Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Haitao Liao

doi:10.1155/2013/570947

Abstract

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.

Highlights

A great attention has been paid to limit cycle oscillations (LCOs) of nonlinear aeroelastic systems, and there are many numerical methods to predict the amplitude and frequency of LCOs
Mathematical Problems in Engineering to analyze the characters of nonlinear systems, the bounds and peak responses of the LCOs were determined in [14] by applying the continuation method along with the incremental harmonic balance method
The objective of the present work is to develop a methodology to determine the LCOs with maximum vibration amplitude of nonlinear aeroelastic system

Summary

Introduction

A great attention has been paid to limit cycle oscillations (LCOs) of nonlinear aeroelastic systems, and there are many numerical methods to predict the amplitude and frequency of LCOs. In [3], the airfoil flutter with multiple strong nonlinearities was investigated via the incremental harmonic balance method. The effects of the linear and cubic stiffness coefficients on LCOs and bifurcations of an airfoil with multiple nonlinearities were analyzed in [11] through the equivalent linearization method. The LCOs and the Hopf bifurcations of an airfoil with uncertainties from the system parameter and the initial condition were investigated in [13] via the stochastic collocation method. Mathematical Problems in Engineering to analyze the characters of nonlinear systems, the bounds and peak responses of the LCOs were determined in [14] by applying the continuation method along with the incremental harmonic balance method. The objective of the present work is to develop a methodology to determine the LCOs with maximum vibration amplitude of nonlinear aeroelastic system.

The Proposed Method

Application to the Nonlinear Aeroelastic System

Conclusions