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Research Papers

A Broadband Internally Resonant Vibratory Energy Harvester

[+] Author and Article Information
Li-Qun Chen

Shanghai Institute of Applied Mathematics and Mechanics;
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China;
Department of Mechanics,
Shanghai University,
Shanghai 200444, China;
e-mail: lqchen@staff.shu.edu.cn

Wen-An Jiang

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China

Meghashyam Panyam

Nonlinear Vibrations and Energy Harvesting Laboratory,
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634

Mohammed F. Daqaq

Nonlinear Vibrations and Energy Harvesting Laboratory,
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: mdaqaq@clemson.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 30, 2015; final manuscript received July 13, 2016; published online August 16, 2016. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 138(6), 061007 (Aug 16, 2016) (10 pages) Paper No: VIB-15-1412; doi: 10.1115/1.4034253 History: Received September 30, 2015; Revised July 13, 2016

The objective of this paper is twofold: first to illustrate that nonlinear modal interactions, namely, a two-to-one internal resonance energy pump, can be exploited to improve the steady-state bandwidth of vibratory energy harvesters; and, second, to investigate the influence of key system’s parameters on the steady-state bandwidth in the presence of the internal resonance. To achieve this objective, an L-shaped piezoelectric cantilevered harvester augmented with frequency tuning magnets is considered. The distance between the magnets is adjusted such that the second modal frequency of the structure is nearly twice its first modal frequency. This facilitates a nonlinear energy exchange between these two commensurate modes resulting in large-amplitude responses over a wider range of frequencies. The harvester is then subjected to a harmonic excitation with a frequency close to the first modal frequency, and the voltage–frequency response curves are generated. Results clearly illustrate an improved bandwidth and output voltage over a case which does not involve an internal resonance. A nonlinear model of the harvester is developed and validated against experimental findings. An approximate analytical solution of the model is obtained using perturbation methods and utilized to draw several conclusions regarding the influence of key design parameters on the harvester’s bandwidth.

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References

Roundy, S. , and Wright, P. , 2004, “ A Piezoelectric Vibration Based Generator for Wireless Electronics,” Smart Mater. Struct., 13(5), pp. 1131–1142. [CrossRef]
Roundy, S. , 2005, “ On the Effectiveness of Vibration-Based Energy Harvesting,” J. Intell. Mater. Syst. Struct., 16(10), pp. 809–823. [CrossRef]
Challa, V. , Prasad, M. , Shi, Y. , and Fisher, F. , 2008, “ A Vibration Energy Harvesting Device With Bidirectional Resonance Frequency Tunability,” Smart Mater. Struct., 75(1), p. 015035. [CrossRef]
Shahruz, S. M. , 2006, “ Design of Mechanical Band-Pass Filters for Energy Scavenging,” J. Sound Vib., 292(9), pp. 987–998. [CrossRef]
Harne, R. , and Wang, K. C. , 2013, “ A Review of the Recent Research on Vibration Energy Harvesting Via Bistable Systems,” Smart Mater. Struct., 24(2), p. 023001. [CrossRef]
Daqaq, M. F. , Masana, R. , Erturk, A. , and Quinn, D. D. , 2014, “ On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion,” ASME Appl. Mech. Rev., 66(4), p. 040801. [CrossRef]
Sebald, G. , Kuwano, H. , Guyomar, D. , and Ducharne, B. , 2011, “ Experimental Duffing Oscillator for Broadband Piezoelectric Energy Harvesting,” Smart Mater. Struct., 20(10), p. 102001. [CrossRef]
Green, P. L. , Worden, K. , Atalla, K. , and Sims, N. D. , 2012, “ The Benefits of Duffing-Type Nonlinearities and Electrical Optimization of a Mono-Stable Energy Harvester Under White Gaussian Excitations,” J. Sound Vib., 331(20), p. 45044517. [CrossRef]
Daqaq, M. F. , 2012, “ On Intentional Introduction of Stiffness Nonlinearities for Energy Harvesting Under White Gaussian Excitations,” Nonlinear Dyn., 69(3), p. 10631079. [CrossRef]
Mann, B. P. , Barton, D. A. W. , and Owen, B. , 2012, “ Uncertainty in Performance for Linear and Nonlinear Energy Harvesting Strategies,” J. Intell. Mater. Syst. Struct., 23(13), pp. 1451–1460. [CrossRef]
Ali, S. F. , Adhikari, S. , Friswell, M. I. , and Narayanan, S. , 2011, “ The Analysis of Piezomagnetoelastic Energy Harvesters Under Broadband Random Excitation,” J. Appl. Phys., 109(7), p. 074904. [CrossRef]
Geiyer, D. , and Kauffman, J. L. , 2015, “ Chaotification as a Means of Broadband Energy Harvesting With Piezoelectric Materials,” ASME J. Vib. Acoust., 137(5), p. 051005. [CrossRef]
Cao, J. , Zhou, S. , Inman, D. J. , and Lin, J. , 2015, “ Nonlinear Dynamic Characteristics of Variable Inclination Magnetically Coupled Piezoelectric Energy Harvesters,” ASME J. Vib. Acoust., 137(2), p. 021015. [CrossRef]
Nguyen, S. D. , Halvorsen, E. , and Paprotny, I. , 2013, “ Bistable Springs for Wideband Microelectromechanical Energy Harvesters,” Appl. Phys. Lett., 102(2), p. 023904. [CrossRef]
Stanton, S. C. , McGehee, C. C. , and Mann, B. P. , 2009, “ Reversible Hysteresis for Broadband Magnetopiezoelastic Energy Harvesting,” Appl. Phys. Lett., 95(17), p. 174103. [CrossRef]
Cottone, F. , Vocca, H. , and Gammaitoni, L. , 2009, “ Nonlinear Energy Harvesting,” Phys. Rev. Lett., 102(8), p. 080601. [CrossRef] [PubMed]
Zhou, S. X. , Cao, J. Y. , Lin, J. , and Wang, Z. Z. , 2014, “ Exploitation of a Tristable Nonlinear Oscillator for Improving Broadband Vibration Energy Harvesting,” Eur. Phys. J. Appl. Phys., 67(3) p. 30902. [CrossRef]
Erturk, A. , Renno, J. M. , and Inman, D. J. , 2009, “ Modeling of Piezoelectric Energy Harvesting From an L-Shaped Beam-Mass Structure With an Application,” J. Intell. Mater. Syst. Struct., 20(5), pp. 529–544. [CrossRef]
Nayfeh, A. H. , 1998, Nonlinear Interactions: Analytical, Computational, and Experimental Methods, Wiley, New York.
El-Bassiouny, A. F. , 2005, “ Internal Resonance of a Nonlinear Vibration Absorber,” Phys. Scr., 72(2–3), pp. 203–211. [CrossRef]
Chen, L.-Q. , and Jiang, W.-A. , 2015, “ Internal Resonance Energy Harvesting,” ASME J. Appl. Mech., 82(3), p. 031004. [CrossRef]
Haddow, A. G. , Barr, A. D. S. , and Mook, D. T. , 1984, “ Theoretical and Experimental Study of Modal Interaction in a Two-Degree-of-Freedom Structure,” J. Sound Vib., 97(3), pp. 451–473. [CrossRef]
Balachandran, B. , and Nayfeh, A. H. , 1990, “ Nonlinear Motions of Beam-Mass Structures,” Nonlinear Dyn., 1(1), pp. 39–61. [CrossRef]
Nayfeh, A. H. , and Mook, D. T. , 1979, Nonlinear Oscillations, Wiley, New York.
Timoshenko, S. , Young, D. H. , and Weaver, W. , 1974, Vibration Problems in Engineering, Wiley, New York.

