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中文核心期刊

弯曲波彩虹捕获效应及其在能量俘获中的应用

RAINBOW TRAPPING OF FLEXURAL WAVES AND ITS APPLICATION IN ENERGY HARVESTING

  • 摘要: 弹性波在色散关系经过设计的梯度结构中传播时会产生空间分频现象和波场能量增强现象, 即不同频率的弹性波会在结构的不同位置停止向前传播并发生能量聚集, 这就是弹性波彩虹捕获效应. 其相关研究成果可以促进结构健康监测、振动控制以及能量俘获等领域的发展. 本文通过所设计的梯度结构梁, 系统地研究了弯曲波彩虹捕获效应及其在压电能量俘获中的应用. 首先, 利用传递矩阵法获得了梯度结构梁元胞能带结构的解析解, 进而分析了弯曲波彩虹捕获效应的产生机理: 不同频率的弯曲波会在不同元胞附近群速度减小到零, 从而停止向前传播并发生反射; 入射波和反射波的叠加, 以及群速度减小带来的能量聚集, 会显著增强反射处的波场能量. 其次, 通过有限元仿真和实验验证了弯曲波彩虹捕获效应的空间分频现象和波场能量增强现象. 最后, 通过有限元多物理场耦合仿真和实验, 研究了粘贴PVDF压电薄膜的梯度结构梁相对于均匀梁的弯曲波能量俘获效果及其随入射波频率的变化规律. 结果表明, 在弯曲波彩虹捕获效应发生频带内, 粘贴在梯度结构梁上的PVDF压电薄膜的输出电压约为粘贴在均匀梁相应位置处的PVDF压电薄膜的输出电压的2倍.

     

    Abstract: When broadband elastic waves with different frequencies propagate in a graded structure with a special dispersion relation, the spatial frequency separation and the wave field energy enhancement will occur, that is, the waves will stop propagating forward and have energy accumulation at different positions of the structure, which is called the rainbow trapping of elastic waves. Researches on the rainbow trapping will promote the development of structural health monitoring, vibration control and energy harvesting. In this paper, the rainbow trapping of flexural waves and its application in piezoelectric energy harvesting are studied by using the designed beam with graded pillars. Firstly, band structures of unit cells of the beam are analytically solved by the transfer matrix method. According to the band structures, the mechanism of the rainbow trapping of flexural waves is analyzed: the group velocities of flexural waves with different frequencies will reduce to zero near different cells, thereby the flexural waves will stop forward propagation and be reflected; the superposition of incident and reflected waves, and the energy accumulation resulted by the reduction of group velocity, will significantly enhance the wave field at the reflection position. Secondly, the spatial frequency separation and the wave field energy enhancement of the rainbow trapping of flexural waves are verified by finite element simulations and experiments. Finally, we quantitatively evaluate the energy harvesting performance of the beam with graded pillars and its variation with the frequency of the incident wave comparing to the corresponding bare uniform beam, where PVDF piezoelectric films are pasted on their surfaces, by using finite element multiphysics coupling simulations and corresponding experiments. The results illustrate that the output voltage of the PVDF piezoelectric film of the beam with graded pillars is about 2 times that of the corresponding bare uniform beam in the bandwidth of the rainbow trapping of flexural waves.

     

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