Ultralow-frequency flexural wave attenuation in a beam with periodically attached quasi-zero-stiffness resonators

Ultralow-frequency band gaps are realized to suppress the ultralow-frequency flexural wave propagation in the beams with periodically attached quasi-zero-stiffness (QZS) resonators, which are designed by inserting quasi-zero-stiffness systems into the mass-in-mass structures. The band structure and the transfer matrix of the QZS locally resonant beam are derived by the transfer matrix method to quantify the wave attenuation performance of band gaps. Then, the effect of the stiffness ratio on the bandgap characteristic is studied. It is shown that, thanks to the introduction of the QZS system, the band gaps can be easily transferred to lower frequency or even ultralow frequency without weakening the static stiffness of the resonators. Finally, the flexural wave propagation in locally resonant beam consisting of multiple periodic arrays of QZS resonators is investigated. The result shows that differential design of the bandgap frequencies can be easily realized by adjusting the negative stiffness coefficient of the QZS resonators, so as to obtain broadband flexural wave suppression performance.