THE USE OF CONTROL TO ELIMINATE SUBHARMONIC AND CHAOTIC IMPACTING MOTIONS OF A DRIVEN BEAM

Results of a numerical investigation are presented of the behaviour of a mathematical model which approximates the response of a thin metal strip, or beam, held vertically and clamped at its base, which is driv en to impact against a motion limiting constraint. Previous theoretica l analyses, in conjunction with numerical studies, have highlighted th e complicated dynamics that the system exhibits following a single or series of grazing bifurcations. Under certain conditions subharmonic s olutions and chaotic impacting motions are unavoidable. These solution s, which involve several impacts per orbital period introducing relati vely large impact velocities, have been viewed experimentally. Meanwhi le research into the control of chaos, in which unstable orbits embedd ed within chaotic motions are stabilized, has advanced over recent yea rs. New control methods have been developed and experimentally impleme nted. The present work brings these two fields together for the first time. Numerical evidence is given for the use of control to eliminate complicated motions by tracking lower periodic solutions. The stabiliz ed motions near the grazing incidence have lower impact velocities tha n the naturally existing stable solutions leading to a significant red uction of the impact force which may have significant engineering rele vance. (C) 1997 Academic Press Limited.