Theoretcal And Experimental Study On Dynamical Characteristics Of A Subsonic Panel

This dissertation focuses on the aeroelasticiy of a plate with one side exposed to subsonic flow and it mainly includes the following topics:the analysis of instability of the plate with different considerations; the nonlinear dynamics of the plate with the effect of several kinds of nonlinearities; the experimental studies of the plate.1. The two-dimensional panel with its both ends simply supported is firstly taken as a theortical model. The boundary element method for the flow considering the plate wake is applied for the aerodynamics pressure on the plate, and then the plate equation is discretized by the differential quadrature method. And a coupled discrete scheme is obtained based on these two methods, and it is successfully applied for the instability of the plate. The results show that the plate undergoes divergence instability only; the plate wake has significant effect on the instability mode of the plate, that is, the instability mode is not symmetric when the plate wake is considered.2. The nonlinear motion of a simply supported panel with geometric nonlinearity in a restrained flow is considered. Firstly, the flow is assumed to be constrained by a rigid plane and the aerodynamic pressure is derived from the potential theory and by using mode expansion. Galerkin method is utilized to discretize the equations of motion, and the the instability and nonlinear dynamics are analyzed. The results show that:the instability of this plate is also divergence; the critical velocities represent a nonlinear variation law with the height of the rigid plane; the effect of the rigid plane decreases with the increasing height of the rigid plane; two symmetric static states appears after the plate lose its stability and the plate will undergoes buckling motions.3. The nonlinear dynamics of a subsonic cantilevered panel with a nonlinear motion constraint is studied. The equations of motion are firstly discretized by Galerkin method and then numerical method is applied for the stability, nonlinear bifurcation and dynamics. The results show the plate undergoes both the static and dynamical stability; the type of the instability is close bound up with the linear stiffness of the motion constraint; when the stiffness is smaller the plate undergoes flutter instability, but divergence for a large stiffness; the plate undergoes limit cycle oscillation after flutter instability; the route from periodic motions to chaos is via the period-doubling bifurcation; the plate will exhibit chaos, period-3 motions.4. The nonlinear motions of a cantilevered plate in subsonic flow with the effect of both an added concentrated mass and a nonlinear motion constraint are presented. The location of the mass is varied along the plate and the motion constraint is located at the trailing end of the plate. The Galerkin method is used to discretize the equation, and the dynamics of this plate is investigated. Then the equivalent linearized method is applied for the limit cycle oscillations. It is shown that the plate loses it stability by flutter, and the critical velocities are closely bound up with the location of the mass; the critical velocities decrease when the mass is placed at some special locations; the results from the equivalent linearized method is in good agreement with the theoretical ones.5. The nonlinear dynamics of a cantilevered panel with large amplitude vibrations are studied. The nonlinear governing equation is firstly derived based on the inextensible condition and the Galerkin method is applied to discretize the equation in space. The nonlinear dynamical behaviors and the limit cycle oscillations are presented by using the numerical method. The results show that:the plate undergoes limit cycle oscillation after supercritical Hopf bifurcation; the plate exhibits both the symmetric and asymmetric limit cycle oscillation; the symmetric limit cycle oscillations become asymmetric by undergoing subcritical pitchfork bifurcation; the amplitudes of limit cycle oscillation increase with the increasing flow velocity; period-3 and chaotic motions may also appear.6. The nonlinear dynamics of cantilevered panel in subsonic flow is experimentally studied by taking wind test. The cantilevered plates with nonlinear spring supported at its trailing end and with geometric nonlinearity are, respectively, considered. The equipment of the generating nonlinear forces and the cantilevered plate with one side exposed to flow are well set up. The experimental results show that the plate could undergo flutter instability and maintain limit cycle oscillations in a range of flow velocity; the experimental results could validate the present theoretical analysis.