Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Role of Stiffness Nonlinearities in the Transduction of Energy Harvesters under White Gaussian Excitations

  • Chapter
  • First Online:
Advances in Energy Harvesting Methods

  • 4142 Accesses

Abstract

This chapter delineates the influence of stiffness-type nonlinearities on the transduction of vibratory energy harvesters (VEHs) under random excitations that can be approximated by a white Gaussian noise process. Both mono- and bistable Duffing-type harvesters are considered. The Fokker–Planck–Kolmogorov equation governing the evolution of the harvester’s transition probability density function is formulated and used to generate the moment differential equations governing the response statistics. The moment equations are then closed using a fourth-order cumulant-neglect closure scheme and solved for the relevant steady-state response statistics. The influence of the nonlinearity, time constant ratio (the ratio between the nominal period of the mechanical subsystem and the time constant of the harvesting circuit), and noise intensity on the mean square value of the electric output (voltage or current) and the average power is detailed. Results are then compared to those obtained by analytically solving the FPK equation for the linear resonant harvester. It is demonstrated that a Duffing-type monostable harvester can never outperform its linear counterpart. A bistable harvester, on the other hand, can outperform a linear harvester only when the time constant ratio is small and its potential energy function is optimized based on a known excitation intensity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The assumption of white noise is not as restrictive as it may appear. If the bandwidth of the excitation is sufficiently larger than that of the harvester’s, then a random excitation can be safely considered to be white.

  2. 2.

    The reader can refer to Renno et al. [41] for more details on the optimization of energy harvesters under sinusoidal deterministic excitations.

  3. 3.

    Cumulants are used to provide a measure of correlation strength among different random variables [42].

References

  1. Gregori S, Li Y, Li H, Liu J, Maloberti F (2004) 2.45 GHz power and data transmission for a low-power autonomous sensors platform. ISLPED 04, pp 269–273

    Google Scholar 

  2. Kim JW, Takao H, Sawada K, Ishida M (2007) Integrated inductors for RF transmitters in CMOS/MEMS smart microsensor systems. Sensors 7:1387–1398

    Article  Google Scholar 

  3. Bracke W, Merken P, Puers R, Van Hoof C (2007) Generic architectures and design methods for autonomous sensors. Sensor Actuator A 135:881–888

    Article  Google Scholar 

  4. Baerta K, Gyselinckxa B, Torfsa T, Leonova V, Yazicioglua F, Brebelsa S, Donnaya S, Vanfleterena J, Beyna E, Van Hoof C (2006) Technologies for highly miniaturized autonomous sensor networks. Microelectron J 37:1563–1568

    Article  Google Scholar 

  5. Paradiso JA, Starner T (2005) Energy scavenging for mobile and wireless electronics. IEEE Pervasive Comput 4:18–27

    Article  Google Scholar 

  6. Sodano H, Inman DJ, Park G (2004) A review of power harvesting from vibration using piezoelectric materials. Shock Vib Digest 36:197–205

    Article  Google Scholar 

  7. Sodano H, Inman DJ, Park G (2005) Generation and storage of electricity from power harvesting devices. J Intell Mater Syst Struct 16:67–75

    Article  Google Scholar 

  8. Roundy S (2005) On the effectiveness of vibration-based energy harvesting. J Intell Mater Struct 16:809–823

    Article  Google Scholar 

  9. Yu P, Yuan Y, Xu J (2002) Study of double hopf bifurcation and chaos for an oscillator with time-delayed feedback. Comm Nonlinear Sci Numer Simulat 7:69

    Article  MathSciNet  Google Scholar 

  10. Chau HL, Wise KD (1987) Noise due to Brownian motion in ultrasensitive solid-state pressure sensors. IEEE Trans Electron Dev 34

    Google Scholar 

  11. Roundy S, Zhang Y (2005) Toward self-tuning adaptive vibration-based micro-generators. In: Smart materials, nano- and micro-smart systems, Sydney, Australia

