A differential Quadrature out-of-plane vibration analysis of axially moving thin plates

The stability of the out-of-plane vibration for axially moving thin plates with two simply supported edges and two built-in edges is investigated. The Galerkin method is employed to discretize the governing partial differential equations into a set of ordinary differential equations. The complex frequencies are computed via Differential Quadrature Method. The result shows that the natural frequencies decrease as the transporting speed increases when the plates traveling at a speed less than the critical speed. The plates may experience divergent and flutter instability at a supercritical transport speed. A second stable region exists above the critical speed. This may propose the possibility to perform stable operation at speeds greater than the critical speed.