Sa. Nayfeh et Ah. Nayfeh, ENERGY-TRANSFER FROM HIGH-FREQUENCY TO LOW-FREQUENCY MODES IN A FLEXIBLE STRUCTURE VIA MODULATION, Journal of vibration and acoustics, 116(2), 1994, pp. 203-207
An experimental study of the response of axially-symmetric (i.e., circ
ular cross-section) cantilever beams to planar external excitations is
presented. Because of the axial symmetry, one-to-one internal resonan
ces occur at each natural frequency. These resonances cause the planar
motions to lose stability and nonplanar (whirling) motions are observ
ed. Under certain conditions, periodically- and chaotically-modulated
motions may occur. In addition, when the beam is excited near one of i
ts high natural frequencies, large first-mode responses accompanied by
slow modulations of the amplitudes and phases of high-frequency modes
are observed. This interaction between high- and low-frequency modes
may be extremely dangerous because the amplitudes of the responses of
the low-frequency modes can be very large compared with those of the d
irectly excited high-frequency modes.