In this study, a semi-analytic approach to optimizing the external load resistance of a bi-stable electromagnetic energy harvester is presented based on the harmonic balance method. The harmonic balance analyses for the primary harmonic (period-1T) and two subharmonic (period-3T and 5T) interwell motions of the energy harvester are performed with the Fourier series solutions of the individual motions determined by spectral analyses. For each motion, an optimization problem for maximizing the output power of the energy harvester is formulated based on the harmonic balance solutions and then solved to estimate the optimal external load resistance. The results of a parametric study show that the optimal load resistance significantly depends on the inductive reactance and internal resistance of a solenoid coil--the higher the oscillation frequency of an interwell motion (or the larger the inductance of the coil) is, the larger the optimal load resistance. In particular, when the frequency of the ambient vibration source is relatively high, the non-linear dynamic characteristics of an interwell motion should be considered in the optimization process of the electromagnetic energy harvester. Compared with conventional resistance-matching techniques, the proposed semi-analytic approach could provide a more accurate estimation of the external load resistance.
Keywords: bi-stable oscillator; electromagnetic energy harvester; frequency response analysis; harmonic balance method; load resistance optimization.