Response of uni-modal duffing-type harvesters to random forced excitations

Research output: Contribution to journalArticle

Abstract

Linear energy harvesters have a narrow frequency bandwidth and hence operate efficiently only when the excitation frequency is very close to the fundamental frequency of the harvester. Consequently, small variations of the excitation frequency around the harvester's fundamental frequency drops its small energy output even further making the energy harvesting process inefficient. To extend the harvester's bandwidth, some recent solutions call for utilizing energy harvesters with stiffness-type nonlinearities. From a steady-state perspective, this hardening-type nonlinearity can extend the coupling between the excitation and the harvester to a wider range of frequencies. In this effort, we investigate the response of such harvesters, which can be modeled as a uni-modal duffing-type oscillator, to White Gaussian and Colored excitations. For White excitations, we solve the Fokker-Plank-Kolmogorov equation for the exact joint probability density function of the response. We show that the expected value of the output power is not even a function of the nonlinearity. As such, under White excitations, nonlinearities in the stiffness do not provide any enhancement over the typical linear harvesters. We also demonstrate that nonlinearities in the damping and inertia may be used to enhance the expected value of the output power. For Colored excitations, we use the Van Kampen expansion and long-time numerical integration to investigate the influence of the nonlinearity on the expected value of the output power. We demonstrate that, regardless of the bandwidth or the center frequency of the excitation, the expected value of the output power decreases with the nonlinearity. With such findings, we conclude that energy harvesters modeled as uni-modal duffingtype oscillators are not good candidates for harvesting energy under forced random excitations. Using a linear transformation, results can be extended to the base excitation case.

Original languageEnglish (US)
Pages (from-to)3621-3631
Number of pages11
JournalJournal of Sound and Vibration
Volume329
Issue number18
DOIs
StatePublished - Jan 1 2010

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Harvesters
nonlinearity
excitation
output
Energy harvesting
Bandwidth
bandwidth
energy
stiffness
Stiffness
oscillators
Linear transformations
linear transformations
Probability density function
probability density functions
trucks
numerical integration
Hardening
hardening
inertia

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Response of uni-modal duffing-type harvesters to random forced excitations. / Daqaq, Mohammed.

In: Journal of Sound and Vibration, Vol. 329, No. 18, 01.01.2010, p. 3621-3631.

Research output: Contribution to journalArticle

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