Controlling vibrational chaos of a curved structure

Abstract

Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbations from the initial forcing. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low-power time-continuous control, carefully tuned to each initial forcing condition, produces large long-term effects on the dynamics toward taming chaos. Without knowledge of the initial forcing, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.