High Harmonic Forces and Predicted Vibrations from Forced In-line and Cross-flow Cylinder Motions

Abstract

String-like ocean structures, such as deep water marine risers are susceptible to a condition of dual lock-in, where both the in-line and transverse natural frequencies are excited due to vortex shedding in the wake. This type of excitation can result in dominant, large amplitude third harmonic forces in the cross-flow direction that do not exist in conditions allowing only cross-flow motion. Forced motions of a rigid cylinder in both the in-line and cross-flow directions are performed to obtain coefficients defining the magnitude of third harmonic lift forces for given cylinder motions. In-line motion amplitude, cross-flow amplitude, phase between in-line and cross-flow motion, and reduced velocity are varied, producing a four-dimensional matrix of data points, at a Reynolds number of 8800. In free vibrations, variation of the effective added mass drives the system to specific steady-state oscillations, under lock-in conditions. These free vibration steady-state oscillations are successfully predicted with the new forced oscillation data set, using the simplifying assumption that lock-in occurs in both the in-line and cross-flow directions, and the necessary assumption that the normalized average power over one cycle must be zero for a free vibration. The new data set and our procedure will allow a more accurate strip-theory approach to marine riser VIV analysis and design.