Vibrations and stability of a moving band

Abstract The problem of a thin strip moving with constant speed in a longitudinal direction is formulated. The effect of a conservative point load acting parallel to the plane of the strip and normal to one of the short sides of the cross section is included in the formulation and a study is made of the lateral and torsional motions of the strip. The equations governing the dynamic motion of the strip are derived by a variational method and it is shown that the presence of the point load couples the lateral and torsional motions both in the system differential equations and in the boundary conditions. The coupled equations have variable coefficients due to the terms involving the initial state of stress arising from the presence of the point load. An exact analytical solution not being feasible, a parametric study of the lowest modes is carried out using a collocation method of solution. The effects of various system parameters on the frequency are studied and the occurrence of a static buckling load is predicted. The results of the study are compared with a previous analysis where the coupling of lateral and torsional motion was neglected. It is shown that in certain cases, the coupling effect is very important and cannot be neglected.