Dynamic behaviour of an axially moving membrane interacting with the surrounding air and making contact with supporting structures
1University of Oulu, Faculty of Technology, Department of Mechanical Engineering
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|Academic Dissertation to be presented with the assent of The Faculty of Technology, University of Oulu, for public discussion in Raahensali (Auditorium L 10), Linnanmaa, on April 29th, 1998, at 12 noon.
Professor Pekka Neittaanmäki
Associate Professor Eero-Matti Salonen
Axially moving material problems are concerned with the dynamic response, vibration and stability of slender members which are in a state of translation. In Finland these are particularly important in the functioning of paper machines, in which out of plane vibration in the paper web, known as flutter, which from the point of view of mechanics is a phenomenon typical of an axially moving material, limits operation speeds and therefore the productivity of the machines. This subject links together a number of physical phenomena associated with aerodynamics, web movement, material behaviour and the geometry of the system. The aim of this research is to present a theoretical and numerical formulation of the nonlinear dynamic analysis of an axially moving web.
The theoretical model is based on a mixed description of the continuum problem in the context of the dynamics of initially stressed solids. Membrane elasticity is included via a finite strain model, and the membrane transport speed through a kinematical study. Hamilton’s principle provides nonlinear equations which describe the three-dimensional motion of the membrane.
The incremental equations of Hamilton’s principle are discretized by the finite element method. The formulation includes geometrically nonlinear effects: large displacements, variations in membrane tension and variations in transport velocity due to deformation. This novel numerical model was implemented by adding an axially moving membrane element to a FEM program which contains acoustic fluid elements and contact algorithms. This allowed analysis of problems including interaction with the surrounding air field and contact between supporting structures.
The model was tested by comparing previous experiments and present nonlinear description of the dynamic behaviour of an axially moving web. The effects of contact between finite rolls and the membrane and interaction between the surrounding air and the membrane were included in the model. The results show that nonlinearities and coupling phenomena have a considerable effect on the dynamic behaviour of the system. The nonlinearities cause a noticeable stiffening of the membrane, and the vibration frequency of nonlinear system increases as the amplitude grows. At high values of transport velocity the first mode frequency passes over the second linear harmonic, and even the third. The results also show that the cylindrical supports have a distinct influence on the behaviour of an axially moving sheet. The boundary of the contact region clearly moves and weakens the nonlinear hardening phenomena that otherwise increase the fundamental frequency. This influence strengthens as the radius of the cylinders increases.
Acta Universitatis Ouluensis. C, Technica
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