Analysis of Bifurcation Behavior of a Piecewise Linear Vibrator with Electromagnetic Coupling for Energy Harvesting Applications

Aroudi, Abdelali El; Ouakad, Hassen M.; Benadero, Luis; Younis, Mohammad I.

doi:10.1142/s0218127414500667

Cited by 16 publications

(9 citation statements)

References 24 publications

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“…Magnets modify the system's stiffness and lead to a double-well potential. As a result, the resonance area is expanded and additional solutions are obtained [19][20][21][22]. Since multiple resonant frequencies can be excited during machine operation, research was carried performed implementing multiple transducers connected in parallel, each of which was tuned to a different frequency [23].…”

Section: Introductionmentioning

confidence: 99%

Multiple Solutions of the Tristable Energy Harvester

et al. 2021

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This paper presents the results of numerical simulations of a non-linear, tristable system for harvesting energy from vibrating mechanical devices. Detailed model tests were carried out in relation to the system consisting of a beam and three permanent magnets. Based on the derived mathematical model and assuming a range of control parameter variability, a three-dimensional image of the distribution of the largest Lyapunov exponent was plotted. On its basis, the regions of chaotic and predictable movement of the considered system exist have been established. With reference to selected plane of the largest Lyapunov exponent cross-sections, possible co-existing solutions were identified. To identify multiple solutions, a diagram of solutions (DS) diagram was used to illustrate the number of existing solutions and their periodicity. The proposed calculation tool is based on the so-called fixed points of Poincaré cross-section. In relation to selected values of the control parameter w, coexisting periodic solutions were identified for which phase trajectories and basins of attraction were presented. Based on the model tests carried out, it was found that in order to efficiently harvest energy, appropriate transducer adjustment is required. Calibration of the transducer is necessary to obtain the greatest amplitude of vibration of the beam, which corresponds to the phase trajectory limited by external energy potential barriers. As expected, the average voltage induced on the electrodes of the piezoelectric transducer and the average electrical power recorded on the resistive element are directly proportional to the amplitude and average kinetic energy of the beam.

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Section: Introductionmentioning

confidence: 99%

Multiple Solutions of the Tristable Energy Harvester

et al. 2021

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“…In the past few years many researchers have focused on the dynamics of energy harvesting devices so that to enhance the efficiency of the energy harvester [1][2][3]. Among the numerous publications reported so far, some of them have focused on harvesting energy based on electromagnetic effect [4][5][6][7][8][9], some have focused on piezoelectric based ones [1,2,[10][11][12][13][14]. Capacitive energy harvesting devices have also been focused in the literature thanks to their ease of fabrication; however, as a major challenge, they require a voltage source to induce electric charges on the electrodes of the variable capacitor and consequently, start the conversion [3,[15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Nonlinear Dynamics of a Capacitive Energy Harvester in the Vicinity of the Primary and Secondary Resonances

Azizi

Madinei

Taghipour

et al. 2021

Preprint

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The impetus of the present study is to examine the effect of nonlinearity on the efficiency enhancement of a capacitive energy harvester. The model consists of a cantilever microbeam underneath which there is an electret layer with a surface voltage, which is responsible for the driving energy. The packaged device is exposed to unwanted harmonic mechanical excitation. The microbeam undergoes mechanical vibration and accordingly the energy is harvested throughout the output circuit. The dynamic formulation accounts for nonlinear curvature, inertia, and nonlinear electrostatic force. The efficiency of the device in the vicinity of the primary and super-harmonic resonances is examined and accordingly the output power is evaluated. Bifurcation analysis is carried out on the dynamics of the system by detecting the bifurcations in the frequency domain and diagnosing their types. One of the challenging issues in the design and analysis of energy harvesting devices is to broaden the bandwidth so that more frequencies are accommodated within the amplification region. In this study the effect of the nonlinearity on the bandwidth broadening, as well as efficiency improvement of the device, is studied.

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“…Both periodic, quasiperiodic, and non-stationary chaotic-like oscillations are observed. El Aroudi et al [ 9 ] analyzed the bifurcation behavior in a piecewise linear vibrator. A rich variety of nonlinear phenomena is detected, and performances are explored in energy harvesting applications.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Prediction of Experimental Jump and Pull-In Dynamics in a MEMS Sensor

Ruzziconi

Ramini

Younis

et al. 2014

Sensors

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The present research study deals with an electrically actuated MEMS device. An experimental investigation is performed, via frequency sweeps in a neighbourhood of the first natural frequency. Resonant behavior is explored, with special attention devoted to jump and pull-in dynamics. A theoretical single degree-of-freedom spring-mass model is derived. Classical numerical simulations are observed to properly predict the main nonlinear features. Nevertheless, some discrepancies arise, which are particularly visible in the resonant branch. They mainly concern the practical range of existence of each attractor and the final outcome after its disappearance. These differences are likely due to disturbances, which are unavoidable in practice, but have not been included in the model. To take disturbances into account, in addition to the classical local investigations, we consider the global dynamics and explore the robustness of the obtained results by performing a dynamical integrity analysis. Our aim is that of developing an applicable confident estimate of the system response. Integrity profiles and integrity charts are built to detect the parameter range where reliability is practically strong and where it becomes weak. Integrity curves exactly follow the experimental data. They inform about the practical range of actuality. We discuss the combined use of integrity charts in the engineering design. Although we refer to a particular case-study, the approach is very general.

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Analysis of Bifurcation Behavior of a Piecewise Linear Vibrator with Electromagnetic Coupling for Energy Harvesting Applications

Cited by 16 publications

References 24 publications

Multiple Solutions of the Tristable Energy Harvester

Multiple Solutions of the Tristable Energy Harvester

Bifurcation Analysis and Nonlinear Dynamics of a Capacitive Energy Harvester in the Vicinity of the Primary and Secondary Resonances

Theoretical Prediction of Experimental Jump and Pull-In Dynamics in a MEMS Sensor

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