Abstract
The paper investigates Vortex-Induced Vibration (VIV) of a horizontal flexible structure with pinned-pinned ends in uniform flow. The fluid – structure interaction is modelled using the wake oscillator approach to describe fluctuations of the fluid forces based on the results, previously reported by Pavlovskaia et al. (2016), Postnikov (2016), and Kurushina et al. (2018). New two-dimensional wake oscillator models are developed in this study employing a number of alternative damping types in the fluid equation. The proposed models are calibrated with the published experimental data by Sanaati and Kato (2012), for VIV of a horizontal flexible structure for the middle cross-section. The calibration is performed with the focus on the maximum of the observed displacement amplitude in the cross-flow direction. One of the models having the Van der Pol – Krenk–Nielsen damping allowed achieving the lowest objective function during the calibration and, hence, was selected for the detailed analysis in 3 and 5 mode approximations. The dynamics of this model is considered in terms of the time histories, changes in the standard deviations of the modal coefficients along the reduced velocity range and frequency response. Also, a comparison with the alternative model versions in terms of the displacements generated at different locations is provided.
In contrast to the previous findings by Kurushina et al. (2018) for VIV of rigid structures, for the flexible structures it was found in this study that both Van der Pol and Rayleigh damping types appear to be applicable for the VIV prediction. A detailed consideration of the 3 mode approximation of the Krenk–Nielsen – Van der Pol model reveals a presence of co-existing solutions in a number of regions of the reduced velocity. They are present in short ranges of reduced velocity in between the lock-in peaks of the in-line displacement coefficient of the first mode. Modulations and co-existing solutions in the in-line modal coefficients make the in-line displacement prediction challenging while the cross-flow displacement amplitudes are described reasonably well by the proposed models.
In contrast to the previous findings by Kurushina et al. (2018) for VIV of rigid structures, for the flexible structures it was found in this study that both Van der Pol and Rayleigh damping types appear to be applicable for the VIV prediction. A detailed consideration of the 3 mode approximation of the Krenk–Nielsen – Van der Pol model reveals a presence of co-existing solutions in a number of regions of the reduced velocity. They are present in short ranges of reduced velocity in between the lock-in peaks of the in-line displacement coefficient of the first mode. Modulations and co-existing solutions in the in-line modal coefficients make the in-line displacement prediction challenging while the cross-flow displacement amplitudes are described reasonably well by the proposed models.
| Original language | English |
|---|---|
| Article number | 103211 |
| Number of pages | 24 |
| Journal | International Journal of Engineering Science |
| Volume | 150 |
| Early online date | 19 Mar 2020 |
| DOIs | |
| Publication status | Published - 1 May 2020 |
Bibliographical note
AcknowledgementsV.K. would like to acknowledge the support of the Industrial University of Tyumen, Tyumen, Russia, and the State Program ”Global Education”, Russia. This work has been performed using the Maxwell High Performance Computing Cluster funded by the University of Aberdeen. Authors would like to express their gratitude to Dr Andrew Starkey for the advices regarding optimisation procedures, to Naveed Khan for the technical advices on accelerating computations and to Dr Andrey Postnikov for the productive discussions.
Keywords
- Vortex-induced vibrations
- Wake oscillator model
- Flexible structure
- Uniform flow
- Model calibration
- Co-existing solutions