Nonlinear Dynamics Of Panels In Supersonic Airflow

The panel is an important structure in modern aerospace vehicles. In the circumstance of high-speed airflow, a static deformation as buckling of the panel can occur, and the flutter may be encountered, which always leads to the fatigue failure of the panel and has harmful influence on the structure reliability. In addition, when the high-speed aircraft vibrates in flight, a complicated and intensive forced-oscillation, including internal resonance, would arise by the combination of high-speed airflow and the support motion, which greatly endangers the flight safety. Now, the structure design of the supersonic aircraft has a flexible and light trend, which makes the panel stability more and more significant. So, the study of the stability and dynamic behavior of the panel under various conditions has practical meanings for the aircraft design. In this dissertation, nonlinear dynamics of the panel in supersonic airflow is investigated. The main contents are as follows:(1) The mechanical system of panels in supersonic airflow is modeled. The aerodynamic load is simplified In terms of the first-order piston theory. Appling the Von Karman deformation strain-displacement relation and Hamilton principle, the partial differential equations of transverse nonlinear vibration for the panels are derived. After nondimensionalization and discretization, a set of ordinary differential equations is obtained.(2) The stability and bifurcations of the panel system are researched. According to the Routh-Hurwitz criterion, the stability regions of the system are obtained. It is found that in some parameter regions, several equilibrium points exist in one region, whose stabilities are determined by calculating the eigenvalues of the corresponding Jacobi matrices. Numerical examples are presented to support the conclusions.(3) Forced vibrations with internal resonance of the panel system are studied through the multiple dimensions Lindstedt-Poincaré(MDLP) method, and the results obtained are compared with those of the incremental harmonic balance (IHB) method. The resonance responses of the first two modes and combination resonance are investigated and the relationship between the internal resonance and excitation amplitude is discussed. The motions of all modes are analyzed. The results show that the internal resonances occur as the excitation frequency is near the first, second natural frequency or half the sum of them under the condition that the second natural frequency is three times the first one, when the first two modes are excited by each other. However some of the internal resonances are decided by the excitation amplitude.