A NUMERICAL-SOLUTION FOR THE TRANSIENT DISPLACEMENT OF A CIRCUMFERENTIALLY MOVING CYLINDRICAL-SHELL

In magnetic tape recording it is important to control the tape displac ement as it is transported over guides and recording heads. In this pa per a numerical solution is presented for the transient motion of a ta pe 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 diffe rence approximations, and time derivatives are discretized by Newmark' s method. The result is a robust computer algorithm that is used in ma king 3D-transient simulations of flexural waves following a radial loa d. This ability is demonstrated to be important for realizing that ref lection of the waves from the lateral sides of the tape has significan t effect on the transient displacement. Results that have been previou sly 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 i s found to be dependent on the tape velocity.