Exploring 1∶3 internal resonance for broadband piezoelectric energy harvesting

M. Aravindan; S. Faruque Ali

摘要

Recent literature has shown that the spectral characteristics of a harvester can be significantly improved by invoking internal resonance between the modes. Taking motivation from this premise, the present work analyzes the nonlinear dynamics and harvesting performance of a 1∶3 internally resonant piezoelectric cantilever beam with a lumped mass under harmonic excitation. The governing modal equations are derived using Galerkin's approach and Hamilton's principle of least action. The method of multiple scales has been used to study the dynamics of the harvester in the proximity of primary resonances. The steady state periodic responses of the harvester are obtained using a pseudo-arc continuation technique and subsequently, their implications on the harvested power are discussed. The frequency responses of the harvested power are shown to boast significantly high magnitudes across a wide frequency band due to the energy transfer between the modes near the primary resonances. Results presented in the study show that the higher mode invoked through internal resonance plays a significant role in broadband power generation. The transfer of energy between the modes is found to occur only within a certain threshold of excitation level which in turn affects the magnitude of harvested power. Numerical simulations have also been carried out the results of which are compared against the analytical results. The outcomes of this first-hand analysis shall aid in the proposition of an efficient design for a broadband energy harvester.

机译：最近的文献表明，通过调用模式之间的内部共振可以显着提高收割机的光谱特性。从这个前提下采取动机，本作工作分析了在谐波激发下具有集体质量的1:3内部谐振压电悬臂梁的非线性动力学和收获性能。使用Galerkin的方法和Hamilton最不采取行动的原则来源的管理模态方程。多种尺度的方法已经用于研究收割机的动态在初级共振的附近。使用伪弧形连续技术获得收割机的稳态周期性响应，随后，讨论了它们对收获功率的影响。由于初级谐振附近的模式之间的能量传递，所收获功率的频率响应显示在宽频带上跨越宽频带的显着高度。研究结果表明，通过内部共振调用的更高模式在宽带发电中起着重要作用。发现模式之间的能量传递仅在激发水平的某个阈值内发生，这反过来影响收获功率的大小。还进行了数值模拟，其结果与分析结果进行了比较。该第一手分析的结果应有助于提出宽带能源收割机的有效设计。

Exploring 1∶3 internal resonance for broadband piezoelectric energy harvesting

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