Modelling and analysis of the quasi-zero-stiffness metamaterial cylindrical shell for low-frequency band gap

Low-frequency vibrations widely exist in various shell structures of aircrafts, ships or rockets, and propagate along shell structures in elastic waves. Aimed at the vibration issue, this paper proposes a novel metamaterial cylindrical shell with quasi-zero-stiffness (QZS) resonators to achieve lowfrequency wave attention within band gaps. Firstly, the resonator is devised to exhibit the QZS feature under appropriate pre-deformation. A simplified dynamic model is established to replace the metamaterial cylindrical shell and derive dispersion relations. Then, the band gap is revealed theoretically by both the plane wave expansion method (PWEM) and the finite element method (FEM). Additionally, the finite element model of the metamaterial cylindrical shell is built to analyze the structural responses and evaluate the transmittance of flexural waves. The results show that the QZS metamaterial cylindrical shell is capable of opening low-frequency band gaps and effectively attenuating flexural waves at low frequencies.