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 journalArticlepeer-review


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
Publication statusPublished - 31 Mar 2015


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


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