Most empirical codes for prediction of vortex-induced vibrations (VIV) has so far been limited to cross-flow response. The reason for this is that cross-flow amplitudes are normally larger that in-line amplitudes. Additionally the in-line response is considered to be driven by the cross-flow vibrations. However since the in-line frequency is twice the cross-flow frequency, fatigue damage from in-line vibrations may become as important and even exceed the damage from cross-flow vibrations. A way to predict in-line vibrations is to apply traditional methods that are used for cross-flow VIV and establish an empirical relationship between the cross-flow and in-line response. Previous work suggests that the ratio between the in-line and cross-flow amplitudes depends on the cross-flow mode number, Baarhom et al. (2004), but the empirical basis for this hypothesis is not strong. The motivation for the present work has been to verify or modify this hypothesis by extensive analysis of observed response. The present analysis uses complex data from experiments with wide variations in the physical parameters of the system, including length-to-diameter ratios from 82 to 4236, tension dominated natural frequencies and bending stiffness dominated natural frequencies, sub-critical and critical Reynolds numbers, different damping coefficients, uniform and sheared flows, standing wave and traveling wave vibrations, mode numbers from 1–25th, and different mass ratios. The conclusion from this work is that the cross-flow mode number is not the important parameter, but whether the frequency of vibration in the cross-flow direction is dominated by bending stiffness of tension.

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