Anisotropic Effective Mass Density Research Articles

Wave propagation in an elastic metamaterial with anisotropic effective mass density

The effect of anisotropic mass density on wave propagation in acoustic/elastic metamaterials is presented in this research. The use of microstructures to achieve mass anisotropy in metamaterials is an intensive field of study. In this work, a numerical continuum model, based on a recently developed cantilever-in-mass model, is proposed. Mass anisotropy in this model is derived based on analytical calculations of a two-dimensional (2D) ‘mass-in-mass’-spring lattice system. The mass–spring lattice is able to portray anisotropic effective mass density in two orthogonal principal directions. Effective mass density along each direction is frequency-dependent. A strong “effective mass anisotropy” is accomplished within the frequency band gap or just below the frequency range of negative effective mass. The proposed mass–cantilever continuum model is used to examine 2D wave propagation. Results show that wave attenuation in a metamaterial with 2D anisotropic mass density is dependent on both input frequency and wave input angle. This study demonstrates a case whereby wave attenuation is achieved by selecting wave input frequency in the band gap region to enact “negative effective mass density”, thereby mitigating wave propagation. In this case, the most efficient attenuation performance is achieved at an input wave angle of 0°. This study also illustrates another case whereby wave attenuation is obtained by mass anisotropy at a frequency just below the local resonance frequency. Wave attenuation is achieved by redirecting wave propagation along the transverse direction, particularly prominent at an input wave angle of 70°. Both numerical calculations of mass–spring lattice model and continuum cantilever-in-mass model show excellent agreement with each other.

Transverse to longitudinal mode conversion via nonlinear inertial effects in a locally resonant metamaterial plate

Acoustic and elastic metamaterials have potential for tailoring wave propagation in ways beyond the capabilities of conventional materials and have been shown to exhibit a myriad of rich dynamical effects, such as negative effective properties, cloaking, extreme damping, and non-reciprocity. However, most of the existing literature has been focused on linear dynamics in which these behaviors are restricted to narrow frequency bands. More recently, nonlinearity has been investigated as a method of increasing this bandwidth, as well as a means to broaden the palette of available dynamics. Past studies on nonlinear acoustic and elastic metamaterials have demonstrated effects not easily accessible in the linear regime, including harmonic generation, mode hopping and conversion, tunable band gaps, chaos, and intrinsic localized modes. In this work, we present a model for a nonlinear elastic plate metamaterial that exhibits mode conversion between transverse and longitudinal waves. The mode conversion is enabled by cantilevered beam attachments undergoing large-angle out-of-plane oscillations. By analyzing the unit cell of this locally-resonant plate, we interpret the transverse-longitudinal coupling as a nonlinear, anisotropic effective mass density. The mode conversion effect is demonstrated via direct numerical simulations. [Work supported by NSF and ARL:UT.]

On the behavior of acoustic/elastic metamaterials with anisotropic mass density

The effect of anisotropic mass density in acoustic/elastic metamaterials on wave propagation is presented in this research. The use of microstructures to achieve anisotropic physical properties in metamaterials is an intensive field of study. In this work, a two-dimensional (2D) ‘mass-in-mass’-spring lattice system is utilized to achieve anisotropic effective mass density in two orthogonal principal directions.In each direction, the effective mass density is frequency-dependent and can be “effectively negative” if it falls within the frequency bandgap region. A 2D numerical continuum model,based on a recently developed cantilever-in-mass model, is further presented and examined to study how wave input angles affect 2D wave propagation. Results show that wave attenuation is dependent on both input frequency and wave input angle in a 2D metamaterial. This study demonstrates a case whereby wave attenuation is achieved,by selecting wave input frequency in the bandgap region to enact “negative effective mass density”. This study also illustrates another case when wave attenuation is obtained for positive anisotropic mass density. This behavior is achieved by directing wave propagation to transverse direction at a specific input wave angle of 60°. Both numerical calculations of mass-spring lattice model and continuum cantilever-in-mass model show good agreement.

