Stochastic Stability And Control Of Aeroelastic System

The flutter phenomenon of aeroelastic system is difficult scientific problems by itself and has veryimportant applications in aerospace engineering, bridge engineering, construction engineering,mechanical engineering and other fields. With the gradual deepening of the study, the randomvibration in the wind-induced vibration can not be avoided. Then, with the development of thestochastic dynamical system, it becomes possible to study the stochastic flutter of aeroelastic systems,which is one of the research hotspots in this area for the last decade.Based on the stochastic dynamical system theory, the dynamic aeroelastic stabilities are investigatedunder random noise excitation by theoretical analysis and numerical simulation. Then articulating thecomprehensive pictures, the dynamic characteristic of aeroelastic system under random noiseexcitation can be intuitively described.In the present thesis, besides the stochastic stabilization of binary airfoil system and viscoelastic platesystem that are parametrically excited by different kinds of noise，center manifold reduction foraeroelastic system with noise exciting and the effectual stochastic control for stochastic flutter withthe second order moment and the largest Lyapunov exponent are also investigated. The main contentsare as follows：1） The dynamic response statistics of a two-dimensional airfoil system under gaussian white noiseare studied. Based on the Monte carlo numerical simulation, the statistic characteristics ofresponse and the maximum Lyapunov exponents of system are given and rich dynamic behaviorsof stochastic dynamical system are obtained. It’s also found that the stochastic flutter point (thestochastic bifurcation point in probability1sense) is always before the deterministic flutter point.2） The stochastic stabilities of a viscoelastic plate subjected to the excitation of wide band noise ornon-gaussian colored noise are investigated. To understand the shtochastic flutter mechanismmore clearly, the approximate analytic expansions of the moment Lyapunov exponents arederived to get the relationships between all system parameters and the stochastic stabilization ofthe system. At last, by comparing influences of different noise on the stochastic stabilization ofthe visicoelastic plate, the different dynamic behaviors of visicoelastic system driven by differentnoise can be obtained.3） The stochastic stabilization of a binary airfoil subjected to the excitation of wide band noises is discussed. Via deriving the approximate analytic expansion of the moment Lyapunov exponents,the relationships between all system parameters and the stochastic stabilization of binary airfoilsystem are obtained. Then, we have an overall understanding to the shtochastic flutter mechanism,the almost-sure stability and moment stability of two-dimensional airfoil system.4） Center manifold reduction for the flutter of airfoils with gust loading is studied. Via the ideas ofcenter-manifold reduction, normal form and the polar coordinates transformation, an explicitpresentation for the stationary probability density function is found as an approximate analyticalsolution of related Fokker-Plank-Komogorov equation. Eventually, we derive that centermanifold reduction for the high dimensional system is effectual and the D-bifurcation point/theflutter point will disappear under vertical gust.5） Astudy is conducted regarding the stability of a two-dimensional airfoil under different stochasticdisturbances with the feedback control. It’s found that the second order differential momentequations of the airfoil system under wide band noise excited are closed, so the effectual controlparameters can be obtained by searching the second moment system. But the second orderdifferential moment equations of the airfoil system under non-gaussian colored noise excited areunclosed, so the effectual control parameters can’t be obtained by searching the second momentsystem. Then a new stochastic controller is developed by the maximum Lyapunov exponent of thesystem with feedback control. Furthermore, the numerical simulations for the two stochasticcontrollers are included to visualize the good performance in flutter suppression.