On Mechanical Modeling of Cantilevered Piezoelectric Vibration Energy Harvesters
On Mechanical Modeling of Cantilevered Piezoelectric Vibration Energy Harvesters
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DOI：
10.1177/1045389x07085639
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发表时间：
2008-11-01
影响因子：
2.7
通讯作者：
Inman, D. J.
中科院分区：
文献类型：
--
作者：
Erturk, A.;Inman, D. J.
压电陶瓷（PZT）层悬臂梁是研究最多的振动能量收集器类型。一种常用的建模方法是收割机光束的单自由度（SDOF）建模，因为它允许简单的电输出表达式。在文献中，由于假定收割机梁上的基激励是谐波的，因此采用了众所周知的SDOF关系进行数学建模。本研究表明，普遍接受的SDOF谐波基激励关系在预测悬臂梁和杆的运动时可能会产生高度不准确的结果。首先，在考虑更复杂的阻尼模型的情况下，回顾了悬臂欧拉-伯努利梁对平动和小旋转给出的一般基础激励的响应。在此基础上，分析了SDOF模型的误差，并推导了改进SDOF谐波基激励模型的修正因子。讨论了处理机械阻尼分量的形式化方法。在推导开路条件下压电陶瓷电输出的简单表达式后，研究了电输出与振动模态振型和电极位置的相关性，并解决了应变节点的问题。
Cantilevered beams with piezoceramic (PZT) layers are the most commonly investigated type of vibration energy harvesters. A frequently used modeling approach is the single-degree-of-freedom (SDOF) modeling of the harvester beam as it allows simple expressions for the electrical outputs. In the literature, since the base excitation on the harvester beam is assumed to be harmonic, the well known SDOF relation is employed for mathematical modeling. In this study, it is shown that the commonly accepted SDOF harmonic base excitation relation may yield highly inaccurate results for predicting the motion of cantilevered beams and bars. First, the response of a cantilevered Euler-Bernoulli beam to general base excitation given in terms of translation and small rotation is reviewed where more sophisticated damping models are considered. Then, the error in the SDOF model is shown and correction factors are derived for improving the SDOF harmonic base excitation model both for transverse and longitudinal vibrations. The formal way of treating the components of mechanical damping is also discussed. After deriving simple expressions for the electrical outputs of the PZT in open-circuit conditions, relevance of the electrical outputs to vibration mode shapes and the electrode locations is investigated and the issue of strain nodes is addressed.