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We propose an accurate approach, based on the precise integration method, to solve the aeroelastic system of an airfoil with a pitch hysteresis. A major procedure for achieving high precision is to design a predictor-corrector algorithm. This algorithm enables accurate determination of switching points resulting from the hysteresis. Numerical examples show that the results obtained by the presented method are in excellent agreement with exact solutions. In addition, the high accuracy can be maintained as the time step increases in a reasonable range. It is also found that the Runge-Kutta method may sometimes provide quite different and even fallacious results, though the step length is much less than that adopted in the presented method. With such high computational accuracy, the presented method could be applicable in dynamical systems with hysteresis nonlinearities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]