Experimental study of the vibrational behaviour of a coupled non-linear mechanical system

The article describes an experimental analysis devised to determine the responses of a multi-degree-of-freedom non-linear mechanical system to various types and degrees of excitation. Such a system was designed and built to permit analysis in the time, frequency and phase-space domains. The system consisted of six planar pendulums that were coupled by springs having non-linear non-symmetric elastic force characteristics. The free responses showed several internal resonances and thus confirmed the expected behaviour of the system. The embedding procedure was adopted in order to reconstruct the abstract phase space from a single time history. As the main intention of the work is to assess the qualitative difference between linear and non-linear behaviour of a given mechanical system under external harmonic excitation, the increase in the complexity of the system's responses with increasing amplitude of excitation is shown using time-history plots, power spectra, bicoherences, delay-time maps, integrals of correlation dimension and greatest Lyapunov exponents. The bicoherence analysis showed the effect of periodicity on the linear behaviour of the system. By estimating bicoherence it was possible to detect the effect of quadratic phase coupling on non-linear behaviour. The effects of different windows and variations in the number of segments in the averaging process are also shown. Convergence was found in correlation dimension estimates with an increasing embedding dimension when the excitation was harmonic. The correlation dimension was found to increase with an increase of the driving force, thus confirming on increased complexity of the system's responses. The estimated greatest Lyapunov exponents showed the non-chaotic character of dynamics. (C) 1999 Academic Press.