Non-transient optimum design of nonlinear electromagnetic vibration-based energy harvester using homotopy perturbation method

In this paper the coupled differential equations governing the vibration of nonlinear electromagnetic energy harvesters are solved by the homotopy perturbation method. The amplitudes of odd harmonics of displacement of the magnet, coil current, and load voltage are derived up to the 5th harmonic. The frequency response of output power is plotted and it peaks at the linear mechanical resonance frequency. It should be noted that the optimum design of coil and load parameters, optimum electromagnetic coupling coefficient, and optimum vibration frequency of the magnet attached to a non-linear spring resulted in a stationary or non-transient vibration. Paying insufficient attention to this point and using typical parameters instead of optimum ones will result in transient vibration. The research aims at a rigorous semi-analytical method on a nonlinear problem which has previously solely investigated by numerical or experimental method.