The dynamic stability of a flexible plate subjected to a parallel flow is investigated when it moves in a flowing fluid. As the flexible flat plates, the papers in a high speed printing machine, the papers discharged by a paper machine, and the thin plastic and metal films, the fluttering flag and the oscillating doom roof caused by wind 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 fluid-structure coupled equation of motion of a flexible flat plate supported simply at the both ends is derived into consideration with the added mass, added damping and added stiffness of a fluid, respectively. In addition, the effect of tension acting on a flexible plate, the influence of velocity of a moving plate and that of a fluid velocity, are also included into the coupled equation of motion respectively. The eigenvalue analysis is performed for the dynamic stability analysis. Changing the velocities of a plate and a fluid, and the specifications of a plate as parameter studies, the influences of these parameters on the dynamic stability of a plate are clarified. It is made clear that the plate moving in a still fluid becomes unstable at slightly lower velocity than the stationary plate subjected to a parallel flow. Moreover, it is found that the present solution shows a good agreement with the already reported experiments in which the flexible flat plate was a paper.

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