Kirigami-based Elastic Metamaterials with Anisotropic Mass Density for Subwavelength Flexural Wave Control

A novel design of an elastic metamaterial with anisotropic mass density is proposed to manipulate flexural waves at a subwavelength scale. The three-dimensional metamaterial is inspired by kirigami, which can be easily manufactured by cutting and folding a thin metallic plate. By attaching the resonant kirigami structures periodically on the top of a host plate, a metamaterial plate can be constructed without any perforation that degrades the strength of the pristine plate. An analytical model is developed to understand the working mechanism of the proposed elastic metamaterial and the dispersion curves are calculated by using an extended plane wave expansion method. As a result, we verify an anisotropic effective mass density stemming from the coupling between the local resonance of the kirigami cells and the global flexural wave propagations in the host plate. Finally, numerical simulations on the directional flexural wave propagation in a two-dimensional array of kirigami metamaterial as well as super-resolution imaging through an elastic hyperlens are conducted to demonstrate the subwavelength-scale flexural wave control abilities. The proposed kirigami-based metamaterial has the advantages of no-perforation design and subwavelength flexural wave manipulation capability, which can be highly useful for engineering applications including non-destructive evaluations and structural health monitoring.

A single-phase elastic hyperbolic metamaterial with anisotropic mass density.

Wave propagation can be manipulated at a deep subwavelength scale through the locally resonant metamaterial that possesses unusual effective material properties. Hyperlens due to metamaterial's anomalous anisotropy can lead to superior-resolution imaging. In this paper, a single-phase elastic metamaterial with strongly anisotropic effective mass density has been designed. The proposed metamaterial utilizes the independently adjustable locally resonant motions of the subwavelength-scale microstructures along the two principal directions. High anisotropy in the effective mass densities obtained by the numerical-based effective medium theory can be found and even have opposite signs. For practical applications, shunted piezoelectric elements are introduced into the microstructure to tailor the effective mass density in a broad frequency range. Finally, to validate the design, an elastic hyperlens made of the single-phase hyperbolic metamaterial is proposed with subwavelength longitudinal wave imaging illustrated numerically. The proposed single-phase hyperbolic metamaterial has many promising applications for high resolution damage imaging in nondestructive evaluation and structural health monitoring.

Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density

We present the experimental realization and characterization of a broadband acoustic metamaterial with strongly anisotropic effective mass density. The metamaterial is composed of arrays of solid inclusions in an air background, and the anisotropy is controlled by the rotational asymmetry of these inclusions. Transmission and reflection measurements inside a one-dimensional waveguide are used to extract the relevant components of the effective density tensor together with the effective bulk modulus of the metamaterial. Its broadband anisotropy is demonstrated by measurements that span 500–3000 Hz. Excellent agreement between these measurements and numerical simulations confirms the accuracy of the design approach.

Locally resonant acoustic metamaterials with 2D anisotropic effective mass density

A two-dimensional (2D) lattice model with anisotropic resonant microstructures is found to provide an anisotropic band gap structure. A 2D continuum with anisotropic effective mass density is introduced to represent this lattice system. Two methods are proposed to derive the equivalent continuum. In the first method, the effective mass density of the equivalent continuum is obtained by matching the dispersion relations for harmonic waves propagating in the principal directions. The second approach employs an approximate estimation of the effective mass density by volume-averaging an effective mass that represents the resonant microstructure. For both equivalent continuum models, the effective mass density is frequency-dependent and may become negative in certain frequency ranges. Subsequently, the effective mass density of the equivalent continuum assumes the form of a second-order tensor. Thus, it suffices to determine the effective mass density tensor with respect to the principle directions. It is shown numerically that the local-resonance effect is accurately described by the equivalent continuum model. In addition, the effect of anisotropic mass density on wave propagation is numerically illustrated and discussed.

Density functional theory calculations of electronic structure in silicon double quantum dots

AbstractThe finite difference method and anisotropic effective mass density functional theory (DFT) are used to calculate the electronic structure and wavefunctions of Silicon isolated double quantum dots. An optimised algorithm for determining the self‐consistent DFT potential was developed.The effects of applying electric fields to push the electrons from one dot to another dot in the double quantum dot are studied. We demonstrate that depending on the structure parameters there are two regimes corresponding to the strong and weak coupling between the two dots. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)