Dynamic characteristics of the out-of-plane vibration for an axially moving membrane

The dynamic characteristics of the out-of-plane vibration for an axially moving membrane are investigated in this study. The equations of in-plane and out-of-plane motions are derived by using the extended Hamilton principle. Two different types of boundary conditions are considered at the rollers: one is the condition of no friction and the other is the condition of no slipping. After discretizing the equations by the Galerkin method, the natural frequencies and mode shapes are computed. From the computation results, it is found that the translating speed, boundary conditions and aspect ratio of the membrane have effects on the natural frequencies, mode shapes and stability for the out-of-plane vibration of the moving membrane. (c) 2005 Elsevier Ltd. All rights reserved.