The multi-mode and dispersion characteristics of guided waves in plate bring great challenges to the manipulation of guided waves and controlling vibration and noise. In this study, the Stroh formalism is developed to establish a theoretical model for deriving the dispersion relations of guided waves in a multilayered piezoelectric plate. The dispersion characteristics under different electrical boundary conditions introduced by periodic shunting circuits are discussed to reveal the influences of external circuits on guided wave propagation. The proper shunting circuit is not only the key point to obtain the specific frequency of bandgap, but also the effective method to control the bandwidth. Furthermore, for the separation of symmetric and anti-symmetric modes of guided waves, the multilayered piezoelectric plate with a mirror plane is studied by using an equivalent model. Results indicate that the propagation behaviors of guided waves in multilayered piezoelectric plates can be interpreted by developed Stroh formalism, and their bandgaps can be effectively manipulated by periodically external circuits. The tunable bandgaps in this work could be helpful for designing smart devices of wave isolation based on multilayered piezoelectric plate.

中文翻译：

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多层压电板中周期性分流电路可调谐导波带隙


板内导波的多模态和色散特性给导波操控、振动和噪声控制带来了巨大挑战。在这项研究中，发展了斯特罗形式主义来建立一个理论模型，用于推导多层压电板中导波的色散关系。讨论了周期性分流电路引入的不同电边界条件下的色散特性，以揭示外部电路对导波传播的影响。合适的分流电路不仅是获得特定带隙频率的关键，也是控制带宽的有效方法。此外，为了分离导波的对称模式和反对称模式，利用等效模型对具有镜面的多层压电板进行了研究。结果表明，多层压电板中导波的传播行为可以用发达的斯特罗形式主义来解释，并且它们的带隙可以通过周期性外部电路有效地操纵。这项工作中的可调带隙有助于设计基于多层压电板的智能隔波器件。