Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial
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Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial Jiaxi Zhou . Hongbin Pan . Changqi Cai . Daolin Xu
Received: 3 July 2020 / Accepted: 21 October 2020 Springer Nature B.V. 2020
Abstract Metamaterials are artificially structured materials that enable wave attenuation in band gaps. However, opening an ultralow-frequency band gap is still a challenge, since it is hard to realize near-zero stiffness in a traditional way. In this paper, a onedimensional tunable quasi-zero-stiffness (QZS) metamaterial is engineered for ultralow-frequency (about a few tens Hertz) wave attenuation. Design optimization on the configuration of this new metamaterial is conducted to achieve quasi-zero stiffness. The dispersion relation is derived theoretically based on a lumped diatomic chain model, and then the band structure is revealed. The characteristics of longitudinal wave propagation in the metamaterial are studied by both numerical analyses and FE simulations, which are also validated by experimental tests. The results indicate that the stiffness is deformation-related, and the band gap can be tuned substantially by just changing the pre-compression. Therefore, the quasizero stiffness and then the ultralow-frequency band gap can be fulfilled by pre-compressing the metamaterial properly. J. Zhou (&) H. Pan C. Cai D. Xu State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Changsha 410082, People’s Republic of China e-mail: [email protected] J. Zhou H. Pan C. Cai D. Xu College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, People’s Republic of China
Keywords Quasi-zero stiffness Metamaterials Ultra-low frequency Band gap Wave attenuation
1 Introduction Metamaterials, artificially periodically structured materials, have excellent ability of manipulating and controlling elastic waves propagation (Kushwaha et al. 1993; Vasseur et al. 2001). In last three decades, numerous works about conceptual designs, theoretical developments and experiments on metamaterials have been done, as well documented by Hussein et al. (2014) and Deymier (2013). Generally, the Bragg scattering is responsible of creating a band gap by phononic crystals, which prohibits elastic waves with wavelength comparable to the lattice constant (Martı´nez-Sala et al. 1995; Sigalas and Economou 1992). However, locally resonant metamaterials can open much lower-frequency band gap and thus stop subwavelength wave (Liu et al. 2000). However, it is still a challenge to mitigate ultralow-frequency wave by metamaterials (Hussein et al. 2014), which is of great concern in engineering practices. Therefore, novel configurations with ultralow stiffness for metamaterials should be developed to resolve such a tough issue. Many attempts were made to achieve low-frequency gaps in metamaterials, such as rods (Shanshan et al. 2008; Wang et al. 2006), beams (Fang et al. 2017; Xiao et al. 2013; Yu et al. 2006; Zhu et al. 2014)
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