A model of a novel metamaterial beam with periodically attached spring–mass combinations is presented. Dispersion relation, reaction forces and power flow are calculated and aided by the finite element method, to help understand the actual band gap generation and wave attenuation mechanism. Results show that multiple large low-frequency band gaps are generated and can be overlapped to form a broad gap with reasonable damping. Reaction force analysis and energy distribution reveal the actual wave attenuation working mechanism of multiple translational absorbers on the beam: some of the resonators create negative inertia, 180° out of phase with the host beam, to counterbalance the positive inertia of some resonators in phase with the host beam, plus the shear force induced by flexural waves, and the different combinations of the resonance open different band gaps. Damping effect on the transmitted power flow is complicated. Therefore, the specific effect of damping needs to be identified in practical engineering when the metamaterial beam is applied.

中文翻译：

---

多带隙声超材料梁的反作用力和潮流分析

提出了一种新型的超材料梁的模型，该梁具有周期性附加的弹簧-质量组合。通过有限元方法计算并辅助了色散关系，反作用力和功率流，以帮助理解实际的带隙产生和波衰减机理。结果表明，产生了多个大的低频带隙，并且可以重叠以形成具有合理阻尼的宽间隙。反作用力分析和能量分布揭示了梁上多个平移吸收器的实际波衰减工作机制：一些谐振器产生负惯性，与主梁异相180°，以抵消某些谐振器的正惯性与主梁，加上弯曲波引起的剪力，共振的不同组合会打开不同的带隙。对传输功率流的阻尼效应很复杂。因此，在应用超材料梁时，在实际工程中需要确定阻尼的具体效果。