NONLINEAR OSCILLATIONS OF CIRCULAR PLATES NEAR A CRITICAL SPEED RESONANCE

The non-linear response of an axisymmetric, thin elastic circular plat e subject to a constant, space-fixed transverse force and rotating nea r a critical speed of an asymmetric mode, is analyzed. A small-stretch , moderate-rotation plate theory of Nowinski [J. Appl. Mech. (1964) 72 -78], leading to von Karman-type field equations is used. This leads t o non-linear modal interactions of a pair of 1-1 internally resonant, asymmetric modes which are studied through first-order averaging. The resulting amplitude equations represent a system whose O(2) symmetry i s broken by a resonant rotating force. The non-linear coupling of the modes induces steady-state solutions that have no apparent evolution f rom any previous linear analyses of this problem. For undamped disks, the analysis of the averaged Hamiltonian predicts two codimension-two bifurcations that give rise to three sets of doubly degenerate, one-di mensional manifolds of steady mixed wave motions. On the addition of t he smallest damping, the branches of the backward travelling waves wit h equal modal content become isolated, and it is proved that these are the only steady motions possible. A simple experiment is used to conf irm the analytical predictions. (C) 1998 Elsevier Science Ltd. All rig hts reserved.