A mathematical simulation to synchronization of a bluff structure

Abstract

When the periodic vortex-shedding frequency of a bluff structure “locks-in” with one of the natural frequencies of the structure, the state is termed synchronization. When this lock-in or detuning state persists over a considerable period of time, fatigue stresses become predominant which then may lead to structural damage and even failure. Vortex-excited oscillations of bluff structures are one of the important problems in wind engineering, and wake oscillator models, especially the Van der Pol or Rayleigh type, have been studied profoundly over the last 20 odd years. The approach of most researchers is to couple one form of the Rayleigh oscillator with the conventional equation of motion of a single degree of freedom system. It is emphasized though that, depending on the form of the Rayleigh equation chosen, convergence to the solution may not be guaranteed, and the problem becomes ill-defined. The proposed semi-empirical model is of the coupled Rayleigh wake-oscillator type with the equation of motion containing a series term for the forcing function. The paper highlights the mathematical suitability of the proposed form for the aerodynamic response of an isolated structure.