VIBRATION OF AN AXIALLY MOVING STRING WITH GEOMETRIC NON-LINEARITY AND TRANSLATING ACCELERATION

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von Karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflections. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by the Galerkin method after they are transformed into the variational equations, i.e., the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized equations, the natural frequencies, the time histories of the deflections, and the distributions of the deflection and stress are investigated. In addition, comparisons between the results of linear and non-linear theories are provided.