Abstract

We report characteristics of Vortex Induced Vibration (VIV) for a cylinder attached to a bi-stable spring, which, unlike linear springs, has two potential wells. We use a Wake Oscillator Model (WOM) as well as an in-house CFD code to study this problem. For small inter-well separation, we observe a widening of the range of reduced velocities over which lock-in occurs. To explain this result, we formulate a theory based on the kinetic energy budget of the cylinder, which balances the rate of energy production and energy dissipation. For harmonic oscillations and large mass ratio, the theory suggests the existence of a universal relationship between the amplitude and frequency of the structure during the lock-in, which we term as the Equilibrium Constraint. Preliminary CFD simulations support the existence of the Equilibrium Constraint.

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