DYNAMICAL BEHAVIOUR OF THE PLANAR NON-LINEAR MECHANICAL SYSTEM — PART II: EXPERIMENT

Abstract

The experimental work has been undertaken on the washing complex dynamics to verify the theoretical approach from Part I. The measured time histories were analyzed by using spectral and phase-space analyses. The correlation dimension and the largest Lyapunov exponent were estimated on a reconstructed phase space through an embedding procedure by using different measured time histories. The largest positive Lyapunov exponent and the non-integer value of the correlation dimension of the attractor confirm the chaotic nature of the washing complex dynamics. The visualization procedure was also implemented in three-dimensional space. Differences were found in the values of the correlation dimension and largest Lyapunov exponent when estimating them from different measured signals. At the same time those estimated values show the same nature of motion. Power spectra and bicoherences have been used to analyze the washing complex dynamical behaviour. It has been found that the dominant mode is the spin-dry frequency, while the higher modes have significantly lower power. The quadratic phase coupling between the second and fifth harmonic is present, thus confirming that the process is non-linear. It is also shown that the bicoherence estimate is sensitive to division by a small number, which can increase its number of peaks. In this case, the magnitude bispectrum has been used to provide a more realistic picture of quadratic phase coupling. The model, described in Part I, is able to simulate the amplitude and the frequency of the predominant harmonic of the washing complex in the steady state, but is unable to simulate all the richness of the motion of the washing complex.