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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 article, a non-linear fluid force model for a freely vibrating cylinder in a cross flow was developed based on an iterative process and the modal analysis approach, which can be evaluated from measured vibration data with the help of the auto-regressive moving averaging (ARMA) technique.

66 citations

Journal ArticleDOI
TL;DR: In this article, the dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow are investigated numerically using a Monte Carlo approach, and the results are examined in terms of the probability structure of the response and the largest Lyapunov exponent.
Abstract: The dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow is investigated numerically using a Monte Carlo approach. Both the longitudinal and vertical components of turbulence, corresponding to parametric (multiplicative) and external (additive) excitation, respectively, are modelled. The properties of the airfoil are chosen such that the underlying non-excited, deterministic system exhibits binary flutter; the loss of stability of the equilibrium point due to flutter then leads to a limit cycle oscillation (LCO) via a supercritical Hopf bifurcation. For the random system, the results are examined in terms of the probability structure of the response and the largest Lyapunov exponent. The airfoil response is interpreted from the point of view of the concepts of D- and P-bifurcations, as defined in random bifurcation theory. It is found that the bifurcation is characterized by a change in shape of the response probability structure, while no discontinuity in the variation of the largest Lyapunov exponent with airspeed is observed. In this sense, the trivial bifurcation obtained for the deterministic airfoil, where the D- and P-bifurcations coincide, appears only as a P-bifurcation for the random case. At low levels of turbulence intensity, the Gaussian-like bell-shaped bi-dimensional PDF bifurcates into a crater shape; this is interpreted as a random fixed point bifurcating into a random LCO. At higher levels of turbulence intensity, the post-bifurcation PDF loses its underlying deterministic LCO structure. The crater is transformed into a two-peaked shape, with a saddle at the origin. From a more universal point of view, the robustness of the random bifurcation scenario is critiqued in light of the relative importance of the two components of turbulent excitation.

60 citations

Journal ArticleDOI
TL;DR: In this article, a single-degree-of-freedom model with velocity-dependent coefficients was proposed to model the vortex-induced vibration of a flexibly supported circular cylinder in air.
Abstract: The analytical work presented in this paper closely follows the data obtained from new experiments on vortex-induced vibration of circular cylinders in air. The experimental data are presented in the companion paper preceding in the journal. The vortex-induced vibration of a flexibly supported circular cylinder is modeled by a new single-degree-of-freedom model with velocity-dependent coefficients. The model is of the ordinary differential equation type with a self-excited, self-limiting van der Pol–type aeroelastic damping pair and an aeroelastic parametric excitation term. The latter term is the innovative addition in the current model. The development of the model equations is outlined, following which it is analyzed and its parameters estimated in conjunction with the data from experiments reported in the companion paper. The model and its parameters have been rendered dimensionless in the analysis, to facilitate universal applicability.

54 citations

Journal ArticleDOI
TL;DR: It is found that for sufficiently high noise intensities a direct transition from the spatially homogeneous state to turbulence via intermittency can be induced.
Abstract: We show experimentally that for the electrohydrodynamic instability in nematic liquid crystals the threshold for the onset of spatial turbulence can be increased by at least a factor of 2 by superimposing noise on the applied voltage. We find that for sufficiently high noise intensities a direct transition from the spatially homogeneous state to turbulence via intermittency can be induced.

48 citations

Journal ArticleDOI
TL;DR: In this article, the aeroelastic response of a NACA 0012 airfoil in the flow regimes prior to flutter is investigated in a wind tunnel, where the authors observe intermittent bursts of periodic oscillations in the pitch and plunge response, that appear in an irregular manner from a background of relatively lower amplitude aperiodic fluctuations.

44 citations