Energy balanced double oscillator model for vortex-induced vibrations

An improved theoretical basis is developed for representation of vortex-ind uced oscillations of structural elements by models consisting of two couple d oscillators. The mutual forcing terms are based on exact transfer of ener gy from the fluid to the structural oscillator. This leads to a system with distinct frequency locking and resonance when fluid and structural natural frequencies are similar. The present work implements a simple quadratic fl uid damping, but more general fluid damping can be introduced without chang ing the basic features of the model. The response curve for stationary osci llations consists of two distinct branches, separated by jumps in frequency , amplitude, and phase closely resembling experimentally observed free vort ex-induced vibrations. A stability analysis shows that the final part of ea ch branch is unstable, and a transient analysis illustrates the transition between the two modes of oscillation for slowly increasing or decreasing fl uid velocity through the lock-in region. Model calibration is discussed and parameters are identified representing available experimental data for loc k-in frequencies and resonance amplitudes for systems with relative structu ral damping in the interval 1.5-3.0 x 10(-3) and different values of the ma ss ratio.