Fractional properties’ effects on a hybrid energy harvesting system dynamics

A vibration-powered harvester modeled by non-smooth coupled oscillators with fractional properties and subjected to harmonic excitation is concerned in this work. By a modified harmonic balance method, the harmonic response of the system is studied, thence the effects of fractional derivatives’ orders (FDOs) on the harvesting behavior of the system are sought. A numerical confirmation is then obtained by the mean of the Newton-Leipnik algorithm. The FDOs effects on the chaotic response and their implication on the harvesting characteristic of the system are also analyzed. For low amplitude excitations, it is found that, depending on the excitation frequency’s band, the power generated by the mean of the electromagnetic transduction mechanism can be maximized either by increasing or reducing the order of the fractional derivative related to the electromagnetic circuit. Contrariwise, the performance of the piezoelectric conversion mechanism is improved by increasing the order of the fractional derivative related to the piezoelectric circuit, irrespective of the excitation frequency. For large amplitude excitations, proper choices of FDOs enable the system to exhibit a regular behavior instead of a chaotic one, so as to harvest a useful power of regular waveform.