Nonlinear elastic metamaterial for tunable bandgap at quasi-static frequency

We propose a new nonlinear elastic metamaterial which shows tunable bandgap at quasi-static frequency, starting from zero frequency. While there have been active researches on nonlinear induced tunable bandgap in elastic metamaterials at high or mid-frequency range, these researches were not suitable to achieve bandgap tunability at the quasi-static frequency range since unfeasible design, such as extremely huge size or unrealistic resonators, was required. Also, achieving sufficient nonlinearity at this frequency range has been a formidable challenge that hinders the realization of bandgap tunability at the quasi-static frequency. Here, we propose the elastic metamaterial which utilizes geometric nonlinearity to realize the bandgap tunability at the quasi-static frequency range. From theoretical investigations, we found that the nonlinearity of the proposed elastic metamaterial provides two kinds of the bandgap tunability - by wave amplitude and by length change of the attached springs. Also, we found that our nonlinear metamaterial exhibits tunable negative effective mass around the quasi-static frequency, due to the nonlinear effect. To support these findings, numerical simulation and experimental realization are carried out. We expect that this research provides a route for opening a new field in vibrations engineering dealing with the quasi-static frequencies