0
Research Papers

Dynamics of Transition Regime in Bistable Vibration Energy Harvesters

[+] Author and Article Information
Alwathiqbellah Ibrahim

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902
e-mail: aibrahi4@binghamton.edu

Shahrzad Towfighian

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902
e-mail: stowfigh@binghamton.edu

Mohammad I. Younis

Department of Mechanical Engineering,
State University of New York at Binghamton,
4400 Vestal Parkway East,
Binghamton, NY 13902;
Physical Science and Engineering Division,
King Abdullah University of Science
and Technology,
Thuwal 23955-6900, Saudi Arabia
e-mails: myounis@binghamton.edu; mohammad.younis@kaust.edu.sa

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 9, 2016; final manuscript received April 13, 2017; published online June 28, 2017. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 139(5), 051008 (Jun 28, 2017) (15 pages) Paper No: VIB-16-1454; doi: 10.1115/1.4036503 History: Received September 09, 2016; Revised April 13, 2017

Vibration energy harvesting can be an effective method for scavenging wasted mechanical energy for use by wireless sensors that have limited battery life. Two major goals in designing energy harvesters are enhancing the power scavenged at low frequency and improving efficiency by increasing the frequency bandwidth. To achieve these goals, we derived a magnetoelastic beam operated at the transition between mono- and bi-stable regions. By improving the mathematical model of the interaction of magnetic force and beam dynamics, we obtained a precise prediction of natural frequencies as the distance of magnets varies. Using the shooting technique for the improved model, we present a fundamental understanding of interesting combined softening and hardening responses that happen at the transition between the two regimes. The transition regime is proposed as the optimal region for energy conversion in terms of frequency bandwidth and output voltage. Using this technique, low-frequency vibration energy harvesting at around 17 Hz was possible. The theoretical results were in good agreement with the experimental results. The target application is to power wildlife biologging devices from bird flights that have consistent high power density around 16 Hz (Shafer et al., 2015, “The Case for Energy Harvesting on Wildlife in Flight,” Smart Mater. Struct., 24(2), p. 025031).

