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

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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 languageEnglish (US)
Title of host publicationAdvances in Energy Harvesting Methods
PublisherSpringer New York
Number of pages28
ISBN (Electronic)9781461457053
ISBN (Print)1461457041, 9781461457046
StatePublished - Sep 1 2013

ASJC Scopus subject areas

  • General Energy


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