A numerical study of the nonlinear dynamics of a light, axially moving band in surrounding fluid

The vibration characteristics of a submerged axially moving band are investigated by a numerical study. A geometrically nonlinear axially moving band model is coupled to the acoustic fluid model and the periodic nonlinear problem is solved by the Fourier–Galerkin–Newton (FGN) method. The nonlinear dynamic behaviour is examined through the dependences between fundamental frequency, axial velocity and the amplitude of nonlinear free vibration. The results are compared with the behaviour of an axially moving band in a vacuum as considered in the companion paper [H. Koivurova, Journal of Sound and Vibration 320 (2009) 373–385]. In the subcritical speed range the system behaved as expected, in that the effect of the surrounding air field reduced the fundamental frequency to about one fifth of the vibration observed in a vacuum. In the supercritical speed range the effects of the surrounding air depended on the amplitude of vibration and its change with increasing geometrical nonlinearity. With linear vibrations the fundamental frequency grows faster as a function of axial velocity than in vacuum, but with nonlinear vibrations the increase in frequency is slower than in a vacuum at near-critical velocities, but with a tendency to increase faster at higher velocities.