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

Abstract

We present theoretically a type of one-dimensional ͑1D͒ 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 ͑ATLM͒. 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.

Elastic metamaterials and dynamic homogenization: a review

“…It was subsequently suggested that acoustic/elastic LHMs could be constructed by mixing two structures that independently exhibit negative density and modulus [30]. Negative modulus could be achieved through a periodic array of Helmholtz resonators [31,32], and the negative density could be achieved through an array of thin membranes [33]. The combination of these two structures was shown to exhibit LHM properties [34,35] Since then, researchers have proposed more complicated acoustic/elastic LHM architectures.…”

Air transparent soundproof window

“…The general form of the effective bulk modulus, B e f f , of acoustic waves is given by the complex form similar to the effective electric permittivity in electric metamaterials 12,14,15,17,18 …”

Phononic layered composites for stress-wave attenuation

“…Metamaterials are phononic crystals that can be micro-architecturally designed for high stress-wave attenuation (Liu et al, 2000;Ho et al, 2003;Cheng et al, 2008;Huang and Sun, 2009). They have overall mechanical properties that are not shared by traditional engineering materials (Guenneau et al, 2007;Torrent and Sanchez-Dehesa, 2007;Milton and Willis, 2007;Torrent and Sanchez-Dehesa, 2008).…”

“…Their results show significant drop in transmission coefficient at resonance frequencies and they used it to make a broadband sonic shield. Cheng et al (2008) designed a 1-D ultrasonic metamaterial with both effective density and effective bulk modulus simultaneously negative. They found the transmission coefficient using acoustic transmission line method (ATLM), finite element method, and experimental measurement and observed a substantial drop in transmission spectrum around the resonance frequency.…”