In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester with base excitation in super-harmonic resonance is investigated. The averaging method is exploited to provide an approximate analytical solution for the system. The displacement and voltage responses are determined depending explicitly on the displacement amplitude and excitation frequency. The explicit approximate analytical expressions of the peak amplitude and corresponding base excitation frequency are also presented. Next, a detailed power flow analysis in super-harmonic resonance is made, then formulations for input mechanical power and energy, useful electrical power and energy, and efficiency are obtained, respectively. Numerical simulations are carried out to show qualitative comparisons between sup- and sub-harmonic cases and linear cases at corresponding base excitation frequencies. It is obtained that super- and sub-harmonic resonances are effective solutions to enlarge the performance of nonlinear piezoelectric energy harvester in wide-band excitation, especially compared to linear one that only works at a single frequency.

在本文中，研究了通过单稳态 Duffing 能量收集器在超谐波共振中具有基础激励来收集振动能量的潜力。利用平均方法为系统提供近似解析解。位移和电压响应明确取决于位移幅度和激励频率。还给出了峰值幅度和相应的基本激励频率的显式近似解析表达式。接下来，对超谐波谐振中的功率流进行了详细分析，然后分别获得了输入机械功率和能量、有用电能和能量以及效率的公式。进行数值模拟以显示在相应基本激励频率下超谐波和次谐波情况与线性情况之间的定性比较。结果表明，超谐波和次谐波谐振是提高非线性压电能量收集器在宽带激励下的性能的有效解决方案，特别是与仅在单一频率下工作的线性压电能量收集器相比。