Semi-analytical solution of random response for nonlinear vibration energy harvesters

Xiaoling Jin, Yong Wang, Ming Xu, Zhilong Huang, M.P. Cartmell

Research output: Contribution to journalArticle

Abstract

Due to the prominent broadband performance of nonlinear vibration energy harvester, theoretical evaluations for the mean-square response to random excitations and the associated mean output power are of great interest. By employing the generalized harmonic transformation and equivalent nonlinearization technique, established here is a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. The semi-analytical solution for stationary probability density of the system response is obtained by two iterative processes. Numerical results for a Duffing-type harvester demonstrate rapid convergence of the iterative processes and high evaluation accuracy for the mean-square response and the mean output power. Furthermore, the influence of harvesting circuit on the mechanical subsystem can be converted to modified quasi-linear damping and stiffness with energy-dependent coefficients, which is different from the traditional viewpoint on the equivalence of constant-coefficient damping and provides more comprehensive explanation on the influence of harvesting circuit.

Original languageEnglish
Pages (from-to)267-282
Number of pages16
JournalJournal of Sound and Vibration
Volume357
DOIs
Publication statusPublished - 31 Mar 2015

Fingerprint

Harvesters
vibration
Damping
Networks (circuits)
damping
White noise
energy
evaluation
output
coefficients
white noise
Stiffness
excitation
equivalence
stiffness
broadband
harmonics

Keywords

  • nonlinear vibration energy harvester
  • random response
  • semi-analytical

Cite this

Jin, Xiaoling ; Wang, Yong ; Xu, Ming ; Huang, Zhilong ; Cartmell, M.P. / Semi-analytical solution of random response for nonlinear vibration energy harvesters. In: Journal of Sound and Vibration. 2015 ; Vol. 357. pp. 267-282.
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Semi-analytical solution of random response for nonlinear vibration energy harvesters. / Jin, Xiaoling; Wang, Yong; Xu, Ming; Huang, Zhilong; Cartmell, M.P.

In: Journal of Sound and Vibration, Vol. 357, 31.03.2015, p. 267-282.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Semi-analytical solution of random response for nonlinear vibration energy harvesters

AU - Jin, Xiaoling

AU - Wang, Yong

AU - Xu, Ming

AU - Huang, Zhilong

AU - Cartmell, M.P.

PY - 2015/3/31

Y1 - 2015/3/31

N2 - Due to the prominent broadband performance of nonlinear vibration energy harvester, theoretical evaluations for the mean-square response to random excitations and the associated mean output power are of great interest. By employing the generalized harmonic transformation and equivalent nonlinearization technique, established here is a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. The semi-analytical solution for stationary probability density of the system response is obtained by two iterative processes. Numerical results for a Duffing-type harvester demonstrate rapid convergence of the iterative processes and high evaluation accuracy for the mean-square response and the mean output power. Furthermore, the influence of harvesting circuit on the mechanical subsystem can be converted to modified quasi-linear damping and stiffness with energy-dependent coefficients, which is different from the traditional viewpoint on the equivalence of constant-coefficient damping and provides more comprehensive explanation on the influence of harvesting circuit.

AB - Due to the prominent broadband performance of nonlinear vibration energy harvester, theoretical evaluations for the mean-square response to random excitations and the associated mean output power are of great interest. By employing the generalized harmonic transformation and equivalent nonlinearization technique, established here is a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. The semi-analytical solution for stationary probability density of the system response is obtained by two iterative processes. Numerical results for a Duffing-type harvester demonstrate rapid convergence of the iterative processes and high evaluation accuracy for the mean-square response and the mean output power. Furthermore, the influence of harvesting circuit on the mechanical subsystem can be converted to modified quasi-linear damping and stiffness with energy-dependent coefficients, which is different from the traditional viewpoint on the equivalence of constant-coefficient damping and provides more comprehensive explanation on the influence of harvesting circuit.

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