An improved van der Pol wake oscillator model for a 1DOF circular cylinder undergoing vortex induced vibrations

Abstract

An optimization procedure is presented for prescribing the empirical coupling parameters of a modified coupled van der Pol (VDP) wake oscillator and mass–spring–damper system for a one degree of freedom (1DOF) circular cylinder system undergoing vortex induced vibrations (VIV). This approach allows for the generalization of the traditional VDP model to cover a large VIV parameter range. The procedure is developed using experimental data covering the parameter space: 3<U∗<11, 8<m∗<20, 0.003<ζ<0.063, ReD=4000. The VDP model contains empirical coupling coefficients that describe the regime specific dynamic damping, ϵ, and wake coupling, β. Two calibration procedures are considered and the improvements over the traditional VDP model in predicting the VIV response are discussed. Subsequently, a regression fit is used to prescribe the two empirical coupling coefficients as functions of m∗, ζ and U∗. The generalized model results in a better prediction of the VIV response in terms of identification of lock-in regimes, lock-in frequency and amplitude response over several regimes when compared to the classical models. The use of a functional representation replaces the need for using tables and reduces user input for determining regime-specific coupling coefficients.