# Comparison of Stochastic Responses of Circular Cylinder Undergoing Vortex-Induced Vibrations with One and Two Degrees of Freedom

01 Jan 2021-pp 521-527

TL;DR: In this paper, a stochastic model of a circular cylinder exhibiting free vibrations with one and two degrees of freedom is presented. And the transverse oscillations of each of the cases under the presence of noise are individually studied.

Abstract: Vortex-induced vibration of a circular cylinder is a major research topic due to the immense applications they have in daily and industrial scenarios. Large numbers of studies have been conducted in this area in numerical and experimental domains with focus on understanding the response types, understanding the range of lock-in, the flow behavior, etc. However, most of the studies till date have been done in a deterministic environment; on the pretext that all factors about the incoming flow and input parameters are exactly known. In real-time flows, there can be a significant amount of uncertainties associated with various system parameters, which are traditionally not taken into consideration for the system. For example, randomness associated with the incoming flow might have significant effect on the associated dynamics. In this study, we do a stochastic modeling on a circular cylinder exhibiting free vibrations with one and two degrees of freedom. For this, we use Duffing Van der Pol combined system and impose fluctuations at every time step in the input flow by modeling them through a uniform distribution. The transverse oscillations of each of the cases under the presence of noise are individually studied. It is seen that noise brings in new dynamical states to the cylinder response compared to the deterministic cases. It is observed that there is a considerable difference between the responses of the single degree of freedom and two-degree of freedom cylinder. These qualitative differences are investigated in detail in the current study.

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General Electric

^{1}TL;DR: In this paper, the authors focus on applications for offshore platforms and piping; wind-induced vibration of buildings, bridges, and towers; and acoustic and mechanical vibration of heat exchangers, power lines, and process ducting.

Abstract: This book focuses on applications for offshore platforms and piping; wind-induced vibration of buildings, bridges, and towers; and acoustic and mechanical vibration of heat exchangers, power lines, and process ducting. Numerous examples drive home the reality of the practical problems encountered here. More than 200 figures and 20 tables complement the text by providing such data as damping factors, lift coefficients, and the formulas needed to apply practical methods directly to a wide range of structures, from heat exchangers to hypersonic aircraft. Devoted to the analysis and prediction of flow-induced vibrations, this volume will prove of immense interest to mechanical, civil, nuclear, marine, structural, and electrical engineers; physicists, designers, and naval architects; and people working in the construction and petroleum industries, power plants, power transmission, ship building, nuclear power, energy production, and defense engineering.

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TL;DR: In this article, the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow were studied for the first time in free vibrations, and the existence of more than one mode transition for low (m*ζ) and high (m *δ) combined mass-damping parameters was analyzed.

Abstract: In this paper, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We use simultaneous force, displacement and vorticity measurements (using DPIV) for the first time in free vibrations. There exist two distinct types of response in such systems, depending on whether one has a high or low combined mass–damping parameter (m*ζ). In the classical high-(m*ζ) case, an ‘initial’ and ‘lower’ amplitude branch are separated by a discontinuous mode transition, whereas in the case of low (m*ζ), a further higher-amplitude ‘upper’ branch of response appears, and there exist two mode transitions.To understand the existence of more than one mode transition for low (m*ζ), we employ two distinct formulations of the equation of motion, one of which uses the ‘total force’, while the other uses the ‘vortex force’, which is related only to the dynamics of vorticity. The first mode transition involves a jump in ‘vortex phase’ (between vortex force and displacement), ϕvortex, at which point the frequency of oscillation (f) passes through the natural frequency of the system in the fluid, f ∼ fNwater. This transition is associated with a jump between 2S [harr ] 2P vortex wake modes, and a corresponding switch in vortex shedding timing. Across the second mode transition, there is a jump in ‘total phase’, phis;total , at which point f ∼ fNvacuum. In this case, there is no jump in ϕvortex, since both branches are associated with the 2P mode, and there is therefore no switch in timing of shedding, contrary to previous assumptions. Interestingly, for the high-(m*ζ) case, the vibration frequency jumps across both fNwater and fNvacuum, corresponding to the simultaneous jumps in ϕvortex and ϕtotal. This causes a switch in the timing of shedding, coincident with the ‘total phase’ jump, in agreement with previous assumptions.For large mass ratios, m* = O(100), the vibration frequency for synchronization lies close to the natural frequency (f* = f/fN ≈ 1.0), but as mass is reduced to m* = O(1), f* can reach remarkably large values. We deduce an expression for the frequency of the lower-branch vibration, as follows:formula herewhich agrees very well with a wide set of experimental data. This frequency equation uncovers the existence of a critical mass ratio, where the frequency f* becomes large: m*crit = 0.54. When m* < m*crit, the lower branch can never be reached and it ceases to exist. The upper-branch large-amplitude vibrations persist for all velocities, no matter how high, and the frequency increases indefinitely with flow velocity. Experiments at m* < m*crit show that the upper-branch vibrations continue to the limits (in flow speed) of our facility.

775 citations

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TL;DR: A class of low-order models for vortex-induced vibrations is analyzed in this article, where a van der Pol equation is used to describe the near wake dynamics describing the fluctuating nature of vortex shedding and several types of linear coupling terms modelling the fluid-structure interaction are considered.

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.

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TL;DR: Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow, the authors observes a rather dramatic departure from previous results, which would suggest a possible modification to offshore design codes.

Abstract: Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow (, that one observes a rather dramatic departure from previous results, which would suggest a possible modification to offshore design codes.

588 citations