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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
TL;DR: In this paper, the authors present a comprehensive review of stochastic dynamics of VIV systems, especially highlighting the presence of novel dynamical states and its implication on the coupled system behaviour that have been reported recently by them.
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.
Citations
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Journal ArticleDOI
TL;DR: In this article, 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 is investigated.

6 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a numerical study of a uniform flow past an elastic circular cylinder using the discrete vortex method incorporating the vortex-in-cell (VIC) technique has been undertaken, where the fluid motion and the structural responses are solved in an iterative way so that the interactions between the fluid and the structure can be accounted for properly.

154 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the dynamical behavior of the disturbed system remains the same for all parameter values, regardless of the intensity of the disturbance, and that for any parameter value all solutions converge to each other almost surely (uniformly in bounded sets).
Abstract: In the deterministic pitchfork bifurcation the dynamical behavior of the system changes as the parameter crosses the bifurcation point. The stable fixed point loses its stability. Two new stable fixed points appear. The respective domains of attraction of those two fixed points split the state space into two macroscopically distinct regions. It is shown here that this bifurcation of the dynamical behavior disappears as soon as additive white noise of arbitrarily small intensity is incorporated the model. The dynamical behavior of the disturbed system remains the same for all parameter values. In particular, the system has a (random) global attractor, and this attractor is a one-point set for all parameter values. For any parameter value all solutions converge to each other almost surely (uniformly in bounded sets). No splitting of the state space into distinct regions occurs, not even into random ones. This holds regardless of the intensity of the disturbance.

151 citations

Journal ArticleDOI
TL;DR: Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator are investigated and the effects of multiplicative noise are rather different from that of additive noise.
Abstract: This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that P and D bifurcations have no direct connection.

146 citations

Journal ArticleDOI
TL;DR: It is found that under the influence of noise, Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution.
Abstract: We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.

134 citations

Journal ArticleDOI
TL;DR: In this article, two regimes of response were found, similar in nature to the upper and lower branch at higher Re, with evidence for this found in the amplitude, frequency and phase response of the cylinder.

131 citations