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Research Papers

Nonlinear Dynamic Characteristics of Variable Inclination Magnetically Coupled Piezoelectric Energy Harvesters

[+] Author and Article Information
Junyi Cao

State Key Laboratory for Manufacturing Systems
Engineering,
Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University,
Xi’an 710049, China;
Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140
e-mail: caojy@mail.xjtu.edu.cn

Shengxi Zhou, Jing Lin

State Key Laboratory for Manufacturing Systems
Engineering,
Research Institute of Diagnostics and Cybernetics,
Xi’an Jiaotong University,
Xi’an 710049, China

Daniel J. Inman

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140
e-mail: daninman@umich.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 3, 2014; final manuscript received November 8, 2014; published online January 20, 2015. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 137(2), 021015 (Apr 01, 2015) (9 pages) Paper No: VIB-14-1203; doi: 10.1115/1.4029076 History: Received June 03, 2014; Revised November 08, 2014; Online January 20, 2015

This paper investigates the nonlinear dynamic characteristics of a magnetically coupled piezoelectric energy harvester under low frequency excitation where the angle of the external magnetic field is adjustable. The nonlinear dynamic equation with the identified nonlinear magnetic force is derived to describe the electromechanical interaction of variable inclination angle harvesters. The effect of excitation amplitude and frequency on dynamic behavior is proposed by using the phase trajectory, power spectrum, and bifurcation diagram. The numerical analysis shows that a rotating magnetically coupled energy harvesting system exhibits rich nonlinear characteristics with the change of external magnet inclination angle. The nonlinear route to and from large amplitude high-energy motion can be clearly observed. It is demonstrated numerically and experimentally that lumped parameters equations with an identified polynomials for magnetic force could adequately describe the characteristics of nonlinear energy harvester. The rotating magnetically coupled energy harvester possesses the usable frequency bandwidth over a wide range of low frequency excitation by adjusting the angular orientation.

