This paper presents a novel form of mass-in-mass metamaterial, in which the internal resonator is replaced by a beam. Additionally, stoppers are installed on either side of the beam connected rigidly with the main mass to produce an impacting response. Employing linear complementary problem (LCP) along with Euler’s discretization, a time domain solver is developed to obtain the response of the impacting metamaterial. The proposed method is first validated for obtaining the chattering response of a cantilever beam subjected to harmonic excitations experimentally and theoretically. Furthermore, to provide a comprehensive validation of the LCP solver, an experimental validation of a beam in mass impacting unit cell is performed. The vibration transmission and the effective mass of the proposed unit cell are then investigated. The development of vibration attenuation band gaps and negative effective mass for the proposed unit cell enhances its capability to be effectively used for vibration control. The same unit cell is then used to form a metamaterial chain comprising of finite number of such unit cells. From the transmittance plot of the last metamaterial unit cell, it is observed that the second propagation band vanishes and a wide vibration attenuation band gap is perceived. Therefore, the proposed metamaterial unit cell has a good future prospect to be a building block of a metamaterial chain.

中文翻译：

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质量冲击超材料中通过悬臂梁的振动传输：分析研究和实验


本文提出了一种新型的质量对质量超材料，其中内部谐振器被梁取代。此外，挡块安装在与主质量刚性连接的梁的两侧，以产生冲击响应。采用线性互补问题 (LCP) 和欧拉离散化，开发了时域求解器来获取撞击超材料的响应。首先通过实验和理论验证所提出的方法，以获得受到谐波激励的悬臂梁的颤振响应。此外，为了提供 LCP 求解器的全面验证，对质量冲击晶胞中的梁进行了实验验证。然后研究所提出的单元的振动传递和有效质量。所提出的单元电池的振动衰减带隙和负有效质量的发展增强了其有效用于振动控制的能力。然后使用相同的晶胞来形成由有限数量的此类晶胞组成的超材料链。从最后一个超材料晶胞的透射率图中可以看出，第二传播带消失，并且感知到较宽的振动衰减带隙。因此，所提出的超材料单元具有良好的未来前景，可以成为超材料链的构建块。