One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus

We present theoretically a type of one-dimensional (1D) structured ultrasonic metamaterial that exhibits a forbidden band where both the effective dynamic density and bulk modulus are simultaneously negative. The material consists of a 1D array of repeated unit cells with shunted Helmholtz resonators. The transmission coefficient, wave vector, negative dynamic density, and modulus are determined by means of the acoustic transmission line method (ATLM). The double negativity in the effective dynamic density and bulk modulus is an acoustic counterpart of negative permittivity and permeability in the electromagnetic metamaterials. The double negative band is ascribed to the local resonance. In order to confirm the ATLM results, we further calculate the field intensity, phase distribution, and transmission coefficient using the finite element method. In addition, the influences of some essential geometric acoustic parameters on the transmission properties, such as periodic constant $L$, are also discussed.