    Google Scholar 

  12. Wu W, Chen Y, Lee B, He J, Peng Y (2006) Tunable resonant frequency power harvesting devices. In: Proceedings of smart structures and materials conference, SPIE, p 61690A, San Diego, CA

    Google Scholar 

  13. Challa V, Prasad M, Shi Y, Fisher F (2008) A vibration energy harvesting device with bidirectional resonance frequency tunability. Smart Mater Struct 75:1–10

    Google Scholar 

  14. Shahruz SM (2006) Design of mechanical band-pass filters for energy scavenging. J Sound Vib 292:987–998

    Article  Google Scholar 

  15. Shahruz SM (2006) Limits of performance of mechanical band-pass filters used in energy harvesting. J Sound Vib 294:449–461

    Article  Google Scholar 

  16. Baker J, Roundy S, Wright P (2005) Alternative geometries for increasing power density in vibration energy scavenging for wireless sensors. In: Proceedings of the third international energy conversion conference, p 959–970, San Francisco, CA

    Google Scholar 

  17. Rastegar J, Pereira C, Nguyen HL (2006) Piezoelectric-based power sources for harvesting energy from platforms with low frequency vibrations. In: Proceedings of smart structures and materials conference, SPIE, p 617101, San Diego, CA

    Google Scholar 

  18. McInnes CR, Gorman DG, Cartmell MP (2008) Enhanced vibrational energy harvesting using nonlinear stochastic resonance. J Sound Vib 318:655–662

    Article  Google Scholar 

  19. Barton D, Burrow S, Clare L (2010) Energy harvesting from vibrations with a nonlinear oscillator. J Vib Acoust 132:0210091

    Article  Google Scholar 

  20. Mann B, Sims N (2008) Energy harvesting from the nonlinear oscillations of magnetic levitation. J Sound Vib 319:515–530

    Article  Google Scholar 

  21. Masana R, Daqaq MF (2011) Electromechanical modeling and nonlinear analysis of axially-loaded energy harvesters. J Vib Acoust 133:011007

    Article  Google Scholar 

  22. Quinn D, Triplett L, Vakakis D, Bergman L (2011) Comparing linear and essentially nonlinear vibration-based energy harvesting. J Vib Acoust 133:011001

    Article  Google Scholar 

  23. Erturk A, Hoffman J, Inman DJ (2009) A piezo-magneto-elastic structure for broadband vibration energy harvesting. Appl Phys Lett 94:254102

    Article  Google Scholar 

  24. Cottone F, Vocca H, Gammaitoni L (2009) Nonlinear energy harvesting. Phys Rev Lett 102:080601–1–080601–4

    Google Scholar 

  25. Daqaq MF, Stabler C, Seuaciuc-Osorio T, Qaroush Y (2009) Investigation of power harvesting via parametric excitations. J Intell Mater Syst Struct 20:545–557

    Article  Google Scholar 

  26. Stanton SC, McGehee CC, Mann BP (2010) Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys D Nonlinear Phenom 239:640–653

    Article  MATH  Google Scholar 

  27. Daqaq MF, Bode D (2010) Exploring the parametric amplification phenomenon for energy harvesting. J Syst Contr Eng 225:456–466

    Google Scholar 

  28. Abdelkefi A, Nayfeh AH, Hajj M (2012) Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters. Nonlinear Dynam 67(2):1147–1160

    Article  MathSciNet  MATH  Google Scholar 

  29. Abdelkefi A, Nayfeh AH, Hajj M (2012) Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation. Nonlinear Dynam 67(2):1221–1232

    Article  MathSciNet  MATH  Google Scholar 

  30. Mann BP, Owens BA (2010) Investigations of a nonlinear energy harvester with a bistable potential well. J Sound Vib 329:1215–1226

