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Random Excitation of Bistable Harvesters

  • Sondipon Adhikari
  • Michael I. Friswell
Chapter

Abstract

This chapter considers nonlinear piezoelastic energy harvesters driven by stationary random noise. A range of devices that exhibit nonlinear dynamics have been proposed, and their response to sinusoidal excitation is often complex, with coexisting periodic solutions or even chaotic solutions. The response of nonlinear harvesters to random noise depends on the statistics of the excitation; the maximum response can occur at particular excitation variances, and this is called stochastic resonance. The stochastic linearisation method is proposed for the optimal design of bistable harvesters subjected to random excitation.

Keywords

Energy Harvester Stochastic Resonance Random Excitation White Noise Excitation Stochastic Resonance Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ali S, Adhikari S, Friswell MI (2010) Piezoelectric energy harvesting with parametric uncertainty. Smart Mater Struct 19(105010)Google Scholar
  2. 2.
    Ali SF, Adhikari S, Friswell MI, Narayanan S (2011) The analysis of magnetopiezoelastic energy harvesters under broadband random excitations. J Appl Phys 109(074904)Google Scholar
  3. 3.
    Amirtharajah R, Chandrakasan A (1998) Self-powered signal processing using vibration-based power generation. IEEE J Solid State Circ 33(5):687–695CrossRefGoogle Scholar
  4. 4.
    Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 16(3):R1–R21CrossRefGoogle Scholar
  5. 5.
    Arnold DP (2007) Review of microscale magnetic power generation. IEEE Trans Magn 43(11):3940–3951CrossRefGoogle Scholar
  6. 6.
    Barton DAW, Burrow SG, Clare LR (2010) Energy harvesting from vibrations with a nonlinear oscillator. J Vib Acoust 132(021009)Google Scholar
  7. 7.
    Beeby SP, Tudor MJ, White NM (2006) Energy harvesting vibration sources for microsystems applications. Meas Sci Tech 17(12):175–195CrossRefGoogle Scholar
  8. 8.
    Beeby SP, Torah RN, Tudor MJ, Glynne-Jones P, O’Donnell T, Saha CR, Roy S (2007) A micro electromagnetic generator for vibration energy harvesting. J Micromechanics Microengineering 17(7):1257–1265CrossRefGoogle Scholar
  9. 9.
    Bolotin VV (1984) Random vibration of elastic systems. Martinus and Nijhoff Publishers, The HagueCrossRefGoogle Scholar
  10. 10.
    Cottone F, Vocca H, Gammaitoni L (2009) Nonlinear energy harvesting. Phys Rev Lett 102(080601)Google Scholar
  11. 11.
    Daqaq M (2010) Response of a uni-modal Duffing-type harvesters to random force excitations. J Sound Vib 329:3621–3631CrossRefGoogle Scholar
  12. 12.
    duToit NE, Wardle BL (2007) Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA J 45(5):1126–1137CrossRefGoogle Scholar
  13. 13.
    Dutoit NE, Wardle BL, Kim SG (2005) Design consideration for mems scale piezoelectric mechanical vibration energy harvesters. Integrated Ferroelectrics Int J 71(1):121–160CrossRefGoogle Scholar
  14. 14.
    Erturk A, Inman DJ (2008a) A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J Vib Acoust 130(041002)Google Scholar
  15. 15.
    Erturk A, Inman DJ (2008b) Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater Struct 17(065016)Google Scholar
  16. 16.
    Erturk A, Inman DJ (2008c) On mechanical modeling of cantilevered piezoelectric vibration energy harvesters. J Intell Mater Syst Struct 19(11):1311–1325CrossRefGoogle Scholar
  17. 17.
    Erturk A, Inman DJ (2009) An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater Struct 18(025009)Google Scholar
  18. 18.
    Erturk A, Inman DJ (2011) Broadband piezoelectric power generation on high-energy orbits of the bistable duffing oscillator with electromechanical coupling. J Sound Vib 330:2339–2353CrossRefGoogle Scholar
  19. 19.
    Erturk A, Hoffmann J, Inman DJ (2009) A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl Phys Lett 94(254102)Google Scholar
  20. 20.
    Ferrari M, Ferrari V, Guizzetti M, Ando B, Baglio S, Trigona C (2010) Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters. Sensor Actuator Phys 162:425–431CrossRefGoogle Scholar
