Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus

Abstract

A mechanical model representing an acoustic metamaterial that exhibits simultaneously negative mass density and negative Young's modulus was proposed. Wave propagation was studied in the frequency range of double negativity. In view of positive energy flow, it was found that the phase velocity in this range is negative. This phenomenon was also observed using transient wave propagation finite-element analyses of a transient sinusoidal wave and a transient wave packet. In contrast to wave propagation in the region of positive mass and modulus, the peculiar backward wave motion in the region of double negativity was clearly displayed.

Low frequency locally resonant metamaterials containing composite inclusions

“…4,5 This last case corresponds to the occurrence of inner resonance. Numerous papers in this field were published that either study the properties of metamaterials from a theoretical approach [6][7][8][9][10] or experimentally display the properties of such materials. [11][12][13][14][15] An important aspect of these works is that the dynamic behaviour exhibits an "effective dynamic mass density," that becomes negative at certain frequencies, as predicted or observed by several authors.…”

Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

“…Periodic chains of scatterers with internal structure (mass-in-mass units) may serve as a waveguide for mechanical energy, and also exhibit negative mass density [10]. Metamaterial behavior, where both the effective mass and the elastic modulus are negative, was predicted for a chain consisting of elastic mass-in-mass units with lateral resonances [11]. The dispersion curve of a chain of acoustic Helmholtz resonators (soda cans) with two scatterers per unit cell has a passing band within a hybridization gap where the effective index of refraction becomes negative [12].…”

Design of double negativity elastic metamaterial

“…The DN region is recognized by negative phase velocity [24]. It is noted that the narrow passing band, 579.28-579.37 Hz, is owing to the rotational mode of the horizontal beam about the joint.…”

“…The metamaterial design in this study is based on the lumped mass model [24]. Since the model is still in the theoretical stage, this study realizes it using an Eden 350 3D printer (Stratasys Ltd., Eden Prairie, MN, USA).…”

“…Expanding upon that concept, Zhu et al [23] created a single-phase solid based on the lumped mass model. The present work is based on the lumped mass model proposed in [24], and the metamaterial was fabricated as a single-phase solid using a 3D printer.…”