Interaction of an axially moving band and surrounding fluid by boundary layer theory

The vibration characteristics of a submerged axially moving band are investigated. Where earlier studies used the ideal fluid assumption for modelling the effect of the surrounding air, the viscous flow of the air particles is included here by using an analytical model of a boundary layer on moving continuous flat surfaces. In order to use this theory to calculate boundary layer thicknesses, the shape of the boundary layer was assumed, so that the additional mass terms coming from the boundary layer flow could then be evaluated. Since the coefficients of the equation of motion for the submerged axially moving band changes as a function of the longitudinal coordinate, due to the change in the boundary layer, the equation is solved by the finite element method. The results show the difference between the present results and earlier ones to be significant, close to the critical velocity.