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- W2365708647 abstract "In the literature, most methods for calculation of the fractal dimension of a nonlinear system usually use the time series of the response. Herein a modified box-counting measure to calculate the box dimension of the Poincare map of responses is proposed. Compared with the traditional G-P algorithm, the improved G-P algorithm and the box-counting approach, the computation time required for the proposed method was drastically reduced. The mode shapes of nonlinear vibratory systems are found to be associated with the box dimensions of Poincare maps. The response is chaotic if the box dimension is less than 1.0, quasi-periodic if equal to 1.0, and periodic if equal to 2.0. The proposed method is demonstrated and validated by a numerical calculation of an impact-rub rotor system supported on squeezed film dampers. The bifurcation diagram of the rotor system was compared with the plot of the box dimension of Poincare maps versus the corresponding control parameter. The great advantage of the proposed algorithm is the saving in the execution time, in addition to other advantages such as the possibility of identifying route to chaos." @default.
- W2365708647 created "2016-06-24" @default.
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- W2365708647 date "2004-01-01" @default.
- W2365708647 modified "2023-09-25" @default.
- W2365708647 title "IDENTIFICATION OF NONLINEAR REGIONS OF SYSTEM RESPONSES USING BOX DIMENSIONS OF POINCAR MAPS" @default.
- W2365708647 hasPublicationYear "2004" @default.
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