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Shafer, M. W. , MacCurdy, R. , Shipley, J. R. , Winkler, D. , Guglielmo, C. G. , and Garcia, E. , 2015, “ The Case for Energy Harvesting on Wildlife in Flight,” Smart Mater. Struct., 24(2), p. 025031. [CrossRef]
Roundy, S. , Wright, P. K. , and Rabaey, J. , 2003, “ A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes,” Comput. Commun., 26(11), pp. 1131–1144. [CrossRef]
Mitcheson, P. D. , Green, T. C. , Yeatman, E. M. , and Holmes, A. S. , 2004, “ Architectures for Vibration-Driven Micropower Generators,” J. Microelectromech. Syst., 13(3), pp. 429–440. [CrossRef]
Cook-Chennault, K. , Thambi, N. , and Sastry, A. , 2008, “ Powering MEMS Portable Devices—A Review of Non-Regenerative and Regenerative Power Supply Systems With Special Emphasis on Piezoelectric Energy Harvesting Systems,” Smart Mater. Struct., 17(4), p. 043001. [CrossRef]
González, J. L. , Rubio, A. , and Moll, F. , 2002, “ Human Powered Piezoelectric Batteries to Supply Power to Wearable Electronic Devices,” Int. J. Soc. Mater. Eng. Resour., 10(1), pp. 34–40. [CrossRef]
Mathúna, C. Ó. , O'Donnell, T. , Martinez-Catala, R. V. , Rohan, J. , and O'Flynn, B. , 2008, “ Energy Scavenging for Long-Term Deployable Wireless Sensor Networks,” Talanta, 75(3), pp. 613–623. [CrossRef] [PubMed]
Torah, R. , Glynne-Jones, P. , Tudor, M. , O'Donnell, T. , Roy, S. , and Beeby, S. , 2008, “ Self-Powered Autonomous Wireless Sensor Node Using Vibration Energy Harvesting,” Meas. Sci. Technol., 19(12), p. 125202. [CrossRef]
Gregori, S. , Li, Y. , Li, H. , Liu, J. , and Maloberti, F. , 2004, “ 2.45 GHZ Power and Data Transmission for a Low-Power Autonomous Sensors Platform,” International Symposium on Low Power Electronics and Design (ISLPED’04), Newport Beach, CA, Aug. 11, pp. 269–273.
Kim, J.-W. , Takao, H. , Sawada, K. , and Ishida, M. , 2007, “ Integrated Inductors for RF Transmitters in CMOS/MEMS Smart Microsensor Systems,” Sensors, 7(8), pp. 1387–1398. [CrossRef]
Bracke, W. , Merken, P. , Puers, R. , and Van Hoof, C. , 2007, “ Generic Architectures and Design Methods for Autonomous Sensors,” Sens. Actuators A, 135(2), pp. 881–888. [CrossRef]
Baert, K. , Gyselinckx, B. , Torfs, T. , Leonov, V. , Yazicioglu, F. , Brebels, S. , Donnay, S. , Vanfleteren, J. , Beyne, E. , and Van Hoof, C. , 2006, “ Technologies for Highly Miniaturized Autonomous Sensor Networks,” Microelectron. J., 37(12), pp. 1563–1568. [CrossRef]
Sodano, H. A. , Inman, D. J. , and Park, G. , 2004, “ A Review of Power Harvesting From Vibration Using Piezoelectric Materials,” Shock Vib. Dig., 36(3), pp. 197–206. [CrossRef]
Sodano, H. A. , Inman, D. J. , and Park, G. , 2005, “ Generation and Storage of Electricity From Power Harvesting Devices,” J. Intell. Mater. Syst. Struct., 16(1), pp. 67–75. [CrossRef]
Roundy, S. , 2005, “ On the Effectiveness of Vibration-Based Energy Harvesting,” J. Intell. Mater. Syst. Struct., 16(10), pp. 809–823. [CrossRef]
Daqaq, M. F. , 2010, “ Response of Uni-Modal Duffing-Type Harvesters to Random Forced Excitations,” J. Sound Vib., 329(18), pp. 3621–3631. [CrossRef]
Mann, B. , and Owens, B. , 2010, “ Investigations of a Nonlinear Energy Harvester With a Bistable Potential Well,” J. Sound Vib., 329(9), pp. 1215–1226. [CrossRef]
Cammarano, A. , Burrow, S. , and Barton, D. , 2011, “ Modelling and Experimental Characterization of an Energy Harvester With Bi-Stable Compliance Characteristics,” Proc. Inst. Mech. Eng., Part I, 225(4), pp. 475–484.
