Abstract: J. Iwaniec, A. Klepka, T. Uhl (2011)

The paper concerns results of the research into dynamic properties and detection of changes in the determinism of undamaged and cracked aluminium plates in the function of excitation frequency. At the stage of identification experiment, the considered plates were excited to vibrations by the application of harmonic signals of frequencies corresponding to the frequencies of the first, third and sixth mode shapes respectively. Analysis of the measured displacement time histories was carried out with the use of the Recurrence Plots and the Recurrence Quantification Analysis methods. The Recurrence Plots method, which is an advanced technique of nonlinear data analysis, was used for detection of qualitative changes in the system dynamic behaviour by visualization of recurrence of system states in a phase space. The smallest sufficient embedding dimension m was estimated with the use of the false nearest neighbours algorithm while for the purposes of time delay Ï„ determining the method of mutual information function was used. In order to facilitate interpretation of information contained in the Recurrence Plots, the Recurrence Quantification Analysis was carried out. For each considered frequency of excitation significant differences in the values of the RQA measures estimated for undamaged and cracked plate were observed. It was proven that the Recurrence Plots and Recurrence Quantification Analysis methods can be used for detection of changes in the dynamic behaviour (determinism) of mechanical systems related to changes in the frequency of excitation or crack propagation. The research was motivated by the results of the spectral and restoring force analysis of measured displacement time histories that, in case of plate with the crack introduced, revealed appearance of various nonlinear and probably chaotic phenomena.

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Recurrence Plots and RQA Analysis for Damage Detection in Mechanical Systems