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On a non-ideal magnetic levitation system: nonlinear dynamical behavior and energy harvesting analyses

  • Rodrigo Tumolin RochaEmail author
  • Jose Manoel Balthazar
  • Angelo Marcelo Tusset
  • Silvio Luiz Thomaz de Souza
  • Frederic Conrad Janzen
  • Hassan Costa Arbex
Original Paper
  • 66 Downloads

Abstract

Nowadays, a novelty of devices that use magnetic restoring forces to generate oscillations has increased substantially. These kinds of devices have been commonly used to energy harvesting area. Therefore, in this paper, numerical and analytical analyses of a non-ideal magnetic levitation system are carried out. The mathematical modeling of the magnetic levitation device is developed and examined considering an electrodynamical shaker to base-excite the main system, which is a non-ideal excitation. The magnetic levitation system has the form of a Duffing oscillator; thus, the nonlinear analysis is required to investigate the energy harvesting potential of this nonlinear system. The novelty here is the use of the shaker to the excitation which is non-ideal. The method of multiple scales is applied to investigate the modes of vibration of the coupled system, which will remark the non-ideality and nonlinear phenomena of the system. The average harvested power is described by through expressions related to the coupling between the mechanical and electrical domains. Moreover, it was developed an expression for the excitation frequency where the maximum harvested power is obtained. The results were obtained based on the numerical method of Runge–Kutta of fourth order with fixed step whose results are shown through phase planes, Poincare maps and parametrical variation. Such results showed multiple existence of behaviors (periodic, quasiperiodic and chaos), coexistence of attractors in a high sensibility of the initial conditions and interesting results of the maximum average power, obtaining high and continuous amount of energy in periodic and chaotic regions.

Keywords

Magnetic levitation Chaotic behavior Method of multiple scales Nonlinear dynamics Energy harvesting Non-ideal excitation 

Notes

Acknowledgements

The authors acknowledge support by CNPq (GRANT: 447539/2014-0) and CAPES, all Brazilian research funding agencies.

Compliance with ethical standards

Conflict of interest

The authors declare there is no conflict of interest.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of ElectronicsFederal University of Technology - ParanaPonta GrossaBrazil
  2. 2.Faculty of Mechanical Engineering of BauruSao Paulo State UniversityBauruBrazil
  3. 3.Physics and Mathematics DepartmentFederal University of Sao Joao del-ReiOuro BrancoBrazil

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