Study on the lock-in delay coefficient in the mathematical model of transversal vortex-induced vibration for a rigid circular cylinder

This study revisits the definition of the lock-in delay coefficient and the interpretation of lock-in delay. A one-degree-of-freedom structural model, along with the classical van der Pol wake oscillator equation, is employed to investigate the inconsistency between the definition and the interpretation. To resolve this issue, the lock-in delay coefficient is redefined, and an improved mathematical model is proposed. This model implies that the corrected Strouhal number solely influences the structure of the wake equation. Two objective functions and two sets of initial empirical coefficients are established for eight distinct mass ratios. The pattern search algorithm in conjunction with published experimental data is utilized to calibrate the new model. The calibrated models are capable of effectively predicting the displacement amplitudes of the cylinder subjected to transversal vortex-induced vibration. To mitigate the high computational costs associated with calibrating the model for all mass ratios using the optimization algorithm, a weighting method is proposed. This method leverages the calibrated empirical coefficients obtained at specific partial mass ratios to extrapolate the empirical coefficients for other mass ratios. Comparative analyses with published experimental data indicate that the calibrated models, derived from the weighting method, provide acceptable predictions for cross-flow oscillations.