Abstract The bending and torsional vibration of the periodic perpendicular cantilever beam-mass resonators (PCBMR) is idealized as translational and rotational oscillators attached to the main beam. In this paper, the effect of that torsional vibration of the PCBMR on the dynamics of an infinitely long Euler-Bernoulli beam is evaluated. The band-structure is explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The combination of the translational and rotational oscillator modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in the band-gap formation. The flexural band-structure is highly sensitive to the torsional vibration while the radius of gyration of the tip mass is considerably higher than the length of the PCBMR. Ill-tuning leads to split and reduction of attenuation band to 50%; whereas, around 38% elongation of the attenuation band in the low frequency regime can be achieved by proper tuning.

中文翻译：

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周期性连接的垂直梁谐振器的扭转振动对欧拉-伯努利梁弯曲带的影响

摘要 周期性垂直悬臂梁质量谐振器 (PCBMR) 的弯曲和扭转振动被理想化为连接到主梁的平移和旋转振荡器。在本文中，评估了 PCBMR 的扭转振动对无限长 Euler-Bernoulli 梁动力学的影响。通过结合 Bloch-Floquet 定理实施传递矩阵方法来探索能带结构。平移和旋转振荡器的组合改变了耦合系数在传递矩阵中的相对位置，这在带隙形成中起着关键作用。弯曲带结构对扭转振动高度敏感，而尖端质量的回转半径远高于 PCBMR 的长度。调谐不良导致衰减带分裂和减少到50%；然而，通过适当的调谐，可以在低频范围内将衰减带延长约 38%。