Figures

Grahic Jump Location
Fig. 1

A schematic diagram of the L-shaped internally resonant VEH

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Fig. 2

Setup used in the experiments

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Fig. 3

The first two flexural normal modes of the internally resonant VEH: (a) mode 1 and (b) mode 2

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Fig. 4

Variation of the output voltage with the excitation frequency and a base acceleration of 0.5 m/s2. The results are obtained for a load resistance of 25 kΩ.

Grahic Jump Location
Fig. 5

Variation of the output voltage with the excitation frequency in the vicinity of the first modal frequency. (a) Linear response in the absence of the magnetic field, (b) nonlinear response in the presence of the magnetic field but away from the internal resonance, (c) internally resonant response, and (d) comparison between the internally and noninternally resonant responses for f1=0.0025. The results are obtained using R = 25 kΩ, a modal damping ratios of ζ1=0.005 and ζ2=0.005, and base accelerations of 0.5 m/s2 and 1 m/s2 for the internally resonant case. Dotted lines represent unstable fixed points of the modulation equations. Markers represent experimental data obtained using the setup shown in Fig. 2.

Grahic Jump Location
Fig. 6

Variation of the output voltage with the excitation frequency in the vicinity of the first modal frequency. (a) Different first-modal damping ratios, second modal damping ratio of ζ2=0.005, and an acceleration level of 0.5 m/s2. (b) Different base acceleration levels 0.5,1, and 1.5 m/s2 and damping ratios of ζ1,2=0.005. The results are obtained using R = 25 kΩ, and dotted lines represent unstable fixed points of the modulation equations.

Grahic Jump Location
Fig. 7

Variation of the output power with the excitation frequency in the vicinity of the first modal frequency. (a) Different load resistances. (b) Different first-modal couplings and R = 25 kΩ. The results are obtained for a base acceleration of 1 m/s2, and modal damping ratios of ζ1,2=0.005. Dotted lines represent unstable fixed points of the modulation equations.

Grahic Jump Location
Fig. 8

Coordinate system used in the derivation

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