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.

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.

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.

Instability of Heated Panels in Supersonic Air Flow

2008 ◽  
Vol 33-37 ◽  
pp. 1101-1108
Author(s):  
Zhi Chun Yang ◽  
Wei Xia
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Static Stability ◽  
Static Deformation ◽  
Limit Cycle Oscillation ◽  
Aerodynamic Load ◽  
Aeroelastic System ◽  
Aerodynamic Pressure ◽  
The Stability

An investigation on the stability of heated panels in supersonic airflow is performed. The nonlinear aeroelastic model for a two-dimensional panel is established using Galerkin method and the thermal effect on the panel stiffness is also considered. The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel. The static and dynamic stabilities for flat panels are studied using Lyapunov indirect method and the stability boundary curve is obtained. The static deformation of a post-buckled panel is then calculated and the local stability of the post-buckling equilibrium is analyzed. The limit cycle oscillation of the post-buckled panel is simulated in time domain. The results show that a two-mode model is suitable for panel static stability analysis and static deformation calculation; but more than four modes are required for dynamic stability analysis. The effects of temperature elevation and dimensionless parameters related to panel length/thickness ratio, material density and Mach number on the stability of heated panel are studied. It is found that panel flutter may occur at relatively low aerodynamic pressure when several stable equilibria exist for the aeroelastic system of heated panel.

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.

Constrained Optimization Shooting Method for Predicting the Periodic Solutions of Nonlinear System

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Haitao Liao
Keyword(s):  
Nonlinear System ◽  
Shooting Method ◽  
Continuation Method ◽  
Inequality Constraints ◽  
Original Method ◽  
Maximization Problem ◽  
Numerical Examples ◽  
Equality And Inequality Constraints ◽  
Parameter Continuation ◽  
Nonlinear Equality

An original method for calculating the maximum vibration amplitude of the periodic solution of a nonlinear system is presented. The problem of determining the worst maximum vibration is transformed into a nonlinear optimization problem. The shooting method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the effectiveness and ability of the proposed approach are illustrated through two numerical examples. Numerical examples show that the proposed method can give results with higher accuracy as compared with numerical results obtained by a parameter continuation method and the ability of the present method is also demonstrated.

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%.

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