Remarks on nonlinear dynamics of a suspension bridge model note on fractional order

Authors

  • Felipe Lima de Abreu Faculty of Engineering, Federal University of Grande Dourados
  • Murilo Cesar Filipus Department of Electrical Engineering, São Paulo State University.
  • Clivaldo de Oliveir Faculty of Engineering, Federal University of Grande Dourados
  • José Manoel Balthaza Department of Electrical Engineering, São Paulo State University
  • Mauricio A. Ribeiro Department of Electrical Engineering, São Paulo State University.
  • Angelo Marcelo Tusset Federal University of Technology –Parana, Ponta Grossa, PR.
  • Marcus Varanis Physics Institute, Federal University of Mato Grosso do Sul (UFMS), Campo Grande,MS.

Abstract

This paper aims to explore the richer dynamics of the Lazer-McKenna suspension bridge model, which is a asymmetric system of equations that has previously shown chaotic dynamics, here the study will be made by means of fractional order differential equations where the order of the entire system is varied. For the solutions it was used integration schemes previously shown in the literature, which were implemented in the Python programming language, the dynamics were then analyzed in the time domain by means of phase-space, Poincaré sections, and bifurcation diagrams, and in the frequency domain by Discrete Fourier Transform (DFT), Continuous Wavelet Transform (CWT) and Hilbert-Huang Transform (HHT). The investigated responses demonstrated a great influence of the fractional order in the system, changing its time dynamics from chaotic to periodic.

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Published

09/01/2024

Issue

Vol. 15 No. 3 (2024): Mathematics in Science, Engineering, and Aerospace (MESA)

Section

Articles