Flow-induced vibrations of axially moving web subjected to shear fluid flow

This paper deals with a theoretical stability analysis of a flexible web axially moving in a fluid-filled narrow space with shear fluid flow. In the stability analysis, governing equation of motion of the axially moving web coupled with the shear fluid flow is derived from Bernoulli-Euler's beam equation and Navier-Stokes equations, and characteristic equation of the system is derived as a function of the axially moving speed of the web. The stability of the system is examined by calculating roots of the characteristic equation of the system. As a result, the analytical results find that divergence type instability and flutter type instability occur in the axially moving web due to the shear fluid flow when the web speed becomes high. Moreover, the analytical results show the instability regions of the divergence and flutter.