Identification of parameters for same-order nonlinear damping terms in polynomial-type vortex-induced force models for bridge decks

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Polynomial-type empirical models have been commonly adopted to describe the vortex-induced force (VIF) on bridge decks in the study of vortex-induced vibration. Previous studies chose different nonlinear damping terms like the Van der Pol or Rayleigh type in such models without explaining whether these same-order terms can be chosen arbitrarily. A novel parameter identification technique is developed in this paper to distinguish different same-order nonlinear terms in the VIF model with additional governing equations based on the orthogonality among motion-induced terms. The parameter identification results obtained from the wind-tunnel tests on a central-slotted box deck indicate that the Rayleigh-type damping terms are the only important ones in the vertical VIF, whilst none of the same-order nonlinear damping terms of the torsional VIF should be ignored. The finding is then theoretically explained assuming that the aerodynamic damping nonlinearity of VIF primarily comes from the continuous change of relative attack angle between the oscillating deck and the incoming wind.