High- to Low-Frequency Modal Interactions in a Cantilever Composite Plate

Abstract

We have shown through experiment a complicated dynamic behavior of a cantilever (90/30/–30/–30/30/90)s graphite-epoxy plate. The plate was base excited using a 2000-lb table shaker near its seventh (third torsional) mode. We monitored the input excitation condition using a base mounted accelerometer and the plate response using a laser vibrometer. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by amplitude and phase modulations of the seventh mode. The energy transfer from the high- to low-frequency modes observed in the plate configuration is similar to those observed in flexible beams by Anderson, Balachandran, and Nayfeh (1994) and Nayfeh and Nayfeh (1994) and in frames by Popovic, Nayfeh, Oh, and Nayfeh (1995). Therefore, we conclude that this type of modal interactions is possible for all ranges of structural stiffnesses and configurations whenever there exist modes whose natural frequencies are much lower than the natural frequencies of the directly excited modes. In addition, we also observed simultaneous activation of a two-to-one internal resonance along with the high- to low-frequency modal interactions for some excitation amplitudes and frequencies. We used time-history and power-spectra plots to characterize the experimental data and force-response plots to characterize the dynamics of the plate.