Abstract
The dynamic stability of rectangular flexible plate often becomes a problem. As the flexible plate, the papers in a high speed printing machine, the thin plastic and metal films, the fluttering flag and the oscillating doom roof are enumerated. By two dimensional analysis, there is a limit in application range of the aspect ratio. In this paper, the dynamic stability of rectangular flexible plate is estimated in three dimensional model. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. The unsteady fluid pressure is determined by using the the integral equations for the pressure along the span and the pressure along the chord under the boundary conditions in the Fourier space. The lateral deflection of plate is assumed to be expressed as a product of the cantilevered beam mode in the streamwise direction and the free-free bending beam mode in the spanwise direction. Applying the Galerkin method for the equation of motion of an elastic plate, the three dimensional coupled equation of motion of a flexible cantilevered plate is derived. The complex eigenvalue analysis is performed for the stability analysis. Changing the mass ratio and the aspect ratio, the root loci and the vibration modes of the plate and the fluid are investigated. And, the relationship between the critical fluid velocity and the mass ratio taking the aspect ratio as a parameter is investigated.
