CHAOTIC VIBRATIONS OF NON-SHALLOW ARCHES

Non-shallow arches inherently possess a nearly two-to-one internal resonance between the lowest modes of symmetric and antisymmetric vibration. This implies that non-linear modal interaction may entirely dominate the dynamic response, even at extremely small excitation levels. In this paper the effects of such non-linearities are studied by perturbation analysis and numerical simulations. Special emphasis is laid on chaotic vibrations, which are shown to occur for excitation levels and frequencies occupying significant areas of the primary region of dynamic instability. Thus, this is a case of a structure in widespread practical use, which may display unpredictable chaotic behaviour not very far from normal operating conditions. Evidence for chaotic motion is given through Poincaré sections, frequency spectres and Lyapunov exponents. The routes to chaos are shown to include quasi-periodic break-up, intermittency and long transients. © 1992 Academic Press Limited.