The stability of limit–cycle oscillations in a nonlinear aeroelastic system

2002 ◽  
Vol 458 (2025) ◽  
pp. 2203-2226 ◽  
Author(s):  
S. T. Trickey ◽  
L. N. Virgin ◽  
E. H. Dowell
Keyword(s):  
Limit Cycle ◽  
Limit Cycle Oscillations ◽  
Aeroelastic System ◽  
The Stability

scholarly journals Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Haitao Liao
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance Method ◽  
Inequality Constraints ◽  
Maximization Problem ◽  
Limit Cycle Oscillation ◽  
Structural Parameter ◽  
Limit Cycle Oscillations ◽  
Aeroelastic System ◽  
Equality And Inequality Constraints ◽  
The Stability

In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

System identification of a low-density jet via its noise-induced dynamics

2019 ◽  
Vol 862 ◽  
pp. 200-215 ◽  
Author(s):  
Minwoo Lee ◽  
Yuanhang Zhu ◽  
Larry K. B. Li ◽  
Vikrant Gupta
Keyword(s):  
System Identification ◽  
Limit Cycle ◽  
Landau Equation ◽  
Nonlinear Behaviour ◽  
Low Density ◽  
Limit Cycle Oscillations ◽  
Unconditionally Stable ◽  
Stable Regime ◽  
The Stability ◽  
Hydrodynamic Systems

Low-density jets are central to many natural and industrial processes. Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator. In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries) and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart–Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using the noise-induced dynamics in only the unconditionally stable regime, i.e. away from the regimes where limit-cycle oscillations may occur. This opens up new possibilities for the prediction and analysis of the stability and nonlinear behaviour of hydrodynamic systems.

Energy harvesting for actuators and sensors using free-floating flaps

2016 ◽  
Vol 28 (2) ◽  
pp. 163-177 ◽  
Author(s):  
Lars O Bernhammer ◽  
Roeland De Breuker ◽  
Moti Karpel
Keyword(s):  
Limit Cycle ◽  
Vibrational Energy ◽  
Stable Limit Cycle ◽  
Electric Circuit ◽  
Electronic System ◽  
Rotational Axis ◽  
Stable Limit ◽  
Limit Cycle Oscillations ◽  
Trailing Edge ◽  
The Stability

A novel configuration of an energy harvester for local actuation and sensing devices using limit cycle oscillations has been modeled, designed and tested. A wing section has been designed with two trailing-edge free-floating flaps. A free-floating flap is a flap that can freely rotate around a hinge axis and is driven by trailing edge tabs. In the rotational axis of each flap a generator is mounted that converts the vibrational energy into electricity. It has been demonstrated numerically how a simple electronic system can be used to keep such a system at stable limit cycle oscillations by varying the resistance in the electric circuit. Additionally, it was shown that the stability of the system is coupled to the charge level of the battery, with increasing charge level leading to a less stable system. The system has been manufactured and tested in the Open Jet Wind Tunnel Facility of the Technical University Delft. The numerical results could be validated successfully and voltage generation could be demonstrated at cost of a decrease in lift of 2%.

Nonlinear Control Methods for High Energy Limit Cycle Oscillations

1999 ◽  
Author(s):  
Thomas Strganac ◽  
John Junkins ◽  
J. Ko ◽  
Andrew J. Kurdila
Keyword(s):  
Nonlinear Control ◽  
Limit Cycle ◽  
Active Control ◽  
High Performance ◽  
High Energy ◽  
Limit Cycle Oscillation ◽  
Limit Cycle Oscillations ◽  
Cycle Oscillation ◽  
The Stability ◽  
Flight Regimes

