A numerical solution for the transient displacement of a circumferentially moving cylindrical shell

In magnetic tape recording it is important to control the tape displacement as it is transported over guides and recording heads. In this paper a numerical solution is presented for the transient motion of a tape that is circumferentially transported. The tape may be modelled as a thin cylindrical shell, with 'gyroscopic' effects arising from the tape transport. Spatial derivatives are discretized with finite difference approximations, and time derivatives are discretized by Newmark's method. The result is a robust computer algorithm that is used in making 3D-transient simulations of flexural waves following a radial load. This ability is demonstrated to be important for realizing that reflection of the waves from the lateral sides of the tape has significant effect on the transient displacement. Results that have been previously published on 'critical' speeds, wave shapes near a concentrated load point, and the dominant period of the load point displacement are further developed. A better approximation of the critical tape speed is presented, and the dominant period of the load point displacement is found to be dependent on the tape velocity.