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.

本工作涉及一种由具有分数特性的非光滑耦合振荡器建模并受到谐波激励的振动动力收割机。通过改进的谐波平衡法，研究了系统的谐波响应，进而寻求分数阶导数(FDO)对系统采集行为的影响。然后通过 Newton-Leipnik 算法的平均值获得数值确认。还分析了 FDO 对混沌响应的影响及其对系统采集特性的影响。对于低振幅激励，发现取决于激励频率的频带，通过增加或减少与电磁电路相关的分数阶导数的阶数，可以使由电磁转换机制的平均值产生的功率最大化。相反，通过增加与压电电路相关的分数阶导数的阶数来提高压电转换机制的性能，而与激励频率无关。对于大振幅激励，正确选择 FDO 可以使系统表现出规则行为而不是混乱行为，从而获得规则波形的有用功率。