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

Y M Chen,J K Liu,C C Cui

doi:10.1155/2016/3049163

Y M Chen, J K Liu + Show 1 more

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https://doi.org/10.1155/2016/3049163

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Abstract

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.

Highlights

The nonlinear aeroelastic system of an airfoil is a typical selfexcited system, which can exhibit lots of nonlinear dynamical behaviors such as bifurcations, limit cycle oscillations (LCO), and chaotic responses [1, 2]
We will present an algorithm to quantify the main statics of LCOs arising in the aeroelastic system with the nonlinear coefficient as a stochastic parameter
We have investigated the LCO of an airfoil aeroelastic system with a nonlinear stiffness

Summary

Introduction

The nonlinear aeroelastic system of an airfoil is a typical selfexcited system, which can exhibit lots of nonlinear dynamical behaviors such as bifurcations, limit cycle oscillations (LCO), and chaotic responses [1, 2]. Quantification of airfoil LCOs via analytical and/or semianalytical techniques has been an active area of research for many years. Due to the design and manufacturing errors, uncertainties are usually inevitable in airfoil aeroelastic systems [10] They usually happen to system parameters as stochastic [11] or uncertain-butbounded variables [12]. The stochastic collocation method was applied by Deng et al [20] to solve the nonlinear aeroelastic system of an airfoil with a control surface Based on these features, we will present an algorithm to quantify the main statics of LCOs arising in the aeroelastic system with the nonlinear coefficient as a stochastic parameter. We will discuss the effects of the nonlinear coefficients on LCO suppression when the airfoil is subjected to Gaussian white noises

Parametric Dependence of LCO

Quantification of LCOs in Nonlinear Aeroelastic Systems

Influence of Nonlinear Stiffness to LCO Suppression

Findings

Conclusions