Study On Nonlinear Flutter And Its Stability Of Panel Aeroelasticity System

The panel flutter is a classical supersonic aeroelastic phenomenon on the outer skin of high-speed aerospace vehicles, which always leads to the fatigue failure of the skin panels and has a harmful influence on the flight perfermance and even flight safety. Based on the piston theory of supersonic aerodynamics, Von Karman large deformation strain-displacement relation and the Galerkin method, the aerothemoelastic stability of the non-linear panel is systematically investigated by numerical method. The main works are as follows:1. The higher order motion differential equations of the two-dimensional panel flutter system are rewritten as the lower order differential equations. Applying the eigenvalue theory and Hopf bifurcation criterian to analyze the Jacobi matrix of the equilibrium points, the analytical solutions of critical conditions of pitchfork bifurcations and Hopf bifurcations are obtained in a two-dimensional parameter plane. The number and the stabilities of the equilibrium points in the different regions of the two-dimension parameter plane are analyzed.2. Based on the quasi-steady theory of thermal stress and the first order piston theory of supersonic aerodynamics, the flutter differential equations of a panel with the thermal effect and the geometrical nonlinearity are established. The Galerkin approach is applied to simplify the equations into the discrete forms, which are solved by the fourth order Ronger-Kutta method. The calculated results show that the critical dynamic pressure of the panel is descended by the temperature loads and the amplitude of limite cycle flutter is raised with the increase of temperature. The bifurcation curve indicates that there are some different period responses in the flutter system when the temperature is changed, especially, the chaotic responses are observed in some special parameter region. When the thermal effect of material is considered, the critical dynamic pressure of the panel is further reduced and the more complex dynamic behaviors in the flutter system are observed. 3 The third order piston theory is employed to calculate the aerodynamic load acting on the panel. A nonlinear aeroelastic system of a three-dimensional panel with the thermal effect is modelled by Galerkin method. The fourth order Runge-Kutta method is utilized to analyze the bifurcation forms of the nonlinear system. The effects of mode number, temperature, nonlinear aerodynamic terms and the length /width ratio of panel on the flutter of the panel are investigated. The results show that the thermal stress is an important parameter for the flutter stability of the panel and with the rise of temperature the critical dynamic pressure of the panel is descended. The bifurcation curve of the system response vs temperature indicates that with the increase of temperature, the flutter system undertakes period 1, period 2, period 4, chaos, quasi-period and so on. The routes to chaos involve period-doubling bifurcation and quasi-period in the system. When the temperature is higher, the system loses its stability into the thermal buckling.4 The dynamical responses of the three-dimensional panel with the thermal effect and geometrical nonlinearity in turbulence are studied. The velocity of atmosphere turbulence is divided into two parts, the mean velocity and the fluctuating velocity. Von Karman's spectrum of atmosphere turbulence and the composition method of trigonometric series are used to calculate the the fluctuating velocity in time domain. The first order piston theory of supersonic aerodynamics is used to calculate the aerodynamic forces. The mean square response of the panel is calculated by random theory. The effects of some main parameters of the turbulence on the mean square roots of response are analyzed, the results of which show that the mean square roots of the response increase with the rise of the mean pressure or temperature when the mean pressure is close to and over the flutter critical pressure. The root mean square response has a pronounce change to the strength of atmosphere turbulence only when the mean pressure is close to the flutter critical pressure, but it is insensitive to the change of integral measure of atmosphere turbulence.5 Based on the Kelvin's viscoelastic damping model, the flutter equations of a three-dimensional panel made of viscoelastic material are set up. The effects of viscoelastic damping, in-plane loads, length-to-width ratios of panel and flow velocity on the flutter of the panel are analyzed. In a two-dimensional parameter plane, the characteristics of the responses of the panel are discussed, the results of which show that with the rise of viscoelastic damping the chaotic region fleetly decreases, so, the viscoelastic damping can control the chaotic response of the panel. But the viscoelastic damping has almost no effect on the buckling region. The bifurcation curve of response vs dynamical pressure shows that the flutter system of the viscoelastic panel may represent complex dynamics characteristics with variation of dynamic pressure. With the increase of dynamical pressure, the response will change into the simple limits cycle oscillation from the chaotic oscillation through a series of bifurcations.6. The nonlinear dynamical characteristics of a three-dimensional panel with boundary conditions relaxation are studied. The conventional boundary value problem of the panel involves time-dependent boundary conditions which are converted to an autonomous form using a special coordinate transformation. The flutter equations of the panel are set up by using Galerkin method. The complex dynamic behaviors in the regions close to the bifurcation points of nonlinear system are simulated with numerical method. Taking the dynamic pressure or the relaxation parameter or the in-plane loading as control parameters, the bifurcation diagrams are drawn, the results of which indicate that with variation of bifurcation parameters there are various bifurcation behaviors in the system, such as hopf bifurcation, pitchfork bifurcation, and the period-3 windows in chaos zone. In addition, in some special parameters region, there exist two stable limit cycles in the system at a same dynamic pressure, depending on different initial conditions respectively.