- Thompson, J. M. T. and Virgin, L. N., PREDICTING A JUMP TO RESONANCE USING TRANSIENT MAPS AND BEATS.,
International Journal of Non-Linear Mechanics, vol. 21 no. 3
pp. 205 - 216 [0020-7462(86)90004-1] .
(last updated on 2007/03/23)
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 omega 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 omega **2 or an omega **4 predictor are explored in digital computations and in an experimental study of a vibrating beam.
MATHEMATICAL TECHNIQUES - Differential Equations;