Dynamic Response Of Piles To Vortex Shedding In Oscillating Flows
Authors: Sarpkaya T. , Rajabi F. 
Published: October 2008

ABSTRACT
An elastically-mounted cylinder may undergo hydroelastic transverse oscillations in harmonic flow when the reduced velocity, Ur= Um/fnD, is about 5.5. At perfect synchronization, the Strouhal number remains constant throughout the cycle and the vortex-shedding frequency locks on to the natural frequency of the cylinder. The lift coefficient is amplified by a factor of about two relative to that for a stationary cylinder in harmonic flow. The relative amplitude of oscillation for both smooth and rough cylinders is a unique function of the response parameter Rp.

INTRODUCTION
The individual members or small groups of members of a deep-water steel platform structure are seldom, if ever, designed to preclude the occurrence of hydroelastic oscillations under the action of waves and/orcurrents. The dynamic magnification of relatively small loads as a consequence of synchronized oscillations rather than statically-applied design-wave loads can give rise to critical stresses and fatigue. Thus, the prediction of the dynamic behavior of individual members as well as that of the entire structure is important. This, in turn, requires the determination of the critical values of the governing parameters and of the amplification factors for the corresponding force-transfer coefficients.
The non-linear vibration of elastically-mounted structures in oscillating flows have not been sufficiently explored. While much progress has been made regarding the in-line and transverse forces acting on stationary structures and regarding the oscillations of elastic structures in steady flows1, there has been relatively little work on the complex dynamic response of elastic structures to oscillating flows.
Laird2 explored the effects of support flexibility by oscillating a vertical cylinder through still water. He found that (i) the forces acting on a flexibly supported oscillating cylinder can exceed 4.5 times the drag force of the cylinder rigidly-mounted while moving at a uniform velocity equal to the maximum velocity during the oscillation; and that (ii) a cylinder, flexible enough to have transverse oscillations with amplitudes more than half the diameter, while performing large amplitude oscillations in water, tends to oscillate transversely at the eddy frequency and to vibrate at twice the eddy frequency in the in-line direction.
Vaicaitis3 investigated the response of deepwater piles due to cross-flow forces generated by wind induced ocean waves. The resulting cross-flow forces were treated as random processes in time-space domain and are assumed to be dependent on fluid velocities and vortex shedding processes.
Verly and Every4 measured wave-induced stress on similar rigid and flexible vertical cylinders in a wave channel at relatively low Keulegan-Carpenter numbers. Even though they were unable to correlate their data with any suitable parameter governing the motion, they concluded that the vibration is caused by the cylinder's response to eddy shedding and that there is no fluid-structure interaction. They found that the vibration occurs if Ur is greater than about unity for any natural frequency, wave frequency, and damping. The reduced velocity U never reached high enough values in Verly and Every?s experiments for the cylinder to undergo self-excited oscillations, as the present investigation has shown.