https://doi.org/10.1140/epjp/s13360-023-04559-0
Regular Article
Fractional dynamical behavior of a new nonlinear smooth and discontinuous (SD) oscillator for vibration energy harvesting with nonlinear magnetic coupling
1
Laboratory of Mechanics, Department of Physics, Faculty of Sciences, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
2
University Institute of Wood Technology, Civil Engineering, The University of Yaounde I, P.O. Box 306, Mbalmayo, Cameroon
3
Department of Physics, Faculty of Sciences, University of Bangui, P.O. Box 1450, Bangui, Central African Republic
4
Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana
Received:
26
August
2023
Accepted:
4
October
2023
Published online:
21
October
2023
The objective of this research is to propose a promising solution approach introducing intentionally the strong nonlinearity due to the geometrical configuration into a piezoelectric energy harvester, sought analytical solutions via the method of harmonic balance and modeled mathematically the damping forces originating from friction and air resistance. Vibratory energy harvesters are scalable power generators that consist of a mechanical oscillator coupled to an electric load via an electromechanical transduction mechanism. Thence, nonlinear dynamic performance appears by a pair of inclined linear elastic springs under harmonic external base excitation. The present work is motivated to explore the gravity through SD oscillator to generate the nonlinearity in an electromagnetic energy harvester with fractional properties and found increased performance by adjusting the size of the geometrical parameter to meet different engineering needs and produce a large output power. A prospective case study is illustrated for electromagnetic energy harvesting, revealing the importance of higher harmonics and the need to explore multiterm harmonic balance for predicting the electrical power output accurately. The work shows the importance of irrational nonlinear restoring forces controlled by geometrical parameters in the engineering structures designing. The result is that the nonlinear piecewise function accurately mimics the nonlinear restoring force and maintains a nonlinearity property. The performance of the system with fractional derivative and through the parameter adjustment is justified numerically by the mean of the Newton–Leipnik algorithm. The new nonlinear SD oscillator can achieve quasi-zero-stiffness characteristic, thence multistable characteristic to provide the chaotic and periodic regions. We use bifurcation diagrams, Test 0–1. A vibration-powered harvester modeled by SD oscillator with the Caputo fractional derivative highlights the benefits of the fractional approach in comparison with the classical integer one provided certainly. The influence of fractional damping on the transition dynamics from smooth to discontinuous, the amplitude–frequency response and the snap-through of the SD oscillator leading to better utilization of the multistability characteristics of the SD oscillator are studied. Harmonic analysis is performed to predict the amplitude of vibration. The positioning of the piezoelectric element over mechanical system to the outer electromagnetic systems is the valorized aspect of this research.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
