Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-17T02:15:41.189Z Has data issue: false hasContentIssue false

On the stochastic dynamics of a nonlinear vibration energy harvester driven by Lévy flight excitations

Published online by Cambridge University Press:  08 October 2018

SUBRAMANIAN RAMAKRISHNAN
Affiliation:
Department of Mechanical and Industrial Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA email: [email protected]
CONNOR EDLUND
Affiliation:
Department of Electrical Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA emails: [email protected]; [email protected]
COLLIN LAMBRECHT
Affiliation:
Department of Mechanical and Industrial Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA email: [email protected]

Abstract

Vibration energy harvesting aims to harness the energy of ambient random vibrations for power generation, particularly in small-scale devices. Typically, stochastic excitation driving the harvester is modelled as a Brownian process and the dynamics are studied in the equilibrium state. However, non-Brownian excitations are of interest, particularly in the nonequilibrium regime of the dynamics. In this work we study the nonequilibrium dynamics of a generic piezoelectric harvester driven by Brownian as well as (non-Brownian) Lévy flight excitation, both in the linear and the Duffing regimes. Both the monostable and the bistable cases of the Duffing regime are studied. The first set of results demonstrate that Lévy flight excitation results in higher expectation values of harvested power. In particular, it is shown that increasing the noise intensity leads to a significant increase in power output. It is also shown that a linearly coupled array of nonlinear harvesters yields improved power output for tailored values of coupling coefficients. The second set of results show that Lévy flight excitation fundamentally alters the bifurcation characteristics of the dynamics. Together, the results underscore the importance of non-Brownian excitation characterised by Lévy flight in vibration energy harvesting, both from a theoretical viewpoint and from the perspective of practical applications.

Type
Papers
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Applebaum, D. (2009) Lévy Processes and Stochastic Calculus, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Barton, D., Burrow, S. & Clare, L. (2010) Energy harvesting from vibrations with a nonlinear oscillator. ASME J. Vib. Acoust. 132, 021009.CrossRefGoogle Scholar
Brennan, M., Kovacic, I., Carrella, A. & Waters, T. (2008) On the jump-up and jump-down frequencies of the Duffing oscillator. J. Sound Vib. 318, 12501261.CrossRefGoogle Scholar
Cook-Chennault, K., Thambi, N. & Sastry, A. (2008) Powering MEMS portable devices– review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct. 17, 143001.CrossRefGoogle Scholar
Cottone, F., Vocca, H. & Gammaitoni, L. (2009) Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601.CrossRefGoogle ScholarPubMed
Daqaq, M., Masana, R., Erturk, A. & Quinn, D. (2014) Closure to “Discussion of ‘On the role of nonlinearities in energy harvesting: a critical review and discussion’”. Appl. Mech. Rev. 66, 040801.CrossRefGoogle Scholar
Deza, J., Deza, R. & Wio, H. (2012) Wide-spectrum energy harvesting out of colored Lévy-like fluctuations, by monostable piezoelectric transducers. EPL 100, 38001.CrossRefGoogle Scholar
Gammaitoni, F.Cottone, L.Neri, I. & Vocca, H. (2009) Noise harvesting. AIP Conf. Proc. 1129, 651.CrossRefGoogle Scholar
Gammaitoni, L., Neri, I. & Vocca, H. (2009) Nonlinear oscillators for vibration energy harvesting. Appl. Phys. Lett. 94, 164102.CrossRefGoogle Scholar
Gammaitoni, L., Hänggi, P., Jung, P. & Marchesoni, F. (1998) Stochastic resonance. Rev. Mod. Phys. 70, 223.CrossRefGoogle Scholar
Gardiner, C. (2009) Stochastic Methods, Vol. 4, Springer, Berlin.Google Scholar
Green, P., Worden, K., Atalla, K. & Sims, N. (2012) The benefits of Duffing-type nonlinearities and electrical optimisation of a mono-stable energy harvester under white Gaussian excitations. J. Sound Vib. 331, 45044517.CrossRefGoogle Scholar
Harne, R. & Wang, K. (2013) A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct. 22, 023001.CrossRefGoogle Scholar
Higham, D. (2001) An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525546.CrossRefGoogle Scholar
Janakiraman, D. & Sebastian, K. (2012) Path-integral formulation for Lévy flights: evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits. Phys. Rev. E 86, 061105.CrossRefGoogle ScholarPubMed
Kim, H., Kim, J. & Kim, J. (2011) A review of piezoelectric energy harvesting based on vibration. Int. J. Precis. Eng. Man. 12, 11291141.CrossRefGoogle Scholar
Masana, R. & Daqaq, M. (2009) Relative performance of a vibratory energy harvester in mono- and bi-stable potentials. J. Sound Vib. 330, 60366052.CrossRefGoogle Scholar
Nayfeh, A. & Mook, D. (1979) Nonlinear Oscillations, Wiley, New York.Google Scholar
Ottman, G., Hofmann, H. & Lesieutre, G. (2003) Optimized piezoelectric energy harvesting circuit using step-down converter in discontinuous conduction mode. IEEE Trans. Power Electron. 18, 696703.CrossRefGoogle Scholar
Paradiso, J. & Starner, T. (2005) Energy scavenging for mobile and wireless electronics. IEEE Pervas. Comput. 4, 1827.CrossRefGoogle Scholar
Pellegrini, S., Tolou, N., Schenk, M. & Herder, J. (2013) Bistable vibration energy harvesters: a review. J. Intell. Mater. Syst. Struct. 24.CrossRefGoogle Scholar
Quinn, D., Triplett, A., Bergman, L. & Vakakis, A. (2011) Energy harvesting from impulsive loads using intentional essential nonlinearities. ASME J. Vib. Acoust. 133, 011001.CrossRefGoogle Scholar
Roundy, S. & Quinn, D. (2005) On the effectiveness of vibration-based energy harvesting. J. Intell. Mater. Syst. Struct. 16, 809823.CrossRefGoogle Scholar
Roundy, S. & Wright, P. (2004) A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct. 13, 11311142.CrossRefGoogle Scholar
Sebald, G., Kuwano, H., Guyomar, D. & Ducharne, B. (2011) Experimental Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mater. Struct. 20, 102001.CrossRefGoogle Scholar
Sebald, G., Kuwano, H., Guyomar, D. & Ducharne, B. (2011) Simulation of a Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mater. Struct. 20, 075022.CrossRefGoogle Scholar
Sodano, H., Inman, D. & Park, G. (2004) A review of power harvesting from vibration using piezoelectric materials. Shock Vib. Dig. 36, 197205.CrossRefGoogle Scholar
Sodano, H., Inman, D. & Park, G. (2005) Generation and storage of electricity from power harvesting devices. J. Intell. Mater. Syst. Struct. 16, 6775.CrossRefGoogle Scholar
Sodano, H., Park, G., Leo, D. & Inman, D. (2003) Use of piezoelectric energy harvesting devices for charging batteries. In: Proc. SPIE 5050, Smart Structures and Materials 2003: Smart Sensor Technology and Measurement Systems, SPIE, The International Society for Optics and Photonics, Bellingham, WA, pp. 101.CrossRefGoogle Scholar
Stanton, S., McGehee, C. & Mann, B. (2010) Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Physica D 239, 640653.CrossRefGoogle Scholar
Yang, X. & Deb, S. (2013) Multiobjective cuckoo search for design optimization. Comp. Oper. Res. 40, 16161624.CrossRefGoogle Scholar