Abstract This paper investigates a technique for broadband vibration suppression using a graded metamaterial beam. A series of local resonators with the same mass but different natural frequencies are attached to the beam. The difference between the natural frequencies of neighboring local resonators is defined as the frequency spacing. The spectral element method (SEM) is used to model the graded metamaterial beam, and is verified by the corresponding finite element model (FEM). Three figures of merit are defined to quantitatively evaluate the vibration suppression performance of the proposed metamaterial beam, in terms of the attenuation bandwidth and attenuation strength. Subsequently, a design strategy is proposed, and used to tune the frequency spacing to get a wide attenuation region. A parametric study is conducted to reveal the effects of the frequency spacing and damping ratio on the vibration suppression performance of the graded metamaterial beam: with increasing frequency spacing, the attenuation region first becomes wider, then multiple discrete attenuation regions appear; and with increasing damping ratio, the transmittance response becomes flatter. A piezoelectric metamaterial beam is used to implement the proposed design strategy. Using a synthetic shunt circuit, the ‘stiffness’ of the local resonator can be tuned using a piezoelectric transducer. The FEM simulation results agree well with the developed theory for the graded metamaterial beam: with tuning of the capacitance spacing (2.4 nF), the attenuation bandwidth can be increased by about 172.8% as compared to the conventional one shunted with identical capacitances.

中文翻译：

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具有梯度局部谐振器的超材料梁用于宽带振动抑制

摘要 本文研究了一种使用渐变超材料梁的宽带振动抑制技术。一系列质量相同但固有频率不同的局部谐振器连接到梁上。相邻局部谐振器的固有频率之间的差异被定义为频率间隔。光谱元法（SEM）用于对渐变超材料梁进行建模，并通过相应的有限元模型（FEM）进行验证。定义了三个品质因数，以定量评估所提出的超材料梁在衰减带宽和衰减强度方面的振动抑制性​​能。随后，提出了一种设计策略，用于调整频率间隔以获得较宽的衰减区域。通过参数研究揭示了频率间距和阻尼比对梯度超材料梁的振动抑制性​​能的影响：随着频率间距的增加，衰减区域首先变宽，然后出现多个离散的衰减区域；并且随着阻尼比的增加，透射率响应变得更平坦。压电超材料梁用于实现所提出的设计策略。使用合成分流电路，可以使用压电换能器调谐局部谐振器的“刚度”。FEM 仿真结果与梯度超材料梁的发展理论非常吻合：通过调整电容间距 (2.4 nF)，衰减带宽可增加约 172。