Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations
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.
About: This article is published in Journal of Fluids and Structures.The article was published on 2004-02-01. It has received 616 citations till now. The article focuses on the topics: Van der Pol oscillator & Vortex.
Citations
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TL;DR: A review of mathematical models used to investigate vortex-induced vibration (VIV) of circular cylinders is given in this article, with a focus on single-degree-of-freedom (SFOF) models.
602 citations
Cites background from "Coupling of Structure and Wake Osci..."
...Three-dimensional features naturally arise in the VIV problem as the real domain is considered as spanwise extended: elastic structures are characterized by their eigenmodes and wake flows show secondary instabilities [ 29 ]....
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...From a numerical point of view, limits arise in the flow-field simulation of 3D domains with large aspect ratios [ 29 ]....
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TL;DR: Recent literature in the field of energy harvesting from aeroelastic vibrations during the last few years is reviewed and Qualitative and quantitative comparisons between different existing flow-induced vibrations energy harvesters are discussed.
368 citations
TL;DR: The paper summarizes the works led to the current wind energy and hydro energy harvesters based on the principle of flow- induced vibrations, including bladeless generator Vortex Bladeless, University of Michigan vortex-induced vibrations aquatic clean energy, Australian BPS company's airfoil tidal energy capture device bioSTREAM, and others.
313 citations
TL;DR: A review of the progress made during the past decade on vortex-induced vibration (VIV) of long slender cylindrical structures is given in this article, where a brief outline is given of numerical methods used in predicting the response of a long slender cylinder undergoing VIV.
294 citations
TL;DR: In this article, the wake dynamics of flexible slender systems undergoing vortex-induced vibration (VIV) are modeled using a distributed wake oscillator coupled to the dynamics of the slender structure, a cable or a tensioned beam.
185 citations
Cites background or methods from "Coupling of Structure and Wake Osci..."
...[7] verified the effect of the cylinder movement on the lift fluctuation via different type of coupling (displacement, velocity and acceleration)....
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...As in [7], the variable q is here defined as the local fluctuating lift coefficient q(z, t) = 2CL(z,t)/CL0, the coefficient CL0 is the amplitude of the fluctuating lift for a fixed rigid cylinder subjected to vortex shedding....
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...[7], using experimental data of VIV of elementary systems (one degree of freedom) in uniform flow....
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...The purpose of this paper is to verify, following [7,8,14], how this simple approach can predict some of the dynamics of cables or flexible beams observed in both DNS and experiments....
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References
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Book•
01 Jan 1981
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Abstract: Algebraic Equations. Integrals. The Duffing Equation. The Linear Damped Oscillator. Self-Excited Oscillators. Systems with Quadratic and Cubic Nonlinearities. General Weakly Nonlinear Systems. Forced Oscillations of the Duffing Equation. Multifrequency Excitations. The Mathieu Equation. Boundary-Layer Problems. Linear Equations with Variable Coefficients. Differential Equations with a Large Parameter. Solvability Conditions. Appendices. Bibliography. Index.
3,020 citations
Book•
01 Jan 1977TL;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.
1,759 citations
TL;DR: In this paper, the authors present a comprehensive review of vortex shedding in two-dimensional bluff-body wakes and present irrespective of whether the separating boundary layers are laminar or turbulent, and if the body is flexible this can cause oscillations.
Abstract: When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-
1,251 citations
TL;DR: In this paper, the authors showed that there exist two distinct types of response in a very low mass and damping regime, depending on whether one has a low combined mass-damping parameter (low m*ζ), or a high mass-ding parameter (highm*δ).
944 citations
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
"Coupling of Structure and Wake Osci..." refers background or methods or result in this paper
...Following [21], in the sequel we will refer to as a vortex lift coefficient and to = = as the total lift coefficient....
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...This latter result is quite consistent with experimental data of [21]....
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...[21], hydrodynamic actions on the structure are here decomposed in two parts: the basic fluid effects, and , are directly included in the structure oscillator through and , equations (2) and (3), while the effects of vortices are modeled by the right-hand side forcing term , to be discussed later....
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...All this has already been observed experimentally for forced [28] and free vibrations [21], and also simulated by 2-D CFD [27,38]....
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...Although the maximum structure displacement and the corresponding lift magnification factor at lock-in are determined by the single combined mass-damping parameter , as verified for the three coupling models in the previous section, the range of lock-in is known to be a function of both ( and D separately [21]....
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