ANALYSIS OF DISPERSION AND ATTENUATION OF SEISMIC WAVES BY A SIMPLE ELASTIC METAMATERIAL WITH NEGATIVE EFFECTIVE PROPERTIES USING WILLIS’ SELF-CONSISTENT APPROACH
A simple self-consistent method, known as Willis’ procedure to dispersion and attenuation of waves in randomly positioned inclusions, is applied in the context of elasticity theory to predict neg-ative elastic parameters in a simple structure consisting of inclusions of elastic cylinders embedded in an elastic matrix. A region of attenuation of P and SV waves is induced by simultaneous negative effective bulk and shear modulus in frequency regions corresponding to seismic waves. The negative behavior is obtained considering realistic materials. At the same time, by applying optimization tools, a broadband frequency range of up to three octaves is reached where negative effective prop-erties appear. Additionally, calculations for SH waves were performed making an analogy between the transverse electric problem. For SH waves, negative effective density is obtained by a resonance mechanism induced by high contrast in the elastic properties of the microstructure constituents. Possible applications in seismology as seismic barriers for building protection and in ultrasonics for shielding sensitive equipment.