REGULAR AND CHAOTIC RESPONSES OF A HAMILTONIAN BEAM MODEL

It is known that a beam that is deformed into the plastic range by a s hort transverse force pulse can exhibit anomalous behavior when its en ds are attached to supports that prohibit axial displacements. In part icular, the resulting elastic vibrations may be chaotic. When attempts are made to compute the final rest displacement, it may turn out that this is strictly unpredictable, as a consequence of the extreme sensi tivity to parameters seen in chaotic vibrations. The present work desc ribes further study of these phenomena by applying Poincare's surface of section technique. The plastic strains in the beam are regarded as fixed in the present investigation, and the ''loading'' is taken as th e imposition of initial conditions of displacement and velocity (actua lly momentum). The origin of the plastic strains is arbitrary. Here we take them as the strains left by a prior pulse loading. Thus the resu lts are relevant to an impact problem, but in fact their principal int erest may lie more generally in uncovering a rich lode of complex phen omena familiar in other physical contexts, but unexpected in the prese nt one.