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Book ChapterDOI

Nonlinear Dynamics of Circular Cylinders Undergoing Vortex Induced Vibrations in Presence of Stochastic Noise

01 Jan 2020-pp 195-214

Abstract: Vortex induced vibrations (VIV) is a widely explored fluid-structure interaction problem with immense applications ranging from heat exchanger tube arrays, power transmission lines to offshore structures. VIV of circular cylinders stands as one of the classical problems in this area, wherein the cylinder undergoes high amplitude vibrations due to the ‘lock-in’ phenomenon. The dynamics of the structure and flow field are well studied in the literature for a varied range of flow and structural parameters. However, real-life situations can be characterized by the presence of ‘noise’, which are fluctuations or uncertainties associated with the incoming flow or geometrical parameters of the system. The dynamical characteristics of the VIV system in the presence of such stochastic fluctuations are a relatively lesser-explored domain of research and not much documentation on this subject is available. In this chapter, we aim to present a comprehensive review of stochastic dynamics of VIV systems, especially we will highlight the presence of novel dynamical states and its implication on the coupled system behaviour that have been reported recently by us. It is known from experimental studies that free-stream noise can increase the response amplitudes of the structure and thus acts as a source of negative aerodynamic damping. Analytical works which model turbulence in experiments as stochastic processes use asymptotic expressions of Lyapunov exponents to determine the stability boundaries of VIV systems. Studies based on mathematical models investigating stochastic dynamics have modelled noise as additive and parametric, in the equations governing the VIV system. The current chapter mainly reviews the literature on stochastic VIV studies based on mathematical models that include wake oscillator models, single degree of freedom and force decomposition models, from a nonlinear dynamics perspective. Brief reviews on previous numerical studies using uncertainty quantification techniques in high fidelity solvers and key experimental results emphasizing the role of free-stream noise are also presented.
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Journal ArticleDOI
M. S. Aswathy1, Sunetra Sarkar1Institutions (1)
Abstract: In this study, we investigate the role of stochastic parametric noise on the phase dynamics and the frequency characteristics of a vortex induced vibration (VIV) system, in the framework of synchronisation theory. In-phase, arbitrary-phase and anti-phase synchronisations exist during pre lock-in, lock-in and post lock-in regimes of the deterministic system, respectively. However the noise induced phase dynamics is found to be considerably different from the corresponding deterministic scenario and is largely dependent on the intensity of noise. Stochastic noise alters the conventional route to instability and is seen to induce new dynamical states such as Noise Induced Intermittency (NII) and quasi-periodicity in the structural response. It is also observed that noise triggers additional system frequencies in both structural and flow responses albeit not the same way. The birth of new dynamical states is strongly linked with these frequency characteristics of the structural and the flow oscillators. Phase can characterise the overall dynamics of coupled oscillators systematically and in the present study relative phase has been exploited in a stochastic framework in terms of both averaged and instantaneous quantities. The stochastic VIV system manifests asynchronous and synchronous phase dynamics as well as regions of phase slips during the transition boundaries of stochastic bifurcations. These are quantitatively and qualitatively monitored through phase coherence values in the desired parametric ranges.

1 citations

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Journal ArticleDOI
Abstract: These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m*ζ), or a high mass-damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ ∼0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*.

812 citations

15 Feb 2007-
Abstract: Elements of Probability Theory.- Stochastic Models of Environmental Fluctuations.- Markovian Diffusion Processes.- Stochastic Differential Equations.- Noise-Induced Nonequilibrium Phase Transitions.- Noise-Induced Transitions in Physics, Chemistry, and Biology.- External Colored Noise.- Markovian Dichotomous Noise: An Exactly Soluble Colored-Noise Case.- The Symbiosis of Noise and Order - Concluding Remarks.

663 citations

Journal ArticleDOI
Rene D. Gabbai1, Haym Benaroya1Institutions (1)
Abstract: This paper reviews the literature on the mathematical models used to investigate vortex-induced vibration (VIV) of circular cylinders. Wake-oscillator models, single-degree-of-freedom, force–decomposition models, and other approaches are discussed in detail. Brief overviews are also given of numerical methods used in solving the fully coupled fluid–structure interaction problem and of key experimental studies highlighting the nature of VIV.

516 citations

Journal ArticleDOI
Abstract: A class of low-order models for vortex-induced vibrations is analyzed. A classical van der Pol equation models the near wake dynamics describing the fluctuating nature of vortex shedding. This wake oscillator interacts with the equation of motion of a one degree-of-freedom structural oscillator and several types of linear coupling terms modelling the fluid–structure interaction are considered. The model dynamics is investigated analytically and discussed with regard to the choice of the coupling terms and the values of model parameters. Closed-form relations of the model response are derived and compared to experimental results on forced and free vortex-induced vibrations. This allows us to set the values of all model parameters, then leads to the choice of the most appropriate coupling model. A linear inertia force acting on the fluid is thus found to describe most of the features of vortex-induced vibration phenomenology, such as Griffin plots and lock-in domains.

478 citations

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