Elastic wave and vibration bandgaps in two-dimensional acoustic metamaterials with resonators and disorders

The vibration properties of two-dimensional (2D) finite acoustic metamaterials (AMs) consisting of discrete masses and springs are investigated in this paper. In order to clarify the mechanisms of the bandgaps in AMs, the infinite symmetrical systems are also studied, especially the impact of the physical asymmetry caused by the discrepant stiffness coefficients of the springs connecting the unit-cells. Although the asymmetry cannot change the bandgap width, the change of the phase velocity and the generation of the shear mode have been proven analytically. To study the vibration properties of the finite AM model, the effective mass of each unit-cell is used. The effective mass properties of the unit-cell with single resonator and multi-resonators in 2D AMs subjected to a time-harmonic excitation are discussed. The effects of the number of the unit-cells, multi-resonators in each unit-cell, graded resonators in the finite AM model on the vibration suppression are thoroughly examined by the frequency response analysis. Numerical results show that the degree of the vibration attenuation is related to the size of the model and the number of the bandgaps changes corresponding to the disorders of the local resonators. Furthermore, imperfections or defects are introduced into the finite AM system. Wave propagation and guiding in a finite model for straight waveguide are investigated and discussed. The defect states induced by changing the central resonator of a supercell are demonstrated. Defect bands are obtained and their location is illustrated.