Wave Induced Vibrations of Flexible Cylinders
Authors: Verley R.L.P. , Every M.J. 
Published: October 2008

ABSTRACT
The wave induced stresses on similar rigid and flexible vertical cylinders have been compared to establish the effects of flexibility.
Eddy shedding causes vibration which is due to the. complex. interaction of structural dynamic and fluid dynamic forces. Vibration was induced when the frequency (Mathematical equation available in full paper) exceeded unity.
The paper describes a three stage experimental investigation into the important parameters controlling the vibration for single isolated cylinders, two cylinders in close proximity and finally a group of 12 cylinders.

INTRODUCTION
Considerable progress has been made in the determination of wave loading of structures since Morison et al1 postulated that the total force on a structure could be considered to be the sum of a drag term and an inertia term, considered separately.
Keulegan and Carpenter2 showed how the coefficient associated with each of these terms must be related to the wake through a parameter VmaxT/D, subsequently known as the Keulegan-Carpenter number. In wave motion the Keulegan-Carpenter number controls the wake to a far greater extent than Reynolds number, as it takes into account the time necessary for a wake to form and compares it with that available before flow-reversal occurs every half wave cycle. Several experimenters, notably Sarpkaya and Tuter3 have produced accurate results for these coefficients and for the lift coefficient. However, these experiments have been conducted in the special case of oscillatory flow, where the particle paths are linear.
In waves the motion is. orbital and also decays with depth, however Bidde4 has shown that the variation of Cd with Keulegan-Carpenter number is very similar to that obtained in oscillatory flows.
Isaacson and Maull5 have indicated the effect on the coefficients of the decay of motion with depth and, by looking at the pressure distribution around a cylinder, have emphasised the relationship between the shed vortices, their length of correlation, and the values of the coefficients.
The physical mechanisms affecting the values of the two coefficients are now reasonably understood however, very little attention has so far been paid to the problem occuring when several members are in close proximity, or when a member is flexible.
Banks of conductor tubes contain several relatively flexible members close together and the fluid loading on them is likely to be the result of complex interactions. The present investigation was undertaken to provide information on the stressing In members of such banks of conductor tubes, and was In 3 stages.
The first stage investigated the loading on a single. isolated cylinder. The aim was to" identify the main parameters governing the vibration response and examine the possibility of fluid/ structure interactions similar to those found in the steady current induced vibrations of structures7.
The second stage considered the effect on the governing parameters of another similar cylinder in close proximity. The cylinders were set both in-line (with respect to the wave advance) and beside each other, at various separations.