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.
As the demand for natural resources drives ocean structures, such as marine risers, to deep water, the necessity for an accurate understanding of the physics of the combined in-line and cross-flow oscillation of these structures due to vortex shedding becomes apparent. The fundamental problem of vortex-induced vibrations and a number of studies on the topic are discussed in various comprehensive reviews. Ocean structures such as risers and cables typically have comparable structural mass compared with the displaced mass of fluid and very low structural damping.
