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Precise and target-oriented control of the low-frequency Lamb wave bandgaps
Journal of Sound and Vibration ( IF 4.7 ) Pub Date : 2021-07-23 , DOI: 10.1016/j.jsv.2021.116367
Yanzheng Wang 1 , Chuanzeng Zhang 1 , Weiqiu Chen 2 , Zhengyang Li 1 , Mikhail V. Golub 3 , Sergey I. Fomenko 3
Affiliation  

Precise and target-oriented control of acoustic/elastic wave bandgaps in phononic crystals or acoustic metamaterials according to particular requirements is of both theoretical and practical importance. A very challenging and also interesting task is to tune the widths and the overall positions of the bandgaps of interest independently and arbitrarily. This work presents a simple and smart acoustic metamaterial structure, which can achieve the above mentioned goal by considering the symmetric Lamb waves. The proposed acoustic metamaterial structure consists of a homogenous piezoelectric plate which is connected to the LC circuits through an array of periodic surface electrodes. The control of the resonance bandgaps (RBGs), which are generated by the coupled resonance of the piezoelectric plate with the external LC circuits, is the focus of this study. To solve the problem at hand, we develop a two-dimensional (2D) spectral element method (SEM) considering the full electro-mechanical coupling, and the high tunability of the RBGs is demonstrated numerically in the low-frequency range. Especially, we find that the upper/lower boundary of a RGB can be intentionally fixed at any specified frequency while changing its’ bandwidth. To explore the corresponding physical phenomena and reveal the regulation mechanism, a simplified theory is developed based on the assumption of thin piezoelectric plates. Several simple analytical formulas are established, which are essential to the precise control of the RBGs for both the thin and thick piezoelectric plates. A numerical example is given to demonstrate the detailed procedure of precisely tuning a RBG in a targeted frequency range, which is also verified by the transmission spectrum for the corresponding finite piezoelectric acoustic metamaterial plate.



中文翻译:

低频兰姆波带隙的精确和面向目标的控制

根据特定要求对声子晶体或声学超材料中的声/弹性波带隙进行精确和目标导向的控制具有理论和实践意义。一个非常具有挑战性和有趣的任务是独立和任意地调整感兴趣的带隙的宽度和整体位置。这项工作提出了一种简单而智能的声学超材料结构,可以通过考虑对称兰姆波来实现上述目标。所提出的声学超材料结构由同质压电板组成,该压电板通过一系列周期性表面电极连接到 LC 电路。谐振带隙 (RBG) 的控制,由压电板与外部 LC 电路的耦合谐振产生,是本研究的重点。为了解决手头的问题,我们开发了一种考虑全机电耦合的二维 (2D) 光谱元素方法 (SEM),并在低频范围内以数值方式证明了 RBG 的高可调性。特别是,我们发现 RGB 的上/下边界可以有意固定在任何指定的频率,同时改变其带宽。为了探索相应的物理现象并揭示调节机制,基于薄压电板的假设开发了一种简化理论。建立了几个简单的分析公式,这对于薄和厚压电板的 RBG 的精确控制至关重要。

更新日期:2021-08-03
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