Linear Stability Approach to Explain Lock-In Transition and Time Sharing in Vortex-Induced Vibrations of Slender Structures

In this paper, we use a linearized version of a wake oscillator model in order to understand VIV of flexible structures. By a simple analytical development on the stability of an infinite cable/wake system, we demonstrate the existence a temporal instability. The theoretical study is pushed further to finite structure, a tensioned cable, for which modes frequency, amplitude growth rate in time and velocity range of instability are easily derived. The developed concepts are used to explain experimentally observed behaviours of a low flexural rigidity tensioned beam undergoing VIV.