Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
Parametrically amplified Mathieu-Duffing nonlinear energy harvesters
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DOI：
10.1016/j.jsv.2020.115677
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发表时间：
2020-08
影响因子：
4.7
通讯作者：
Danilo Karličić;Tanmoy Chatterjee;Milan Cajić;S. Adhikari
中科院分区：
文献类型：
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作者：
Danilo Karličić;Tanmoy Chatterjee;Milan Cajić;S. Adhikari
基于Mathieu-Duffing非线性振子模型，研究了非线性压电能量采集器在外部激励和参数激励下的稳态响应。参数激励被引入以放大外部谐波激励并扩展非线性压电能量采集器装置的能力。为了获得能量采集器的位移和电压的非线性周期响应的近似解，采用增量谐波平衡法结合路径跟踪技术。假设所提出的非线性模型由三次和二次非线性组成，其中参数放大以三角函数的形式出现。频率被调谐为外部激励和参数激励之间的一比一和一比二比率。详细研究了二次和三次非线性以及参数放大的影响，并说明了它们在扩展收割机应用性能方面的令人难以置信的特性。它明确地表明，对于一些特定的组合的系统参数，振动幅度和收获的功率可以被放大到三到五倍相比，经典的宽带非线性能量采集器的基础上强迫Duffing振荡器。这种非凡的放大作用是在实践中实现拟议概念的关键动机。组合的二次和三次非线性的存在导致硬化和软化弹簧行为，并导致在幅频响应中共存的周期解的外观。所提出的方法得到的周期轨道进行了验证，从直接数值积分的结果和精细协议证明。此外，在时间响应图中揭示了参数放大对瞬时功率的显著影响，从而显示了所提出的能量采集器系统的更好性能。
The steady-state response of a nonlinear piezoelectric energy harvester subjected to external and parametric excitation is investigated based on the Mathieu-Duffing nonlinear oscillator model. The parametric excitation is introduced to amplify the external harmonic excitation and extend the capabilities of the nonlinear piezoelectric energy harvester device. To obtain the approximated solution of the nonlinear periodic responses for displacement and electrical voltage of the energy harvester, the incremental harmonic balance method in combination with the path-following technique is adopted. It is assumed that the proposed nonlinear model consists of cubic and quadratic nonlinearity, where parametric amplification appears in the form of a trigonometric function. The frequency is tuned as one-to-one and the one-to-two ratio between external and parametric excitation. The effects of quadratic and cubic nonlinearity as well as parametric amplification are studied in detail, and their incredible properties to extend harvester application performance is illustrated. It is explicitly demonstrated that for some particular combination of the system parameters, vibration amplitudes and harvested power can be amplified up to three or five times in comparison to the classical broadband nonlinear energy harvester based on the forced Duffing oscillator. This extraordinary amplification shown to be a key motivation to realize the proposed concept in practice. The presence of combined quadratic and cubic nonlinearities resulted in both hardening and softening spring behavior and leading to the appearance of coexisting periodic solutions in the amplitude-frequency responses. Periodic orbits obtained by the proposed methodology are verified with the results from direct numerical integration and fine agreement is demonstrated. Moreover, a significant influence of the parametric amplification on the instantaneous power is revealed in time response diagrams, thus showing better performance of the proposed energy harvester system.