Stability and vibration characteristics of axially moving plates

Stability and vibration characteristics of two dimensional axially moving plates have been investigated. The closed form solution of the speed at the onset of instability is predicted by linear plate theory and exact boundary conditions. The speed at the onset of instability is the lowest speed at which non-trivial equilibrium position exists (static analysis) or the lowest speed at which the real part of one eigenvalue impends to be non-zero (dynamic analysis). The critical speed is the speed at which the transport speed of the plate equals the propagation speed of a transverse wave in the plate. The results show that the critical speed equals the speed at the onset of instability predicted by static and dynamic analyses. The speed at the onset of instability increases as the ratio of the length to the width of the plate decreases and as the flexural stiffness of the plate increases. One dimensional beam theory always overestimates the speed at the onset of instability and string theory always underestimates that speed. The plate may experience divergent or flutter instability at supercritical transport speed. A second stable region above the critical speed may exist for plates with slenderness ratio greater than a critical value determined by the stiffness ratio and Poisson's ratio. This opens the possibility of stable operation at speeds greater than the critical speed. (C) 1997 Elsevier Science Ltd.