Complicated Responses Of Supersonic Flutter System With Structural Nonlinearities

The flutter phenomenon of aeroelastic systems is one of the most important problems in many areas, such as aviation, wind power generation, civil engineering and etc. The bifurcation and complex response of the nonlinear aeroelastic systems are the research hotspot in this area. Based on the modern nonlinear dynamics theory, the bifurcations and complex dynamical responses of nonlinear aeroelastical systems are investigated by analytical and numerical simulation methods in this dissertation, and the main contributions are as follows:1 Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of an airfoil with cubic stiffness in pitching direction are established. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of the system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system, the results of which show that the number and the stability of equilibrium points of the system are changed with the increasing of the flow speed. In addition to the simple limit cycle response of period 1, there are the period-doubling responses and the chaotic motions in the flutter system. The route leading to chaos in the aeroealstic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos are narrow.2 The limit cycle flutter of an airfoil with free-play in pitching direction is investigated. The dynamic force and moment are calculated by using the local piston theory. The equivalent linearization method based on the first order asymptotic solution of the KBM method is used to obtain the equivalent stiffness, which is the function of amplitude of limit cycle. The nonlinear system is equivalent to a linear system. Then, the flutter boundary curve of flutter speed versus the amplitude of limit cycle is determined. The results are compared with those of numerical integration. It is shown that the system is in the state of double stable limit cycle flutter in some speed region. The different limit cycle occurs with the different initial condition.3. The dynamical response of a two-dimensional wing to atmosphere turbulence is investigated. The aerodynamical forces are divided into two parts, free vibrating aerodynamics and fluctuating aerodynamics. The root of mean square of response of system is calculated by using the random theory. It is the focal point to analyze the effects of the mean velocity, the strength of turbulence and the integral measure of turbulence on the root of mean square of structure response. The results show that when the flow velocity is over the flutter critical speed, the root of mean square of response prominently increases with increasing of the flow velocity. However, the root of mean square of response is insensitive to the change of the integral measure of turbulence.4 A two-dimension wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the chaotic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condition of stable limit cycle flutters of the aeroelastic system, the vibration in the plunging and pitching of the wing can approximately be considered to be simple harmonic excitation to the control surface. The motion of the control surface can be modeled by a nonlinear oscillator of one-degree-of-freedom. Then, the range of the chaotic response of the control surface is approximately determined. The theoretical analysis is verified by the numerical results.5 By nonlinear dynamic model of a wing with a control surface with asymmetric piecewise linear stiffness, the emphasis focuses on the complex responses of the nonlinear aeroelastic system. The region of flow speed of limit cycle flutter is presented by the equivalent linearization method based on the second order asymptotic solution of the KBM method. The complex dynamic behaviors close by the bifurcation points of nonlinear system are posted by numerical simulation. The results show that, for the wing with a control surface model with asymmetric piecewise linear nonlinearity, there are many complex phenomena. The system has stable limit cycle or quasi-periodical motion in the same flow speed. With the increase of flow speed, chaotic motion even occurs. 6 An approximate method is developed to analyze the subharmonic bifurcation of a wing with a store aeroelastic system, of which the junction stiffness is piecewise linear with clearance. The store separated from wing is treated as a forced oscillator under harmonic excitation excited through the junction from the wing in limit cycle flutter states. By using the equivalent linearization method, the approximate bifurcation equation is derived and is applied to predict the subharmonic response of a wing/store system. The results of numerical simulation show that the approximate approach is feasible.