Resonant Oscillations of a Beam-Pendulum System

Abstract

The resonance phenomena and energy transfer associated with a set of coupled nonlinear differential equations are analyzed using asymptotic methods. The equations describe the motion of a beam-pendulum system which exhibits autoparametric excitation. Precise conditions under which resonant or nonresonant oscillations arise, are obtained. These conditions not only depend upon the physical parameters of the system but also upon the energy of the oscillations (i.e., initial conditions). In general, the envelopes of the resonant oscillations are periodic of long period and there is intermittent energy transfer between the pendulum and beam modes.