Ando, B. , Baglio, S. , Trigona, C. , Dumas, N. , Latorre, L. , and Nouet, P. , 2010, “ Nonlinear Mechanism in MEMS Devices for Energy Harvesting Applications,” J. Micromech. Microeng., 20(12), p. 125020. [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]
Ibrahim, A. , Towfighian, S. , Younis, M. , and Su, Q. , 2016, “ Magnetoelastic Beam With Extended Polymer for Low Frequency Vibration Energy Harvesting,” Proc. SPIE, 9806, p. 98060B.
Beeby, S. P. , Tudor, M. J. , and White, N. , 2006, “ Energy Harvesting Vibration Sources for Microsystems Applications,” Meas. Sci. Technol., 17(12), p. R175. [CrossRef]
Mitcheson, P. D. , Yeatman, E. M. , Rao, G. K. , Holmes, A. S. , and Green, T. C. , 2008, “ Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices,” Proc. IEEE, 96(9), pp. 1457–1486. [CrossRef]
Sterken, T. , Baert, K. , Van Hoof, C. , Puers, R. , Borghs, G. , and Fiorini, P. , 2004, “ Comparative Modelling for Vibration Scavengers [MEMS Energy Scavengers],” 3rd IEEE Conference on Sensors (SENSORS), Vienna, Austria, Oct. 24–27, pp. 1249–1252.
James, E. , Tudor, M. , Beeby, S. , Harris, N. , Glynne-Jones, P. , Ross, J. , and White, N. , 2004, “ An Investigation of Self-Powered Systems for Condition Monitoring Applications,” Sens. Actuators A, 110(1), pp. 171–176. [CrossRef]
Roundy, S. , and Wright, P. K. , 2004, “ A Piezoelectric Vibration Based Generator for Wireless Electronics,” Smart Mater. Struct., 13(5), p. 1131. [CrossRef]
Ottman, G. K. , Hofmann, H. F. , Bhatt, A. C. , and Lesieutre, G. A. , 2002, “ Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply,” IEEE Trans. Power Electron., 17(5), pp. 669–676. [CrossRef]
Ferrari, M. , Ferrari, V. , Marioli, D. , and Taroni, A. , 2006, “ Modeling, Fabrication and Performance Measurements of a Piezoelectric Energy Converter for Power Harvesting in Autonomous Microsystems,” IEEE Trans. Instrum. Meas., 55(6), pp. 2096–2101. [CrossRef]
Ferrari, M. , Ferrari, V. , Guizzetti, M. , and Marioli, D. , 2009, “ An Autonomous Battery-Less Sensor Module Powered by Piezoelectric Energy Harvesting With RF Transmission of Multiple Measurement Signals,” Smart Mater. Struct., 18(8), p. 085023. [CrossRef]
Masana, R. , and Daqaq, M. F. , 2011, “ Relative Performance of a Vibratory Energy Harvester in Mono- and Bi-Stable Potentials,” J. Sound Vib., 330(24), pp. 6036–6052. [CrossRef]
Sneller, A. , Cette, P. , and Mann, B. , 2011, “ Experimental Investigation of a Post-Buckled Piezoelectric Beam With an Attached Central Mass Used to Harvest Energy,” Proc. Inst. Mech. Eng., Part I, 225(4), pp. 497–509. [CrossRef]
Arrieta, A. , Hagedorn, P. , Erturk, A. , and Inman, D. , 2010, “ A Piezoelectric Bistable Plate for Nonlinear Broadband Energy Harvesting,” Appl. Phys. Lett., 97(10), p. 104102. [CrossRef]
Masana, R. , and Daqaq, M. F. , 2012, “ Energy Harvesting in the Super-Harmonic Frequency Region of a Twin-Well Oscillator,” J. Appl. Phys., 111(4), p. 044501. [CrossRef]
Ferrari, M. , Bau, M. , Guizzetti, M. , and Ferrari, V. , 2011, “ A Single-Magnet Nonlinear Piezoelectric Converter for Enhanced Energy Harvesting From Random Vibrations,” Sens. Actuators A, 172(1), pp. 287–292. [CrossRef]
Ferrari, M. , Ferrari, V. , Guizzetti, M. , Andò, B. , Baglio, S. , and Trigona, C. , 2010, “ Improved Energy Harvesting From Wideband Vibrations by Nonlinear Piezoelectric Converters,” Sens. Actuators A, 162(2), pp. 425–431. [CrossRef]
Litak, G. , Friswell, M. , and Adhikari, S. , 2010, “ Magnetopiezoelastic Energy Harvesting Driven by Random Excitations,” Appl. Phys. Lett., 96(21), p. 214103. [CrossRef]
Lin, J.-T. , Lee, B. , and Alphenaar, B. , 2010, “ The Magnetic Coupling of a Piezoelectric Cantilever for Enhanced Energy Harvesting Efficiency,” Smart Mater. Struct., 19(4), p. 045012. [CrossRef]