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References

Pearson, M. R., Eaton, M. J., Pullin, R., Featherston, C. A., and Holford, K. M., 2012, “Energy Harvesting for Aerospace Structural Health Monitoring Systems,” J. Phys. Conf. Ser., 382(1), p. 012025. [CrossRef]
Qing, X. P., Chan, H. L., and Beard, S. J., 2006, “An Active Diagnostic System for Structural Health Monitoring of Rocket Engines,” J. Intell. Mater. Syst. Struct., 17(7), pp. 619–628. [CrossRef]
Ihn, J. B., and Chang, F. K., 2004, “Detection and Monitoring of Hidden Fatigue Crack Growth Using a Built-In Piezoelectric Sensor/Actuator Network: I. Diagnostics,” Smart Mater. Struct., 13(3), pp. 609–620. [CrossRef]
Lynch, J. P., and Loh, K. J., 2006, “A Summary Review of Wireless Sensors and Sensor Networks for Structural Health Monitoring,” Shock Vib. Dig., 38(2), pp. 91–128. [CrossRef]
Lu, K. C., Loh, C., Yang, Y., Lynch, J. P., and Law, K. H., 2008, “Real-Time Structural Damage Detection Using Wireless Sensing and Monitoring System,” Smart Struct. Syst., 4(6), pp. 759–778. [CrossRef]
Zhao, X., Gao, H., Zhang, G., Ayhan, B., Yan, F., Kwan, K., and Rose, J. L., 2007, “Active Health Monitoring of an Aircraft Wing With Embedded Piezoelectric Sensor/Actuator Network: I. Defect Detection, Localization and Growth Monitoring,” Smart Mater. Struct.16(4), pp. 1208–1225. [CrossRef]
Marinkovic, B., and Koser, H., 2012, “Demonstration of Wide Bandwidth Energy Harvesting From Vibrations,” Smart Mater. Struct., 21(6), p. 065006. [CrossRef]
Marinkovic, B., and Koser, H., 2009, “Smart Sand—A Wide Bandwidth Vibration Energy Harvesting Platform,” Appl. Phys. Lett., 94(10), p. 103505. [CrossRef]
Blarigan, L. V., Danzl, P., and Moehlis, J., 2012, “A Broadband Vibrational Energy Harvester,” Appl. Phys. Lett., 100(25), p. 253904. [CrossRef]
Quinn, D. D., Triplett, A. L., Bergman, L. A., and Vakakis, A. F., 2011,“Comparing Linear and Essentially Nonlinear Vibration-Based Energy Harvesting,” ASME J. Vib. Acoust., 133(1), p. 011001. [CrossRef]
Hajati, A., and Kim, S. G., 2011, “Ultra-Wide Bandwidth Piezoelectric Energy Harvesting,” Appl. Phys. Lett., 99(8), p. 083105. [CrossRef]
Tang, L., Yang, Y., and Soh, C. K., 2010, “Toward Broadband Vibration-Based Energy Harvesting,” J. Intell. Mater. Syst. Struct., 21(18), pp. 1867–1897. [CrossRef]
Leland, E. S., and Wright, P. K., 2006, “Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload,” Smart Mater. Struct., 15(5), pp. 1413–1420. [CrossRef]
Masana, R., and Daqaq, M. F., 2011, “Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters,” ASME J. Vib. Acoust., 133(1), p. 011007. [CrossRef]
Rhimi, M., and Lajnef, N., 2012, “Passive Temperature Compensation in Piezoelectric Vibrators Using Shape Memory Alloy-Induced Axial Loading,” J. Intell. Mater. Syst. Struct., 23(15), pp. 1759–1770. [CrossRef]
Lallart, M., Anton, S. R., and Inman, D. J., 2010, “Frequency Self-Tuning Scheme for Broadband Vibration Energy Harvesting,” J. Intell. Mater. Syst. Struct., 21(9), pp. 897–906. [CrossRef]
Eichhorn, C., Tchagsim, R., Wilhelm, N., and Woias, P., 2011, “A Smart and Self-Sufficient Frequency Tunable Vibration Energy Harvester,” J. Micromech. Microeng., 21(10), p. 104003. [CrossRef]
Mann, B. P., and Sims, N. D., 2009, “Energy Harvesting From the Nonlinear Oscillations of Magnetic Levitation,” J. Sound Vib., 319(1–2), pp. 515–530. [CrossRef]
Burrow, S., Clare, L. R., Carrella, A., and Barton, D., 2008, “Vibration Energy Harvesters With Nonlinear Compliance,” Proc. SPIE, 6928, p. 692807.
Ramlan, R., Brennan, M. J., Mace, B. R., and Kovacic, I., 2009, “Potential Benefits of an On-Linear Stiffness in an Energy Harvesting Device,” Nonlinear Dyn., 59(4), pp. 545–558. [CrossRef]
Stanton, S. C., McGehee, C. C., and Mann, B. P., 2010, “Reversible Hysteresis for Broadband Magnetopiezoelastic Energy Harvesting,” Appl. Phys. Lett., 95(17), p. 174103. [CrossRef]
Daqaq, M., Stabler, C., Qaroush, Y., and Seuaciuc-Osorio, T., 2009, “Investigation of Power Harvesting Via Parametric Excitations,” J. Intell. Mater. Syst. Struct., 20(5), pp. 545–557. [CrossRef]
Shahruz, S., 2004, “Increasing the Efficiency of Energy Scavengers by Magnets,” ASME J. Comput. Nonlinear Dyn., 3(4), p. 041001. [CrossRef]
Cottone, F., Vocca, H., and Gammaitoni, L., 2009, “Nonlinear Energy Harvesting,” Phys. Rev. Lett., 102(8), p. 080601. [CrossRef] [PubMed]
Erturk, A., Hoffmann, J., and Inman, D. J., 2009, “A Piezo-Magneto-Elastic Structure for Broadband Vibration Energy Harvesting,” Appl. Phys. Lett.94(25), p. 254102. [CrossRef]
Gammaitoni, L., Neri, I., and Vocca, H., 2009, “Nonlinear Oscillators for Vibration Energy Harvesting,” Appl. Phys. Lett.94(16), p. 164102. [CrossRef]
Stanton, S. C., McGehee, C. C., and Mann, B. P., 2010, “Nonlinear Dynamics for Broadband Energy Harvesting: Investigation of a Bistable Piezoelectric Inertial Generator,” Physica D, 239(10), pp. 640–653. [CrossRef]
Erturk, A., and Inman, D. J., 2011, “Broadband Piezoelectric Power Generation on High-Energy Orbits of the Bistable Duffing Oscillator With Electromechanical Coupling,” J. Sound Vib., 330(10), pp. 2339–2353. [CrossRef]
Masana, R., and Daqaqa, M. F., 2012, “Energy Harvesting in the Super-Harmonic Frequency Region of a Twin-Well Oscillator,” J. Appl. Phys.111(4), p. 044501. [CrossRef]
Pellegrini, S. P., Tolou, N., Schenk, M., and Herder, J. L., 2013, “Bistable Vibration Energy Harvesters: A Review,” J. Intell. Mater. Syst. Struct., 24(11), pp. 1303–1312. [CrossRef]
Harne, R. L., and Wang, K. W., 2013, “A Review of the Recent Research on Vibration Energy Harvesting Via Bistable Systems,” Smart Mater. Struct., 22(2), p. 023001. [CrossRef]
Zhou, S., Cao, J., Erturk, A., and Lin, J., 2013, “Enhanced Broadband Piezoelectric Energy Harvesting Using Rotatable Magnets,” Appl. Phys. Lett., 102(17), p. 173901. [CrossRef]
Zhou, S., Cao, J., Inman, D. J., Lin, J., Liu, S., and Wang, Z., 2014, “Broadband Tristable Energy Harvester: Modeling and Experiment Verification,” Appl. Energy, 133(C), pp. 33–39. [CrossRef]

