Recent theoretical studies indicate that whereas large excitation amplitudes are needed to produce chaotic motions in single-degree-of-freedom systems, extremely small excitation levels can produce chaotic motions in multi-degree-of-freedom systems if they possess autoparametric resonances. To verify these results, we conducted an experimental study of the response of a two-degree-of-freedom structure with quadratic nonlinearities and a two-to-one internal resonance to a primary resonant excitation of the second mode. The responses were analyzed using hardware and software developed for performing time-dependent modal decomposition. We observed periodic, quasi-periodic, and chaotic responses, as predicted by theory. Conditions were found under which extremely small excitation levels produced chaotic motions.
An Experimental Investigation of Complicated Responses of a Two-Degree-of-Freedom Structure
Nayfeh, A. H., Balachandran, B., Colbert, M. A., and Nayfeh, M. A. (December 1, 1989). "An Experimental Investigation of Complicated Responses of a Two-Degree-of-Freedom Structure." ASME. J. Appl. Mech. December 1989; 56(4): 960–967. https://doi.org/10.1115/1.3176197
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