平行流を受ける柔軟平板の動的安定性における 3 次元性の影響

抄録

Dynamic stability of rectangular flexible plate often becomes 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 2 dimensional analysis, there is a limit in application range of the aspect ratio. In this paper, dynamic stability of rectangular flexible plate is estimated in 3 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 coupled equation of motion of a flexible cantilevered plate is derived into consideration with the added mass, added damping and added stiffness respectively. Galerkin method and the complex eigenvalue analysis is performed for the stability analysis. In order to consider effect of 3 dimensional analysis on dynamic stability, results by 3 dimensional analysis was compared with them by 2 dimensional analysis. When the mass ratio of a fluid system for a structure system is small, the critical velocity calculated by 3 dimensional analysis is higher than that calculated by 2 dimensional analysis. And, when mass ratio is large, the critical velocity calculated by 3 dimensional analysis is lower than that calculated by 2 dimensional analysis. Moreover, in order to consider the effect of gap width of channel flow, the critical velocity is calculated in different gap width.