ENERGY-TRANSFER FROM HIGH-FREQUENCY TO LOW-FREQUENCY MODES IN A FLEXIBLE STRUCTURE VIA MODULATION

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.