Exact and semi-analytical finite strip for vibration and dynamic stability of traveling plates with intermediate supports

Sing the exact finite strip method, a precise solution for linear free vibration and stability of an axially moving plate subjected to plane stresses is obtained. The plate may travel over multiple line supports. Exact natural frequencies and the speed at the onset of instability in the travelling plate can be identified for different boundary conditions and plate dimensions. In addition, a semi-analytical finite strip formulation has been developed for traveling plates with arbitrary boundary conditions and various in-plane loads. Modelling with a system of elastic springs, allows interior point and line supports for the plates to be taken into account. For moving plates, the effect of dimensional ratio in-plane loads and boundary conditions on free vibration, and stability characteristics of the plates were investigated and are described in this article. The influence of speed of plate motion and interior supports on the vibration frequency of the moving plates has also been studied and is illustrated with examples.