Lateral Vibration of Axially Moving Wire or Belt Form Materials

Theoretical analysis was performed for the lateral vibration of an axially moving linear material which is supported by pullies. The oscillation of this kind has some peculier characters, by the effect of centrifugal force the oscillation degenerates to unstable character, the modes of natural oscillation take a form of wave motion, the frequencies of free oscillation deminish with increasing velocity and there occur self excited vibrations over the critical speeds. The boundary conditions in the analysis are assumed to be constant curvature at two points of support ends. The method of solution is to simplify the characteristic equation and to unify the unknown variables. The numerical calculation by the iterative method leads to the solutions of frequency curves. Another method of analysis by the complex Fourier series gives an approximate but clear perspective of the solution.