Fokker-Planck Equation Analysis of Randomly Excited Nonlinear Energy Harvester

P Kumar, S Narayanan (IIT Madra, India), S Adhikari & MI Friswell (Swansea University)

Journal of Sound and Vibration, Vol. 333, No. 7, March 2014, pp. 2040-2053


The probability structure of the response and energy harvested from a nonlinear oscillator subjected to white noise excitation is investigated by solution of the corresponding Fokker-Planck (FP) equation. The nonlinear oscillator is the classical double well potential Duffing oscillator corresponding to the first mode vibration of a cantilever beam suspended between permanent magnets and with bonded piezoelectric patches for purposes of energy harvesting. The FP equation of the coupled electro mechanical system of equations is derived. The finite element method is used to solve the FP equation giving the joint probability density functions of the response as well as the voltage generated from the piezoelectric patches. The FE method is also applied to the nonlinear inductive energy harvester of Daqaq and the results compared. The mean square response and voltage are obtained for different white noise intensities. The effects of the system parameters on the mean square voltage are studied. It is observed that the energy harvested can be enhanced by suitable choice of the excitation intensity and the parameters. The results of the FP approach agree very well with Monte Carlo Simulation (MCS) results.

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This material has been published in the Journal of Sound and Vibration, Vol. 333, No. 7, March 2014, pp. 2040-2053. Unfortunately the copyright agreement with Elsevier does not allow for the PDF file of the paper to be available on this website. However the paper is available from ScienceDirect - see the link below.

Link to paper using doi: 10.1016/j.jsv.2013.11.011

Journal of Sound and Vibration on ScienceDirect