TY - JOUR
T1 - Analysis of bifurcation behavior of a piecewise linear vibrator with electromagnetic coupling for energy harvesting applications
AU - El Aroudi, A.
AU - Ouakad, H.
AU - Benadero, L.
AU - Younis, M.
N1 - Funding Information:
The authors would like to thank the anonymous reviewers and the associate editor for many comments and suggestions that have helped to improve an original version of this paper. This work has been partially supported by the Spanish Ministry of Science and Innovation under grant DPI2010-16481.
PY - 2014
Y1 - 2014
N2 - Recently, nonlinearities have been shown to play an important role in increasing the extracted energy of vibration-based energy harvesting systems. In this paper, we study the dynamical behavior of a piecewise linear (PWL) spring-mass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. Different configurations of the PWL model and their corresponding state-space regions are derived. Then, from this PWL model, extensive numerical simulations are carried out by computing time-domain waveforms, state-space trajectories and frequency responses under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Filippov method, Poincaré map modeling and finite difference method (FDM). The Floquet multipliers are calculated using these three approaches and a good concordance is obtained among them. The performance of the system in terms of the harvested energy is studied by considering both purely harmonic excitation and a noisy vibrational source. A frequency-domain analysis shows that the harvested energy could be larger at low frequencies as compared to an equivalent linear system, in particular, for relatively low excitation intensities. This could be an advantage for potential use of this system in low frequency ambient vibrational-based energy harvesting applications.
AB - Recently, nonlinearities have been shown to play an important role in increasing the extracted energy of vibration-based energy harvesting systems. In this paper, we study the dynamical behavior of a piecewise linear (PWL) spring-mass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. Different configurations of the PWL model and their corresponding state-space regions are derived. Then, from this PWL model, extensive numerical simulations are carried out by computing time-domain waveforms, state-space trajectories and frequency responses under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Filippov method, Poincaré map modeling and finite difference method (FDM). The Floquet multipliers are calculated using these three approaches and a good concordance is obtained among them. The performance of the system in terms of the harvested energy is studied by considering both purely harmonic excitation and a noisy vibrational source. A frequency-domain analysis shows that the harvested energy could be larger at low frequencies as compared to an equivalent linear system, in particular, for relatively low excitation intensities. This could be an advantage for potential use of this system in low frequency ambient vibrational-based energy harvesting applications.
KW - Bifurcations
KW - Filippov method
KW - Finite difference method
KW - Floquet theory
KW - Nonlinear energy harvester
KW - Poincaré map
KW - Stability analysis
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U2 - 10.1142/S0218127414500667
DO - 10.1142/S0218127414500667
M3 - Article
AN - SCOPUS:84906099204
SN - 0218-1274
VL - 24
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 5
M1 - 1450066
ER -