축방향으로 이송되는 박막의 비선형 진동

Abstract

The vibration of an axially moving membrane is investigated considering geometric non-linearity and aspect ratio. By using the extended Hamilton’s principle, the coupled non-linear partial differential equations are derived, which describe the out-of –plane motions as well as the in-plane motions. These equations of motions are discretized through the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. The new model is tested by comparing previous linear vibration. The results show that geometric nonlinearity and aspect ratio have significant effect on the nonlinear vibration of the moving membrane.