In this paper, we present the first realization of an elastic metamaterial allowing independent tuning of negative density and stiffness for elastic waves propagating along a designated direction. In electromagnetic (or acoustic) metamaterials, it is now possible to tune permittivity (bulk modulus) and permeability (density) independently. Apparently, the tuning methods seem to be directly applicable for elastic case, but no realization has yet been made due to the unique tensorial physics of elasticity that makes wave motions coupled in a peculiar way. To realize independent tunability, we developed a single-phased elastic metamaterial supported by theoretical analysis and numerical/experimental validations.

The free vibration analysis of general convex polygonal membranes is carried out. The selected based functions for the analysis are wave-type functions which propagate in one direction and vary sinusoidally in the other direction. The key feature of the present technique is to use the base functions that satisfy the governing differential equation exactly, so that only the boundary conditions need to be satisfied. If base functions are not chosen carefully, the dependence problem of the base functions may occur and a technique to select independent base functions is suggested.

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