The periodic shedding of vortices that accompanies cross flow past a bluff cylinder body can excite the body into resonant transverse oscillations when the vortex shedding and body natural frequencies are sufficiently near to one another. Examples of where these oscillations occur, sometimes with destructive consequences, range from offshore platforms and towers to towed or moored cables. The understanding and prediction of vortex-excited vibrations from the basic principles of fluid and structural mechanics is apparently far in the future, waiting the development of appropriate algorithms and computing machinery. However, immediate engineering needs require that intermediate approaches to predicting these vibrations be developed. Here, one such approach is reviewed. A modified Van der Pol equation is employed as the governing equation for the fluctuating lift on the cylinder and is coupled to the equation for the oscillatory motion of the body. When appropriate choices are made for the empirical parameters in the model, the calculated responses of four spring mounted systems are in good quantitative agreement with the observed responses from wind tunnel experiments. A set of relations is postulated between the empirical parameters and the physical mass and damping parameters that govern the oscillatory response. These relations are then employed with the model to calculate the vortex-excited responses of several other systems. Good quantitative agreement with the measured data is again obtained.
Structures containing bluff cylinders exposed to a flow frequently experience vortex-excited oscillations. To isolate the nature of these oscillations, various investigators [1-8] have experimentally studied the flow-induced vibrations of spring-mounted and elastically mounted cylinders. These studies have revealed a complex fluid-structural interaction which is characterized by a region of flow velocities where the vortex shedding frequency and the cylinder response frequency are locked together at a value near the cylinder natural frequency. Over this velocity range, the amplitudes of both the cylinder response and the oscillating lift force on the cylinder experience a resonant behavior marked by large increases in their magnitudes. Two comprehensive overviews of this important family of fluid-structural interaction problems have recently appeared [9,10].
Several mathematical models which attempt to duplicate the experimental observations have been postulated [11-14]. Thus far, the most successful of these models has been that of the authors . In the present paper, this heuristic mathematical model for vortex-excited oscillations is reviewed and extended to the most recently available experimental results .
A modified Van der Pol equation, containing several empirical constants, is introduced as the governing equation for the oscillating lift force on the cylinder. As originally pointed out by Hartlen and Currie , this type of nonlinear differential equation possesses solutions which qualitatively are similar to the vortex shedding process.