NONLINEAR VIBRATION OF AXIALLY MOVING MEMBRANE BY FINITE-ELEMENT METHOD

A theoretical and numerical formulation for nonlinear axially moving m embrane is presented. The model is based on a Lagrangian description o f the continuum problem in the context of dynamics of initially stress ed solids. Membrane elasticity is included via a finite strain model a nd the membrane transport speed is included by using conservation of t he membrane mass. Hamilton's principle provides nonlinear equations, w hich describe the three-dimensional motion of the membrane. The increm ental equations of Hamilton's principle are discretized by the finite element method. The formulation includes geometrically nonlinear effec ts: large displacements, variation of membrane tension and variations in axial velocity due to deformation. Implementation of this novel num erical model was done by adding an axially moving membrane element int o a FEM program, which contains acoustic fluid elements and contact al gorithms. Hence, analysis of problems containing interaction with the surrounding air field and contact between supporting structures was po ssible. The model was tested by comparing previous linear and present nonlinear dynamic behaviour of an axially moving web. The effects of c ontact between finite rolls and the membrane and interaction between t he surrounding air and the membrane were included in the model. The re sults show, that nonlinearities and coupling phenomena have a consider able effect on the dynamic behaviour of the system.