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Análise dinâmica por Wavelets em um sistema com fricção seca e amortecimento

2002; Linguagem: Inglês

2639-6459

Danilo Carlos Pereira,

Chaos control and synchronization

In this work we analyzed a non-linear oscillator under dry friction conditions and damping via wavelets. Initially we presented a review on wavelets, comparing them with Fourier Transforms, detaching the principal wavelets types and the expansion of a function using wavelets as a basis. Then, varying the frequency of external excitations, we reproduced the data obtained by S. Narayanan and K. Jayaraman [1991] integrating the equations with Runge Kutta method and further obtaining the time series, the Phase Plane, the Poincare Map and the Fast Fourier Transform for each external frequency. Finally, we probed the system via the wavelets analysis obtaining the wavelet spectrum, or scalogram, and we observed that when the system passes from a periodic to a chaotic regime, wavelets turns out to be a powerful method for a precise diagnosis of the system.