Figures

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Fig. 1

The nonlinear energy harvester with external magnets of variable inclination

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Fig. 2

Magnetic force curves under different inclination angles

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Fig. 3

Potential energy under different inclination angles

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Fig. 4

Bifurcation diagram of voltage output versus f when θ = 0 deg and A = 0.56 g

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Fig. 5

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 4 Hz

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Fig. 6

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 5 Hz

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Fig. 7

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 9.9 Hz

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Fig. 8

Phase orbit, Poincare map, output voltage, and its power spectrum for f = 13 Hz

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Fig. 9

Bifurcations diagrams for θ = 30 deg, 60 deg, 90 deg, and no magnets

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Fig. 10

Bifurcation diagram of voltage output versus A when θ = 0 deg and f = 10 Hz

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Fig. 11

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.4 g

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Fig. 12

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.45 g

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Fig. 13

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.5 g

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Fig. 14

Phase orbit, Poincare map, output voltage, and its power spectrum for A = 0.8 g.

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Fig. 15

Experimental setup

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Fig. 16

Increasing frequency sweep experiment for A = 0.56 g

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Fig. 17

Increasing frequency experimental results for f = 8.5 Hz, A = 0.56 g, and θ = 0 deg

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Fig. 18

Different excitation voltage response for θ = 0 deg

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Fig. 19

Constant frequency experimental results for f = 8 Hz, A = 0.56 g, and θ = 0 deg

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Fig. 20

Experimental results for f = 5.2 Hz and A = 0.56 g

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Fig. 21

Experimental results for f = 10 Hz and A = 0.56 g

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Fig. 22

Voltage response under different inclination angles

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Fig. 23

Amplitude sweep voltage responses for θ = 0 deg

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Fig. 24

Amplitude sweep voltage responses for θ = 30 deg

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Fig. 25

Experimental results for f = 10 Hz and A = 0.4 g

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Fig. 26

Experimental results for f = 10 Hz and A = 0.8 g

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Fig. 27

Constant excitation voltage output for θ = 0 deg

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Fig. 28

Constant excitation voltage output for θ = 30 deg

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Fig. 29

Constant excitation voltage output for θ = 60 deg

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