Experimental investigation of coupling between widely spaced modes of a beam using higher-order spectra

Experimental studies related to a thin isotropic steel beam are presented. The beam was harmonically excited along its axis creating a situation of parametric excitation. A possible two-to-one internal resonance was considered between the third and fourth modes of the beam with an external resonance of its fourth mode. The coupling phenomenon responsible for transfer of energy from high frequency modes to a widely spaced low frequency mode was studied by using conventional tools and higher-order spectra (third-order spectrum (bispectrum) and fourth-order spectrum (trispectrum)). Pointwise dimensions of the attractors were examined to ascertain their chaotic character. The potential of higher-order spectra in detecting the quadratic and cubic phase couplings among the participating modes during bifurcations, periodically modulated motions, and chaotically modulated motions was also examined. The experimental results are provided in the form of power spectra, fractal dimensions, bispectra, bicoherence spectra, and trispectrum. Experimental observations of transitions from periodic to periodically modulated to chaotically-modulated motions are also presented. (author)