Abstract
The stability of a flexible cantilevered plate subjected to a parallel flow is investigated. As the flexible flat plates, the papers in a high speed printing machine, the thin plastic and metal films, the fluttering flag and the oscillating doom roof are enumerated. 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. The complex eigenvalue analysis is performed for the stability analysis. In order to consider the accuracy of dynamic stability analysis, three stability analysis method are proposed. Firstly, the analysis method based on boundary conditions in the half space surrounded by leading edge and trailing edge is performed. Hereafter, let's call it the coupled solution. Secondly, the analysis method based on the non-circulatory aerodynamic theory is performed. Let's call it the non-circulatory solution.Thirdly, the analysis method which fulfills Kutta condition is performed. Let's call it the circulatory solution.The following is made to be clear through three solutions. When the mass ratio of a fluid system for a structure system is small, the flutter of the lower mode such as a second mode become predominant. And, when the mass ratio is large, the higher mode flutter appears. Although the critical velocities of the coupled solution and the non-circulatory solution are higher than that of the circulatory solution in the second mode flutter with lower mass ratio, the critical velocities of the circulatory solution becomes higher than those of the coupled solution and the non-circulatory solution when the mass ratio increases.
