惯性放大谐振腔的固有非线性阻尼
Inherent Non-Linear Damping in Resonators with Inertia Amplification
摘要：
惯性放大是一种耦合振动结构内的自由度的机制。其目标是实现明显的高动态质量和相应的低谐振频率。已经描述了这种结构用于局部共振超材料和声子晶体中，以降低带隙的起始频率而不增加系统的质量。这项研究表明，平移或旋转振动之间的任何非线性运动耦合导致的振幅依赖阻尼的外观。具有惯性放大的谐振器的运动方程的解析推导在阻尼过程中产生洞察力，并且示出振动阻尼随着其振幅而增加。两种类型的惯性放大谐振器的实验证据验证了理论研究。最后，振幅相关的阻尼的重要性，说明当结构被用作调谐质量阻尼器的悬臂梁。
英文摘要：
Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in locally resonant metamaterials and phononic crystals to lower the starting frequency of a band gap without adding mass to the system. This study shows that any non-linear kinematic coupling between translational or rotational vibrations leads to the appearance of amplitude-dependent damping. The analytical derivation of the equation of motion of a resonator with inertia amplification creates insight in the damping process, and shows that the vibration damping increases with its amplitude. The theoretical study is validated by experimental evidence from two types of inertia-amplification resonators. Finally, the importance of amplitude-dependent damping is illustrated when the structure is used as a tuned mass damper for a cantilever beam.
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