an ice failure, as a result of the interaction between a moving ice and a structure. Here we propose a model, which develops the known models in this field, in particular, the Matlock-Sodhi model. Similar to the Matlock model, a structure is considered as a single oscillator. In this paper, we study the ice rod-structure interaction in more details. The deformations of the ice rod are described taking into account a permanent contact between the oscillator and the rod. For calculation of the oscillator-ice rod interaction, an extrusion effect is taken into account. The aforementioned effects make the problem more complicated: partial differential equations (PDE’s) for the ice rod and ordinary differential equations, (ODE’s) for the structure are involved. The main difficulty of the problem is that these PDE and ODEs are coupled via boundary conditions for ice rod interaction force and displacement. Nonetheless, it is possible to resolve this problem using a new asymptotic approach. This approach allows us to find the ODE for the oscillator, where the ice displacement is excluded. This equation describes nonlinear oscillations of the oscillator. The terms in that equation admit transparent physical interpretations and relate to: 1) the effect of water extrusion under an ice rod pressure, which leads to a particular type of a friction force and nonlinear effects; 2) the contact interaction between ice rod and the oscillator, which leads to additional nonlinearities and to the oscillator frequency shift. The main result of the asymptotic investigation and numerical simulations is the origin of a negative friction for some ice rod velocities. Moreover, the resonance like peak shape of the amplitude on velocity dependence is a result of an instability of the vibrations regime. The investigation of an instability onset for these vibrations lead us to the conclusion that instability can be the reason of a lock-in regime of vibrations.

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