Modelling of coupled cross-flow/in-line vortex-induced vibrations using double Duffing and van der Pol oscillators

OCEAN ENGINEERING

卷:53

Article

Srinil, Narakorn¹  Zanganeh, Hossein¹ 

[1] Univ Strathclyde, Dept Naval Architecture & Marine Engn, Glasgow G4 0LZ, Lanark, Scotland

关键词: Vortex-induced vibration (VIV);    Circular cylinder;    Cross-flow oscillation;    In-line oscillation;    Fluid-structure interaction;    Wake oscillator;   

DOI  :  10.1016/j.oceaneng.2012.06.025

来源: Elsevier

【 摘 要 】

Many studies have typically applied a linear structural spring-mass-damper oscillator and a van der Pol wake oscillator to model a one-dimensional cross-flow vortex-induced vibration (VIV). In this study, an advanced model for predicting a two-dimensional coupled cross-flow/in-line VIV of a flexibly mounted circular cylinder in a uniform flow is proposed and validated. The ensuing dynamical system is based on double Duffing-van der Pol (structural-wake) oscillators with the two structural equations containing both cubic and quadratic nonlinear terms. The cubic nonlinearities capture the geometrical coupling of cross-flow/in-line displacements excited by hydrodynamic lift/drag forces whereas the quadratic nonlinearities allow the wake-cylinder interactions. Some empirical coefficients are calibrated against published experimental results to establish a new generic analytical function accounting for the dependence of VIV on a physical mass and/or damping parameter. By varying flow velocities in the numerical simulations, the derived low-order model captures several important VIV characteristics including a two-dimensional lock-in, hysteresis phenomenon and figure-of-eight trajectory tracing the periodically coupled in-line/cross-flow oscillations with their tuned two-to-one resonant frequencies. By making use of a newly derived empirical formula, the predicted maximum cross-flow/in-line VIV amplitudes and associated lock-in ranges compare well with several experimental results for cylinders with low/high mass or damping ratios. Moreover, the parametric studies highlight the important effect of geometrical nonlinearities through new displacement coupling terms and the ratio of in-line to cross-flow natural frequencies of the freely vibrating cylinder. (C) 2012 Elsevier Ltd. All rights reserved.

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