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Motion-amplitude-dependent nonlinear VIV model and maximum response over a full-bridge span

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Abstract

Nonlinear motion-amplitude \((y_{T} )\)-dependent energy-trapping properties of a bridge model undergoing vortex-induced vibration (VIV) are investigated. Energy-trapping properties of the model undergoing a full-process from still to a limit cycle oscillation (LCO) state are identified. A van der Pol-type model is adapted to describe the amplitude-dependent aerodynamic properties. Nonlinear parameter-amplitude relations, \(\varepsilon {-}y_{T}\) and \(\xi_{\varepsilon } {-}y_{T}\), are established. Nonlinear aerodynamic damping is separated into two parts: the initial damping which varies with the reduced wind speed, and the \(\varepsilon \)-related part which varies with both the reduced wind speed and the motion amplitude. The initial aerodynamic damping determines the threshold of VIV, while the \(\varepsilon \)-related part dominates the evolution process and the LCO. The identified nonlinear analytical model is capable of predicting VIV responses at higher mechanical damping ratios. The energy-trapping properties of a section model in time are transformed into nonlinear properties distributed in space along an elongated 3-D elastic bridge span. According to this “time-space” transformation, the convection coefficient, which links the maximum response of a 3-D structure with that of a 2-D (1-DOF) sectional model, can be determined. Compared with a constant-parameter analytical model, an adapted nonlinear one brings to light significantly larger convection coefficients. Finally, parameter overflowing phenomena are revealed and discussed.

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Data Availability

A part of the datasets generated during and analyzed during the current study are not publicly available due to the large data size but are available from the corresponding author on reasonable request.

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Acknowledgements

The author would like to express his gratitude for the financial support provided by the Hainan Provincial Natural Science Foundation of China (Grant Number 520CXTD433). He is also indebted to the National Natural Science Foundation of China (Grant Number 51938012 and 52268073). The author is also thankful to graduate student Hongxin Chen and Ph. D student Kai Qie for the experimental and part of the data processing work.

Funding

This study was funded by the Hainan Provincial Natural Science Foundation of China (Grant Number 520CXTD433) and the National Natural Science Foundation of China (51938012).

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  1. College of Civil Engineering and Architecture, Hainan University, Haikou, China

    Zhitian Zhang

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Zhang, Z. Motion-amplitude-dependent nonlinear VIV model and maximum response over a full-bridge span. Nonlinear Dyn 111, 12733–12747 (2023). https://doi.org/10.1007/s11071-023-08565-w

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