    Article  Google Scholar 

  31. Masana R, Daqaq MF (2011) Comparing the performance of a nonlinear energy harvester in mono- and bi-stable potentials. In: Proceedings of the ASME 2011 international design engineering technical conference and computers and information in engineering conference, Washington, DC

    Google Scholar 

  32. Adhikari S, Friswell MI, Inman DJ (2009) Piezoelectric energy harvesting from broadband random vibrations. Smart Mater Struct 18:115005

    Article  Google Scholar 

  33. Seuaciuc-Osorio T, Daqaq MF (2010) Energy harvesting under excitations of time-varying frequency. J Sound Vib 329:2497–2515

    Article  Google Scholar 

  34. Barton D, Burrow S, Clare L (2009) Energy harvesting from vibrations with a nonlinear oscillator. In: Proceedings of the ASME 2009 international design engineering technical conference and computers and information in engineering conference, San Diego, CA

    Google Scholar 

  35. Daqaq MF (2010) Response of uni-modal duffing type harvesters to random forced excitations. J Sound Vib 329:3621–3631

    Article  Google Scholar 

  36. Gammaitoni L, Neri I, Vocca H (2009) Nonlinear oscillators for vibration energy harvesting. Appl Phys Lett 94(16):164102

    Article  Google Scholar 

  37. Daqaq MF (2011) Transduction of a bistable inductive generator driven by white and exponentially correlated gaussian noise. J Sound Vib 330:2554–2564

    Article  Google Scholar 

  38. Daqaq MF (2012) On intentional introduction of stiffness nonlinearities for energy harvesting under White Gaussian excitations. Nonlinear Dynam. DOI: 10.1007/s11071-012-0327-0

    Google Scholar 

  39. Ito K (1944) Stochastic integral. Proc Imper Acad Tokyo 20:519–524

    Article  MATH  Google Scholar 

  40. Jazwinski AH (1970) Stochastic processes and filtering theory. Academic, New York

    MATH  Google Scholar 

  41. Renno J, Daqaq MF, Inman DJ (2009) On the optimal energy harvesting from a vibration source. J Sound Vib 320:386–405

    Article  Google Scholar 

  42. Ibrahim RA (1985) Parametric random vibrations. Research Studies Press, NY

    Google Scholar 

  43. Wojtkiewicz S, Spencer B, Bergman LA (1995) On the cumulant-neglect closure method in stochastic dynamics. Int J Non Lin Mech 95:657–684

    Google Scholar 

  44. Triplett A, Quinn D (2009) The effect of non-linear piezoelectric coupling on vibration-based energy harvesting. J Intell Mater Syst Struct 20(16):1959–1967

    Article  Google Scholar 

  45. Mahmoodi N, Daqaq MF, Jalili N (2009) Modeling, nonlinear dynamics, and identification of a piezoelectrically actuated microcantilever sensor. IEEE/ASME Trans Mechatron 13(1):58–65

    Article  Google Scholar 

Download references

Acknowledgements

This material is based upon work supported by the National Science Foundation under CAREER Grant No. 1055419. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Author information

Authors and Affiliations

  1. Clemson University, Clemson, SC, 29634, USA

    Mohammed F. Daqaq

Authors
  1. Mohammed F. Daqaq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed F. Daqaq .

Editor information

Editors and Affiliations

  1. Steinman Hall T-228, The City College of New York, Street at Convent Avenue 140, New York, 10031, New York, USA

    Niell Elvin

  2. , G. W. Woodruff School of, Georgia Institute of Technology, J. Erskine Love Jr. Manufacturing Building 126, Atlanta, 30332, Georgia, USA

    Alper Erturk

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Daqaq, M.F. (2013). Role of Stiffness Nonlinearities in the Transduction of Energy Harvesters under White Gaussian Excitations. In: Elvin, N., Erturk, A. (eds) Advances in Energy Harvesting Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5705-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-5705-3_7

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-5704-6

  • Online ISBN: 978-1-4614-5705-3

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation