Flutter Analysis Of Plate In Supersonic Flow

The flutter analysis of rectangular plate in supersonic air flow is carried out in this paper. The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel. With the theory of elasticity, aerodynamics and Newton’s second law, we established the plate balance equation. Beam model is adopted to structure the approximate mode functions of rectangular plate.The paper is divided into two parts. One part is that we neglected the influence of the nonlinearity and studied the flutter of plate in supersonic air flow. Beside this, we analyzed the influence of the parameters on the stability of the panel and came to the critical Mach number. The second part is that we consider the nonlinearity in the equation and calculating the nonlinear vibration frequency of plate in supersonic air flow by the method of multiple scales. We also studied the influence of the different parameters. The results show that only parts of the modes are directly related with the flutter in all modes of the structure, and it is appeared in pairs. Also can be drawn, only the two specific modal frequency of overlap can make the flutter phenomenon occurred. Plate and flow parameters have a great impact on the Eigen value of the system. Air density and plate density decided the initial energy of the system, the length and width ratio affects the critical Mach number when the flutter occurs. The nonlinear frequency increases with the growth of the flow speed and the initial amplitudes, and it increases dramatically for the speed approaching the critical speed. Besides, the weak nonlinearity also reduces the effect of the nonlinear characteristic. The effects of the initial amplitudes, the flow speed , and the nonlinear term is more significant in higher order mode.