Predicting Limit Cycle Oscillation in an Aeroelastic System Using Nonlinear Normal Modes

2013 ◽  
Vol 50 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Christopher W. Emory ◽  
Mayuresh J. Patil
Keyword(s):  
Limit Cycle ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Limit Cycle Oscillation ◽  
Aeroelastic System ◽  
Cycle Oscillation ◽  
Nonlinear Normal

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 Quantification of Limit Cycle Oscillations in Nonlinear Aeroelastic Systems with Stochastic Parameters

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
C. C. Cui ◽  
J. K. Liu ◽  
Y. M. Chen
Keyword(s):  
Limit Cycle ◽  
Distribution Functions ◽  
Limit Cycle Oscillation ◽  
Nonlinear Stiffness ◽  
Aeroelastic System ◽  
Vibration Displacement ◽  
Flutter Suppression ◽  
Stochastic Parameters ◽  
Cycle Oscillation ◽  
White Noises

This paper presents an analytical feature for limit cycle oscillation (LCO) in the nonlinear aeroelastic system of an airfoil, with major emphasis on its applications in LCO quantification. The nonlinear stiffness is modeled as the product of the pth power of vibration displacement and the qth power of velocity, with its coefficient as a stochastic parameter. One interesting finding is that the LCO amplitude is directly proportional to the 1/(1-p-q)th power of the coefficient, whereas the frequency is independent of the coefficient. Based on this feature, the statistics and distribution functions of the LCO amplitude are obtained semianalytically, which are validated by Monte Carlo simulations. In addition, we discuss the possible influences of the nonlinear stiffness on flutter suppression of the airfoil subjected to Gaussian white noises. Surprisingly, increasing the nonlinear stiffness alone does not necessarily reduce the vibration amplitude as expected. Instead, it may sometimes induce disastrous subcritical LCOs with much higher vibration amplitudes.

Reduced Order Modeling of Limit Cycle Oscillation for Aeroelasticity Systems

2002 ◽  
Author(s):  
Philip S. Beran ◽  
David J. Lucia ◽  
Chris L. Pettit
Keyword(s):  
Limit Cycle ◽  
Degrees Of Freedom ◽  
Galerkin Approximation ◽  
Computational Cost ◽  
Coupled System ◽  
Low Rank ◽  
Limit Cycle Oscillation ◽  
Aeroelastic System ◽  
Reduced Order ◽  
Cycle Oscillation

Limit-cycle oscillations of a nonlinear panel in supersonic flow are computed using a reduced-order aeroelastic model. Panel dynamics are governed by the large-deflection, nonlinear, von Ka´rma´n equation as expressed in low-order form through a Galerkin approximation. The aerodynamics are described by the Euler equations, which are reduced in order using proper orthogonal decomposition. The coupled system of equations is implicitly time integrated with second-order temporal accuracy to predict limit-cycle oscillation (LCO) amplitude, and linearly analyzed to predict LCO onset. The fluid is synchronized with the structure in time through subiteration, using only 18 degrees of freedom to describe the aeroelastic system. The Jacobian employed in the fully implicit analysis is of equivalently low rank, enabling rapid analysis. Using the reduced order model, LCO onset is predicted directly at a computational cost of approximately 400 time steps with a high accuracy verified by full-order analysis.

scholarly journals Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Gang Chen ◽  
Yingtao Zuo ◽  
Jian Sun ◽  
Yueming Li
Keyword(s):  
Support Vector Machine ◽  
Limit Cycle ◽  
Unsteady Aerodynamics ◽  
Reduced Order Model ◽  
Support Vector ◽  
Limit Cycle Oscillation ◽  
Order Model ◽  
Aeroelastic System ◽  
Reduced Order ◽  
Cycle Oscillation

It is not easy for the system identification-based reduced-order model (ROM) and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM-) based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

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