### 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.

Original language | English (US) |
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Title of host publication | Advances in Energy Harvesting Methods |

Publisher | Springer New York |

Pages | 163-190 |

Number of pages | 28 |

Volume | 9781461457053 |

ISBN (Electronic) | 9781461457053 |

ISBN (Print) | 1461457041, 9781461457046 |

DOIs | |

State | Published - Sep 1 2013 |

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### ASJC Scopus subject areas

- Energy(all)

### Cite this

*Advances in Energy Harvesting Methods*(Vol. 9781461457053, pp. 163-190). Springer New York. https://doi.org/10.1007/978-1-4614-5705-3_7

**Role of stiffness nonlinearities in the transduction of energy harvesters under white gaussian excitations.** / Daqaq, Mohammed.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Energy Harvesting Methods.*vol. 9781461457053, Springer New York, pp. 163-190. https://doi.org/10.1007/978-1-4614-5705-3_7

}

TY - CHAP

T1 - Role of stiffness nonlinearities in the transduction of energy harvesters under white gaussian excitations

AU - Daqaq, Mohammed

PY - 2013/9/1

Y1 - 2013/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84949176056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949176056&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-5705-3_7

DO - 10.1007/978-1-4614-5705-3_7

M3 - Chapter

AN - SCOPUS:84949176056

SN - 1461457041

SN - 9781461457046

VL - 9781461457053

SP - 163

EP - 190

BT - Advances in Energy Harvesting Methods

PB - Springer New York

ER -