Ali, S. , Adhikari, S. , Friswell, M. , and Narayanan, S. , 2011, “ The Analysis of Piezomagnetoelastic Energy Harvesters Under Broadband Random Excitations,” J. Appl. Phys., 109(7), p. 074904. [CrossRef]
Roundy, S. , and Zhang, Y. , 2005, “ Toward Self-Tuning Adaptive Vibration-Based Microgenerators,” Proc. SPIE, 5649, pp. 373–384.
Wu, W.-J. , Chen, Y.-Y. , Lee, B.-S. , He, J.-J. , and Peng, Y.-T. , 2006, “ Tunable Resonant Frequency Power Harvesting Devices,” Proc. SPIE, 6169, p. 61690A.
Challa, V. R. , Prasad, M. , Shi, Y. , and Fisher, F. T. , 2008, “ A Vibration Energy Harvesting Device With Bidirectional Resonance Frequency Tunability,” Smart Mater. Struct., 17(1), p. 015035. [CrossRef]
Shahruz, S. , 2006, “ Design of Mechanical Band-Pass Filters for Energy Scavenging,” J. Sound Vib., 292(3), pp. 987–998. [CrossRef]
Shahruz, S. , 2006, “ Limits of Performance of Mechanical Band-Pass Filters Used in Energy Scavenging,” J. Sound Vib., 293(1), pp. 449–461. [CrossRef]
Baker, J. , Roundy, S. , and Wright, P. , 2005, “ Alternative Geometries for Increasing Power Density in Vibration Energy Scavenging for Wireless Sensor Networks,” 3rd International Energy Conversion Engineering Conference (IECEC), San Francisco, CA, Aug. 15–18, pp. 959–970.
Rastegar, J. , Pereira, C. , and Nguyen, H.-L. , 2006, “ Piezoelectric-Based Power Sources for Harvesting Energy From Platforms With Low-Frequency Vibration,” Proc. SPIE, 6171, p. 617101.
Al-Ashtari, W. , Hunstig, M. , Hemsel, T. , and Sextro, W. , 2012, “ Frequency Tuning of Piezoelectric Energy Harvesters by Magnetic Force,” Smart Mater. Struct., 21(3), p. 035019. [CrossRef]
Yang, W. , and Towfighian, S. , 2017, “ A Hybrid Nonlinear Vibration Energy Harvester,” Mech. Syst. Signal Process., 90, pp. 317–333. [CrossRef]
Moon, F. , and Holmes, P. J. , 1979, “ A Magnetoelastic Strange Attractor,” J. Sound Vib., 65(2), pp. 275–296. [CrossRef]
Quinn, D. D. , Vakakis, A. F. , and Bergman, L. A. , 2007, “ Vibration-Based Energy Harvesting With Essential Nonlinearities,” ASME Paper No. DETC2007-35457.
Mann, B. , and Sims, N. , 2009, “ Energy Harvesting From the Nonlinear Oscillations of Magnetic Levitation,” J. Sound Vib., 319(1), pp. 515–530. [CrossRef]
Burrow, S. , and Clare, L. , 2007, “ A Resonant Generator With Non-Linear Compliance for Energy Harvesting in High Vibrational Environments,” IEEE International Electric Machines and Drives Conference (IEMDC), Antalya, Turkey, May 3–5, Vol. 1, pp. 715–720.
Beeby, S. P. , Torah, R. , Tudor, M. , Glynne-Jones, P. , O'Donnell, T. , Saha, C. , and Roy, S. , 2007, “ A Micro Electromagnetic Generator for Vibration Energy Harvesting,” J. Micromech. Microeng., 17(7), p. 1257. [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. , 2009, “ A Piezomagnetoelastic Structure for Broadband Vibration Energy Harvesting,” Appl. Phys. Lett., 94(25), p. 254102. [CrossRef]
Barton, D. A. , Burrow, S. G. , and Clare, L. R. , 2010, “ Energy Harvesting From Vibrations With a Nonlinear Oscillator,” ASME J. Vib. Acoust., 132(2), p. 021009. [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]
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]
Stanton, S. C. , Owens, B. A. , and Mann, B. P. , 2012, “ Harmonic Balance Analysis of the Bistable Piezoelectric Inertial Generator,” J. Sound Vib., 331(15), pp. 3617–3627. [CrossRef]
Bilgen, O. , Friswell, M. I. , Ali, S. F. , and Litak, G. , 2015, “ Broadband Vibration Energy Harvesting From a Vertical Cantilever Piezocomposite Beam With Tip Mass,” Int. J. Struct. Stab. Dyn., 15(2), p. 1450038. [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, pp. 33–39. [CrossRef]
