A new two-dimensional elastic metamaterial system with multiple local resonances

A new two-dimensional periodic elastic metamaterial system is proposed, which exhibits multiple local resonances and can generate negative effective parameters. In certain frequency ranges, negative bulk modulus, negative shear modulus and negative mass density can be achieved simultaneously. Analytical study of the new metamaterial system is performed based on a simplified model to study the effects of main material and geometric parameters. Numerical analysis is further conducted to simulate elastic wave propagation in the current metamaterial. The results show clearly the existence of negative dispersion. The association of negative mass and modulus with the mode of local resonance, the eigenstate, is evaluated. In the frequency range for negative parameters, negative phase velocities of the longitudinal and shear waves can be observed in the simulation. The developed metamaterial shows strong anisotropic properties. It can support both longitudinal and shear waves in general directions but in specific directions only longitudinal wave can propagate. In the latter case, it exhibits fluid-like properties. Typical examples of the current metamaterial under different loading conditions are presented to show both the modal response and the property of elastic wave propagation in the metamaterial.