Predicting a jump to resonance using transient maps and beats

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 Poincaré map, or measured directly from the beats superimposed on the steady state oscillation. The relative advantages of using an ω2 or an ω4 predictor are explored in digital computations and in an experimental study of a vibrating beam. © 1986.