Gammaitoni, L. , Neri, I. , and Vocca, H. , 2009, “ Nonlinear Oscillators for Vibration Energy Harvesting,” Appl. Phys. Lett., 94(16), p. 164102. [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]
Marinkovic, B. , and Koser, H. , 2009, “ Smart Sand—A Wide Bandwidth Vibration Energy Harvesting Platform,” Appl. Phys. Lett., 94(10), p. 103505. [CrossRef]
Tvedt, L. G. W. , Nguyen, D. S. , and Halvorsen, E. , 2010, “ Nonlinear Behavior of an Electrostatic Energy Harvester Under Wide-and Narrowband Excitation,” J. Microelectromech. Syst., 19(2), pp. 305–316. [CrossRef]
Miki, D. , Honzumi, M. , Suzuki, Y. , and Kasagi, N. , 2010, “ Large-Amplitude MEMS Electret Generator With Nonlinear Spring,” IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS), Wanchai, Hong Kong, China, Jan. 24–28, pp. 176–179.
Nguyen, D. , Halvorsen, E. , Jensen, G. , and Vogl, A. , 2010, “ Fabrication and Characterization of a Wideband MEMS Energy Harvester Utilizing Nonlinear Springs,” J. Micromech. Microeng., 20(12), p. 125009. [CrossRef]
Erturk, A. , and Inman, D. , 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]
Stanton, S. C. , and Mann, B. P. , 2009, “ Harvesting Energy From the Nonlinear Oscillations of a Bistable Piezoelectric Inertial Energy Generator,” ASME Paper No. DETC2009-86902.
Tang, L. , Wu, H. , Yang, Y. , and Soh, C. K. , 2011, “ Optimal Performance of Nonlinear Energy Harvesters,” 22nd International Conference on Adaptive Structures and Technologies, Corfu, Greece, Oct. 10–12, Paper No. ICAST2011 #075.
Tang, L. , Yang, Y. , and Soh, C.-K. , 2012, “ Improving Functionality of Vibration Energy Harvesters Using Magnets,” J. Intell. Mater. Syst. Struct., 23(13), pp. 1433–1449.
Harne, R. , Thota, M. , and Wang, K. , 2013, “ Concise and High-Fidelity Predictive Criteria for Maximizing Performance and Robustness of Bistable Energy Harvesters,” Appl. Phys. Lett., 102(5), p. 053903. [CrossRef]
Stanton, S. C. , Mann, B. P. , and Owens, B. A. , 2012, “ Melnikov Theoretic Methods for Characterizing the Dynamics of the Bistable Piezoelectric Inertial Generator in Complex Spectral Environments,” Physica D, 241(6), pp. 711–720. [CrossRef]
Azizi, S. , Chorsi, M. T. , and Bakhtiari-Nejad, F. , 2016, “ On the Secondary Resonance of a MEMS Resonator: A Conceptual Study Based on Shooting and Perturbation Methods,” Int. J. Non-Linear Mech., 82, pp. 59–68. [CrossRef]
Karami, M. A. , and Inman, D. J. , 2011, “ Electromechanical Modeling of the Low-Frequency Zigzag Micro-Energy Harvester,” J. Intell. Mater. Syst. Struct., 22(3), pp. 271–282. [CrossRef]
Arrieta, A. , Delpero, T. , Bergamini, A. , and Ermanni, P. , 2013, “ Broadband Vibration Energy Harvesting Based on Cantilevered Piezoelectric Bi-Stable Composites,” Appl. Phys. Lett., 102(17), p. 173904. [CrossRef]
Gu, L. , 2011, “ Low-Frequency Piezoelectric Energy Harvesting Prototype Suitable for the MEMS Implementation,” Microelectron. J., 42(2), pp. 277–282. [CrossRef]
Karami, M. A. , and Inman, D. J. , 2011, “ Equivalent Damping and Frequency Change for Linear and Nonlinear Hybrid Vibrational Energy Harvesting Systems,” J. Sound Vib., 330(23), pp. 5583–5597. [CrossRef]
Tang, L. , and Yang, Y. , 2012, “ A Nonlinear Piezoelectric Energy Harvester With Magnetic Oscillator,” Appl. Phys. Lett., 101(9), p. 094102. [CrossRef]
Younis, M. I. , 2011, MEMS Linear and Nonlinear Statics and Dynamics, Vol. 20, Springer Science and Business Media, New York.
Wolfram, S. , 1987, “ Mathematica,” Springer, New York.

