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On approximating the effective bandwidth of bi-stable energy harvesters

机译：近似双稳态能量收集器的有效带宽

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摘要

This paper aims to establish an analytical framework to define the effective bandwidth of bi-stable vibratory energy harvesters possessing a symmetric quartic potential function. To achieve this goal, the method of multiple scales is utilized to construct analytical solutions describing the amplitude and stability of the intra- and inter-well dynamics of the harvester. Using these solutions, critical bifurcations in the parameters' space are identified and used to define an effective frequency bandwidth of the harvester. The influence of three critical design parameters, namely the time constant ratio (ratio between the time constant of the harvesting circuit and the period of the mechanical system), the electromechanical coupling, and the shape of the potential function, on the effective frequency bandwidth is analyzed. It is shown that, while the time constant ratio has very little influence on the effective bandwidth of the harvester, increasing the electromechanical coupling and/or designing the potential function with deeper potential wells serve to shrink the effective bandwidth for a given level of excitation. In general, it is also observed that narrowing of the effective bandwidth is accompanied by an increase in the electric output further highlighting the competing nature of these two desired objectives.
机译：本文旨在建立一个分析框架，以定义具有对称四次势函数的双稳态振动能量采集器的有效带宽。为了实现此目标，采用了多种尺度的方法来构建描述收获器井内和井间动力学的幅度和稳定性的分析解决方案。使用这些解决方案，可以确定参数空间中的关键分支，并用于定义采集器的有效频率带宽。时间常数比率（采集电路的时间常数与机械系统的周期之间的比率），机电耦合以及势函数的形状这三个关键设计参数对有效频率带宽的影响为分析。结果表明，尽管时间常数比对收割机的有效带宽影响很小，但是在给定的激发水平下，增加机电耦合和/或设计势阱更深的势函数有助于缩小有效带宽。通常，还观察到有效带宽的缩小伴随着电输出的增加，进一步突出了这两个期望目标的竞争性质。

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