Quasi-static stop band with flexural metamaterial having zero rotational stiffness

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.