In this work, the dynamic behaviors of L-shaped piezoelectric vibration energy harvester that result from the combination internal resonance are numerically, analytically and experimentally presented. The electromechanically coupled governing equations of the energy harvester were employed in accordence with our previous study. The multi-branch approximate responses of the system are derived by using the method of multiple scales. The stability of the system is determined by the eigenvalues of the Jacobi matrix. Parameterized analyses are conducted on the output response as the external excitation frequency approaches the differential combination frequency of the energy harvester. The effects of acceleration excitation and external resistance on the output performance of the system are analyzed. The nonlinear responses of the system under various initial conditions are numerically analyzed using time response curves, spectrograms, Poincaré maps, and bifurcation diagrams. The effects of external resistance and external excitation frequency on the attractor basin are investigated. The particular nonlinear phenomena identified in the theory are experimentally verified for the combination resonance. The broad frequency range of the LPEH ranges from 15 Hz to 16.82 Hz. The study of combination resonance and internal resonance of the piezoelectric energy harvester will help to understand its complex vibration characteristics and predict the dynamic behavior.

中文翻译：

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L型压电振动能量采集器组合内谐的理论与实验研究


在这项工作中，从数值、分析和实验的角度介绍了由组合内部谐振产生的 L 形压电振动能量收集器的动力学行为。能量收集器的机电耦合控制方程与我们之前的研究一致。采用多尺度方法推导了系统的多分支近似响应。系统的稳定性由 Jacobi 矩阵的特征值决定。当外部激励频率接近能量采集器的差分组合频率时，对输出响应进行参数化分析。分析了加速度激励和外部阻力对系统输出性能的影响。使用时间响应曲线、频谱图、庞加莱图和分叉图对系统在各种初始条件下的非线性响应进行数值分析。研究了外阻和外励磁频率对吸引子盆的影响。理论中确定的特定非线性现象针对组合共振进行了实验验证。LPEH 的宽频率范围为 15 Hz 至 16.82 Hz。对压电能量采集器的组合谐振和内谐振的研究将有助于理解其复杂的振动特性并预测其动力学行为。