Free, Periodic, Nonlinear Oscillation of an Axially Moving Strip

Abstract

The free, nonlinear, fundamental period of transverse oscillation of axially moving strips (e.g., tapes, fibers, belts, and band saws) is determined by the approximate solution of two, coupled, nonlinear, partial differential equations. One equation describes longitudinal motion and the other transverse motion. A solution method is developed that permits accurate and efficient period calculations. The results indicate that the existence of the axial transport velocity reduces the fundamental period of oscillation and increases the relative importance of the nonlinear terms in the equations of motion. In many cases of practical interest the linear analysis is shown to be seriously in error and one may be led to erroneous conclusions because of its limited range of applicability. Curves are presented that assist one to estimate the accuracy of the linear period calculation.