Dynamic Response Of Acantilever Pile To Vortex Shedding In Regular Waves
Authors: Zedan Mohamed F. , Yeung Jimmy Y. , Salane Harold J. , Fischer F.J. 
Published: October 2008

ABSTRACT
This paper summarizes an experimental investigation of cantilever pile dynamics in response to wave excitation under vortex shedding "lock-in" conditions. The study was carried out in regular waves for two conditions of wave length in relation to water depth. Pile response was measured in terms of top accelerations and bottom strains in both the in-line and transverse directions. The study covered Reynolds numbers from 40 × 103 to 70 × 103 and Keulegan-Carpenter numbers from 10 to 14.5. Results indicate that the vortex shedding frequency is twice the wave frequency for most tests discussed here. Most pile response energy in the transverse direction occurs at the pile natural frequency fn and twice the wave frequency 2fw. As for the in-line direction, most response energy exists at fw and 2fw with a smaller contribution at fn. As "lock-in" is achieved, response in both directions becomes mono-harmonic with a frequency of 2fw. Vortex shedding "lock-in" is shown to produce substantial dynamic amplification of deflection not only in the transverse direction but also in the in-line direction.
The Morison equation so widely used in engineering practice to estimate wave forces, particularly for static structural design, assumes that hydrodynamic excitation will occur at the wave frequency fw. Experimental results presented here suggest that this assumption should be re-examined when vortex shedding is expected to affect force variations substantially, especially near "lock-in" conditions.

INTRODUCTION
Test data presented in this paper were obtained as part of a larger experimental program to study dynamic response of a surface-piercing cantilever pile, fixed at the bottom of a wave tank, to both regular and irregular waves. Full discussion of the complete test program is beyond the scope of this paper; therefore, focus is restricted to pile dynamic response under vortex shedding "lock-in" conditions in regular waves.
Although a cantilever pile is geometrically simple in comparison with many ocean structures such as offshore platforms, it is representative of certain structural geometries that have practical engineering importance. Examples include single-well production caissons, single-standingpiles in marine terminals before capping and individual tethers in a tension leg platform mooring system. Further, geometric simplicity permits a clearer view of the dynamic interaction between hydrodynamic excitation and structural response that occurs during vortex shedding "lockin". Vortex shedding and possibly "lock-in" may have been associated with a number of structural failures reported in the last two decades. One example is the failure of Texas Tower No. 4 off the New Jersey coast (Bidde2).

HYDRODYNAMIC EXCITATION FORCES
Hydrodynamic excitation forces must be specified for offshore structures design. In most cases, the problem reduces to calculating wave forces on cylindrical members. Wave forces can be classified as inertia, drag and lift, the relative importance of which depends on wave length and height in relation to cylinder diameter. Individual members in offshore structures of greatest practical interest are characterized by a ratio of member diameter/wave length less than 1/5. In this region, diffraction effects are usually neglected and therefore are not considered here.