Abstract Limit cycle oscillations, as they manifest in high performance fighter aircraft, remain an area of scrutiny by the aerospace industry and military. Tools for the simulation and prediction of the onset for limit cycle oscillations have matured significantly over the years. Suprisingly, less progress has been made in the derivation of active control methodologies for these inherently nonlinear dynamic phenomena. Even in the cases where it is known that limit cycle oscillation may be observed in particular flight regimes, and active control methodologies are employed to attenuate response, there are very few analytical results that study the stability of the closed loop system. In part, this may be attributed to the difficulty in characterizing the nature of the contributing nonlinear structural and nonlinear aerodynamic interactions that account for the motion. This paper reviews recent progress made by the authors in the derivation, development and implementation of nonlinear control methodologies for a class of low speed flutter problems. Both analytical and experimental results are summarized. Directions for future study, and in particular technical barriers that must be overcome, are summarized in the paper.

scholarly journals Limit cycle oscillation control and suppression

1999 ◽  
Vol 103 (1023) ◽  
pp. 257-263 ◽  
Author(s):  
G. Dimitriadis ◽  
J. E. Cooper
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Harmonic Balance Method ◽  
Limit Cycle Oscillation ◽  
Aeroelastic System ◽  
Oscillation Control ◽  
Control Scheme ◽  
Non Linear ◽  
Cycle Oscillation ◽  
The Stability

Abstract The prediction and characterisation of the limit cycle oscillation (LCO) behaviour of non-linear aeroelastic systems has become of great interest recently. However, much of this work has concentrated on determining the existence of LCOs. This paper concentrates on LCO stability. By considering the energy present in different limit cycles, and also using the harmonic balance method, it is shown how the stability of limit cycles can be determined. The analysis is then extended to show that limit cycles can be controlled, or even suppressed, by the use of suitable excitation signals. A basic control scheme is developed to achieve this, and is demonstrated on a simple simulated non-linear aeroelastic system.

scholarly journals Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
M. Ghommem ◽  
A. H. Nayfeh ◽  
M. R. Hajj
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Limit Cycle Oscillations ◽  
Feedback Controls ◽  
Aeroelastic System ◽  
Freestream Velocity ◽  
Nonlinear Springs ◽  
Subcritical Hopf Bifurcation ◽  
Static Feedback ◽  
Nonlinear Static

Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.

scholarly journals Identifying route to stall flutter through stochastic bifurcation analysis

2018 ◽  
Vol 211 ◽  
pp. 02011
Author(s):  
Rajagopal V Bethi ◽  
Sai Vishal Reddy Gali ◽  
J Venkatramani
Keyword(s):  
Fluid Flow ◽  
Limit Cycle ◽  
Bifurcation Analysis ◽  
Period Doubling ◽  
Stochastic Bifurcation ◽  
Nonlinear Phenomenon ◽  
Limit Cycle Oscillations ◽  
Viscous Effects ◽  
Stall Flutter ◽  
The Stability

The interaction of an elastic structure such as an airfoil and fluid flow can give rise to nonlinear phenomenon such as limit cycle oscillations, period doubling or chaos. These phenomena are indicated by a change in the stability behaviour of the dynamical known as bifurcations. Presence of viscous effects in the fluid flow can give rise to flow separation which causes a stability change in the system that is identified to happen via a Hopf bifurcation. In such cases, the airfoil exhibits limit cycle oscillations which are torsionally dominant, known as stall flutter. Despite identifying the route to stall flutter under uniform flow conditions, investigating a stall problem under stochastic wind has received minimal attention. The ability of fluctuating flows to change the stability boundaries and disrupt the route to flutter, compels the need to carry out a stochastic analysis of stalling airfoils. Study of stall flutter in such systems under the influence of a time varying sinusoidal gust is undertaken and the route to flutter is identified by carrying out a stochastic bifurcation analysis.

An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system

2012 ◽  
Vol 71 (1-2) ◽  
pp. 159-173 ◽  
Author(s):  
Abdessattar Abdelkefi ◽  
Rui Vasconcellos ◽  
Ali H. Nayfeh ◽  
Muhammad R. Hajj
Keyword(s):  
Experimental Investigation ◽  
Limit Cycle ◽  
Limit Cycle Oscillations ◽  
Aeroelastic System
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