Metamaterial plate with compliant quasi-zero-stiffness resonators for ultra-low-frequency band gap

To achieve wave attenuation at ultra-low frequencies, a novel metamaterial plate with attached compliant quasi-zero-stiffness (QZS) resonators is proposed. Firstly, the compliant resonator is designed to fulfill the QZS feature under proper pre-compression. Then, theoretical investigations are conducted to derive the dispersion relation and reveal the band gap of the QZS metamaterial plate using both the plane wave expansion (PWE) method and the finite element (FE) method. In addition, dynamic responses of the QZS metamaterial plate are obtained using FE simulations to estimate the performance of wave attenuation in the band gap. Finally, the prototype of the QZS metamaterial plate is fabricated and experiments are carried out to study the propagation characteristics of the flexural wave, which shows excellent attenuation in the ultra-low-frequency band gaps. Therefore, the compliant QZS resonator is able to open ultra-low-frequency band gaps, and thus enables attenuation of the flexural wave in the QZS metamaterial plate at ultra-low frequencies.