USE OF CONTROL TO MAINTAIN PERIOD-1 MOTIONS DURING WIND-UP OR WIND-DOWN OPERATIONS OF AN IMPACTING DRIVEN BEAM

We consider the dynamical response of a thin beam held fixed at one-en d while excited by an external driving force. A motion limiting constr aint, or stop, causes the beam to impact. During wind-up or wind-down operations, in which the driving frequency is continuously altered, th e system can undergo complicated motions close to the value of frequen cy at which impacts may first occur, the glazing bifurcation. In this region, the beam may experience several impacts within a long period-r epeating solution or even chaotic behavior which, in practical terms, may be undesirable to the long-term integrity of the system. The first task is to identify the zones in the space of parameters (forcing amp litude or, alternatively, the gap between the beam and the stop) in wh ich period-1 motions can be guaranteed. In this paper, in the areas in which complicated or chaotic motion occurs, a control strategy is pro posed which stabilises unstable period-1 motions. As a consequence, nu merical simulations indicate that, for any choice of parameter in the range, simple period-1 motions can be maintained, limiting the number of impacts (together with their velocity). (C) 1998 Elsevier Science L td. All rights reserved.