Abstract
Metamaterials realizing stop bands have attracted much attentions recently since they can break-through the well-known mass law. However, achieving the stop band at extremely low frequency has been still a big challenge in the fields of elastic metamaterials. In this paper, we propose a new metamaterial based on the idea of the zero rotational stiffness, to achieve extremely low frequency stop band for flexural elastic waves. Unlike the previous ways to achieve the stop band, we found that the zero rotational stiffness can provide a broad stop band at extremely low frequency, which starts from even almost zero frequency. To achieve the zero rotational stiffness, we propose a new elastic metamaterial consisting of blocks and links with the hinge connection. Analytic developments as well as numerical simulations evidence that this new metamaterial can exhibit extremely low and broad stop band, even at the quasi-static ranges. In addition, the metamaterial is shown to exhibit the negative group velocity at extremely low frequency ranges, as well as the quasi-static stop band, if it is properly designed.
Highlights
Metamaterials realizing stop bands have attracted much attentions recently since they can breakthrough the well-known mass law
There has been a limitation that the stop bands in phononic crystals generally exist at too high frequencies to be applied in vibration or acoustic devices
We proposed a new idea of the zero rotational stiffness to achieve extremely low frequency stop band, which may cover even the quasi-static frequency range
Summary
Metamaterials realizing stop bands have attracted much attentions recently since they can breakthrough the well-known mass law. We propose a new metamaterial based on the idea of the zero rotational stiffness, to achieve extremely low frequency stop band for flexural elastic waves. Analytic developments as well as numerical simulations evidence that this new metamaterial can exhibit extremely low and broad stop band, even at the quasi-static ranges. The metamaterial is shown to exhibit the negative group velocity at extremely low frequency ranges, as well as the quasi-static stop band, if it is properly designed. Recent researches on the resonance-based metamaterials have realized a stop band at relatively low frequencies where the wavelength is much larger than the size of the unit cell. Zhu et al.[9,10] realized the chiral elastic metamaterials having broad stop band and double negativity, respectively. For the best of the author’s knowledge, there has been no research to obtain the elastic metamaterial with the quasi-static stop band by its intrinsic dynamic characteristics only
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