Vibrations of axially moving strings with in-plane oscillating supports

For a traveling string moving in the plane we analyze analytically the transverse vibrations arising from oscillation of the string supports. Of special interest is the excitation typical of roller chain drives, where meshing between chain and sprockets cause both noise and vibration. Considering a uniform, heavy string moving at subcritical speed with prescribed endpoint motion, and ignoring longitudinal inertia, one obtains a continuous, nonlinear, gyroscopic, parametrically and externally excited system.

By employing a single-mode approximation, using velocity dependent mode shapes, the system response is approximated using the method of multiple scales. Vibrations from support oscillations characteristic of roller chain drives are investigated. Conclusions about critical values for chain drive parameters such as pretension and meshing frequency are sought and identified.