Analysis of tristable energy harvesting system having fractional order viscoelastic material
Abstract
A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the system response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intrawell motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.
 Authors:
 Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé (Cameroon)
 Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, Pennsylvania 19085 (United States)
 Publication Date:
 OSTI Identifier:
 22402526
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; CONTROL; ELECTRIC POWER; FLEXIBILITY; FRACTALS; INTERACTIONS; LYAPUNOV METHOD; MAGNETS; NONLINEAR PROBLEMS; PERIODICITY; POWER GENERATION
Citation Formats
Oumbé Tékam, G. T., Woafo, P., and Kitio Kwuimy, C. A.. Analysis of tristable energy harvesting system having fractional order viscoelastic material. United States: N. p., 2015.
Web. doi:10.1063/1.4905276.
Oumbé Tékam, G. T., Woafo, P., & Kitio Kwuimy, C. A.. Analysis of tristable energy harvesting system having fractional order viscoelastic material. United States. doi:10.1063/1.4905276.
Oumbé Tékam, G. T., Woafo, P., and Kitio Kwuimy, C. A.. 2015.
"Analysis of tristable energy harvesting system having fractional order viscoelastic material". United States.
doi:10.1063/1.4905276.
@article{osti_22402526,
title = {Analysis of tristable energy harvesting system having fractional order viscoelastic material},
author = {Oumbé Tékam, G. T. and Woafo, P. and Kitio Kwuimy, C. A.},
abstractNote = {A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the system response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intrawell motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.},
doi = {10.1063/1.4905276},
journal = {Chaos (Woodbury, N. Y.)},
number = 1,
volume = 25,
place = {United States},
year = 2015,
month = 1
}

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