Predicting a jump to resonance using transient maps and beats

Abstract In this paper it is shown how the transient frequencies can be used to predict an incipient jump to resonance of a lightly damped non-linear oscillator. The appropriate frequency ω can be determined from the rotation number of a Poincare map, or measured directly from the beats superimposed on the steady state oscillation. The relative advantages of using an ω 2 or an ω 4 predictor are explored in digital computations and in an experimental study of a vibrating beam.