  21. 21.
    Gammaitoni L, Hanggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70(1):223–287CrossRefGoogle Scholar
  22. 22.
    Gammaitoni L, Neri I, Vocca H (2009) Nonlinear oscillators for vibration energy harvesting. Appl Phys Lett 94:164102CrossRefGoogle Scholar
  23. 23.
    Gammaitoni L, Neri I, Vocca H (2010) The benefits of noise and nonlinearity: extracting energy from random vibrations. Chem Phys 375:435–438CrossRefGoogle Scholar
  24. 24.
    Halvorsen E (2008) Energy harvesters driven by broadband random vibrations. J Microelectromech Syst 17(5):1061–1071CrossRefGoogle Scholar
  25. 25.
    Kazakov IE (1965) Generalization of methods of statistical linearizarion to multidimensional systems. Autom Rem Contr 26:1201–1206MathSciNetGoogle Scholar
  26. 26.
    Lin YK (1967) Probabilistic theory of structural dynamics. McGraw-Hill, New YorkGoogle Scholar
  27. 27.
    Litak G, Friswell MI, Adhikari S (2010) Magnetopiezoelastic energy harvesting driven by random excitations. Appl Phys Lett 96(21):214,103CrossRefGoogle Scholar
  28. 28.
    Mann BP, Owens BA (2010) Investigations of a nonlinear energy harvester with a bistable potential well. J Sound Vib 329:1215–1226CrossRefGoogle Scholar
  29. 29.
    Mann BP, Sims ND (2009) Energy harvesting from the nonlinear oscillations of magnetic levitation. J Sound Vib 319(1–2):515–530CrossRefGoogle Scholar
  30. 30.
    Marinkovic B, Koser H (2009) Smart sand-a wide bandwidth vibration energy harvesting platform. Appl Phys Lett 94(103505)Google Scholar
  31. 31.
    Masana R, Daqaq MF (2011) Relative performance of a vibratory energy harvester in mono- and bi-stable potentials. J Sound Vib 330:6036–6052CrossRefGoogle Scholar
  32. 32.
    McInnes C, Gorman D, Cartmell M (2010) Enhanced vibrational energy harvesting using nonlinear stochastic resonance. J Sound Vib 318(4–5):655–662Google Scholar
  33. 33.
    Moon FC, Holmes PJ (1979) A magnetoelastic strange attractor. J Sound Vib 65(2):275–296zbMATHCrossRefGoogle Scholar
  34. 34.
    Newland DE (1989) Mechanical vibration analysis and computation. Longman, Harlow and Wiley, New YorkGoogle Scholar
  35. 35.
    Nigam NC (1983) Introduction to random vibration. MIT, Cambridge, MAGoogle Scholar
  36. 36.
    Priya S (2007) Advances in energy harvesting using low profile piezoelectric transducers. J Electroceramics 19(1):167–184MathSciNetCrossRefGoogle Scholar
  37. 37.
    Quinn DD, Triplett AL, Bergman LA, Vakakis AF (2011) Comparing linear and essentially nonlinear vibration-based energy harvesting. J Vib Acoust 133(011001)Google Scholar
  38. 38.
    Ramlan R, Brennan MJ, Mace BR, Kovacic I (2010) Potential benefits of a non-linear stiffness in an energy harvesting device. Nonlinear Dynam 59:545–558zbMATHCrossRefGoogle Scholar
  39. 39.
    Renno JM, Daqaq MF, Inman DJ (2009) On the optimal energy harvesting from a vibration source. J Sound Vib 320(1–2):386–405CrossRefGoogle Scholar
  40. 40.
    Roberts JB, Spanos PD (1990) Random vibration and statistical linearization. Wiley, ChichesterzbMATHGoogle Scholar
  41. 41.
    Roberts JB, Spanos PD (2003) Random vibration and statistical linearization. Dover Publications, Mineola, New YorkzbMATHGoogle Scholar
  42. 42.
    Sebald G, Kuwano H, Guyomar D, Ducharne B (2011) Experimental Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mater Struct 20(102001)Google Scholar
  43. 43.
    Sodano HA, Inman DJ, Park G (2004a) A review of power harvesting from vibration using piezoelectric materials. Shock Vib Digest 36(3):197–205CrossRefGoogle Scholar
  44. 44.
    Sodano HA, Park G, Inman DJ (2004b) Estimation of electric charge output for piezoelectric energy harvesting. Strain 40(2):49–58CrossRefGoogle Scholar
  45. 45.
    Stanton SC, McGehee CC, Mann BP (2010) Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys D 640–653Google Scholar
  46. 46.
    Williams C, Yates R (1996) Analysis of a micro-electric generator for microsystems. Sensor Actuator Phys 52:8–11CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of EngineeringSwansea UniversitySwanseaUK

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