Figures

Grahic Jump Location
Fig. 1

Schematic of the experimental setup and the stability configurations of the resonator: (a) schematic of the experimental setup and (b) monostable and bistable configurations

Grahic Jump Location
Fig. 2

The experimental setup of the piezoelectric energy harvesting, cantilever harvester to the right, and PUMA spectral dynamics analyzer to the left

Grahic Jump Location
Fig. 3

Schematic for the total magnetic force acting on the tip mass

Grahic Jump Location
Fig. 4

The tip mass static response with the separation distance, d, between the two magnets. Threshold value, dth, found to be 20 mm. Two values for monostable and bistable regions are selected for analysis.

Grahic Jump Location
Fig. 5

First normalized mode shape plotted at different distances between the two magnets, where d = 20 mm is the threshold distance

Grahic Jump Location
Fig. 6

Variation of the first natural frequency with the distance, d, between the two magnets. Threshold value match static profile with value of dth = 20 mm.

Grahic Jump Location
Fig. 7

Experimental and simulated forward sweep frequency and voltage responses for monostable resonator at d = 40 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 8

Experimental frequency forward swept responses for monostable resonator at d = 40 mm at different excitation levels: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 9

Experimental frequency forward swept responses for monostable resonator at d = 22 mm at different excitation levels: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 10

Experimental frequency responses for bistable resonator at d = 5 mm: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 11

Experimental and simulated frequency responses for bistable resonator at d = 18 mm, A = 0.5 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 12

Bistable simulated results for the nonlinear energy harvester at d = 18 mm, A = 1.0 g, and damping μ = 0.038: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 13

The basin of attraction for the resonator for (a) d = 18 mm at 1.0 g, Ω = 18 Hz, and μ = 0.038 and (b) d = 18 mm at 1.0 g, fold frequency Ω = 16.7 Hz, and μ = 0.038. Light area is the basin of attraction for lower branch, while the dark area is the basin of attraction for the upper branch.

Grahic Jump Location
Fig. 14

Experimental frequency responses for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage

Grahic Jump Location
Fig. 15

Simulated frequency responses with shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038

Grahic Jump Location
Fig. 16

Simulated frequency responses with long time integration and shooting methods for bistable resonator at d = 18 mm: (a) tip mass displacement and (b) output voltage, damping μ = 0.038

Grahic Jump Location
Fig. 17

Maximum output voltage with increasing the resistance up to 10 MΩ for an excitation level of 0.3 g, separation distance of 18 mm, and damping of μ = 0.038

Grahic Jump Location
Fig. 18

The bifurcation diagram of the actuator constructed from a force (excitation level) sweep at the threshold distance (dth = 20 mm) and its natural frequency of Ω = 12.59 Hz, single-sided Poincaré sections obtained at the period of excitation

Grahic Jump Location
Fig. 19

Chaotic response for the harvester at dth = 20 mm, Ω = 12.59 Hz, and 0.2228 g excitation level: (a) phase portrait and (b) Poincaré map

Grahic Jump Location
Fig. 20

The bifurcation diagram sweeping the frequency of excitation at dth = 20 mm and Amp = 0.2 g, single-sided Poincaré sections obtained at the period of excitation

Grahic Jump Location
Fig. 21

(a) Maximum output voltage as the distance between magnets varies at the excitation level of 1.0 g and (b) dynamics behavior for energy harvester

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In