In this paper, a type of metamaterial isolation beam consisting a cantilever beam with flexoelectric film attached is provided. Electrodes interconnect on the surface to create parallel resonant shunt circuits, enabling band-stop filtering. The electromechanical control equations are derived using the Hamiltonian principle. A closed-form analytical expression for the bandgap range is obtained via the root locus method. Theoretical results are validated through finite element methods. Findings reveal that the operational bandgap of millimeter-scale flexoelectric metamaterial isolation beams is 5.2 times greater than that of conventional piezoelectric metamaterial beams. Furthermore, the vibration excitation amplitude is reduced by 99.9%. These results highlight the significant advantages of flexoelectric materials for microscale high-frequency passive isolation, providing superior stability in complex vibration environments. The research investigates the effects of end mass, electrode plate count, and external resistance on the vibration isolation performance of flexoelectric metamaterial beams. The study also examines the variations in relative bandgap width between flexoelectric and piezoelectric metamaterial beams concerning material, size, and structural parameters, identifying optimal values. Notable differences in bandgap characteristics are observed between flexoelectric and piezoelectric beams; for instance, while piezoelectric beams have an optimal substrate elastic modulus, flexoelectric beams do not, and the optimal film thickness for flexoelectric beams is 2.2 times that for piezoelectric beams.

中文翻译：

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具有挠电效应的微尺度隔振超材料梁的机电带隙研究


本文提出了一种超材料隔离梁，由悬臂梁附着挠性电薄膜组成。电极在表面互连以创建并联谐振分流电路，从而实现带阻滤波。机电控制方程是利用哈密顿原理推导出来的。通过根轨迹法获得带隙范围的封闭式解析表达式。理论结果通过有限元方法得到验证。研究结果表明，毫米级挠曲电超材料隔离梁的工作带隙是传统压电超材料梁的5.2倍。此外，振动激励幅度降低了99.9%。这些结果凸显了柔性电材料在微尺度高频无源隔离方面的显着优势，可在复杂振动环境中提供卓越的稳定性。该研究研究了端部质量、电极板数量和外部电阻对挠电超材料梁隔振性能的影响。该研究还研究了挠曲电和压电超材料梁之间相对带隙宽度在材料、尺寸和结构参数方面的变化，以确定最佳值。在挠性电梁和压电梁之间观察到带隙特性存在显着差异；例如，压电梁具有最佳的基板弹性模量，而挠曲电梁则没有，并且挠曲电梁的最佳膜厚度是压电梁的2.2倍。