Harmonic-balance analysis of nonlinear energy harvester models

Nonlinear dynamics can be a means to improve the properties of energy harvesting devices. Mathematical analysis of these systems as a tool for design or interpretation of experiments requires the solution of nonlinear differential equations. Most works use the third-order polynomial force (Duffing model) in order to qualitatively model mechanically nonlinear features. However, under large vibrations, higher orders may be necessary for accuracy and should be considered. In addition, the electromechanical transduction should be accounted for. Here we analyze a mathematical model with third and higher order mechanical nonlinearities and with electromechanical transduction. The harmonic balance method was chosen as the analytical tool due to the large displacement range and thereby strong nonlinearities. The harmonic-balance results are compared with lumped-model time-domain simulations.