Gengkai Hu

Experimental study on negative effective mass in a 1D mass–spring system

A mass–spring system with negative effective mass is experimentally realized, and its transmission property is examined in the low-frequency range. The local resonance of the basic unit is observed and explained by Newtons theory. The negative effective mass is confirmed by experiments through the transmission properties of a finite periodic system composed of such basic units. In the negative mass range, low transmissions of the system are observed and it is well predicted by the theory. In addition, zero effective mass is discussed and experimentally investigated, which gives rise to no phase shifts in the system. Finally, the anti-vibration effect with a negative mass system is also analyzed. The relevant results are helpful for a better understanding of the resonant nature of metamaterials.

Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial

Negative refraction of elastic waves has been studied and experimentally demonstrated in three- and two-dimensional phononic crystals, but Bragg scattering is impractical for low-frequency wave control because of the need to scale the structures to manageable sizes. Here we present an elastic metamaterial with chiral microstructure made of a single-phase solid material that aims to achieve subwavelength negative refraction of elastic waves. Both negative effective mass density and modulus are observed owing to simultaneous translational and rotational resonances. We experimentally demonstrate negative refraction of the longitudinal elastic wave at the deep-subwavelength scale in the metamaterial fabricated in a stainless steel plate. The experimental measurements are in good agreement with numerical simulations. Moreover, wave mode conversion related with negative refraction is revealed and discussed. The proposed elastic metamaterial may thus be used as a flat lens for elastic wave focusing.

Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation

In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplaces equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplaces equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplaces equation. Full-wave simulations based on the Maxwells equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.

Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries

Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the functional devices. Since inverse Laplaces equation with sliding boundary condition will determine a quasi-conformal mapping, and a quasi-conformal mapping will minimize the transformation material anisotropy, so in this work, the inverse Laplaces equation with sliding boundary condition is proposed for quasi-isotropic transformation material design. Examples of quasi-isotropic arbitrary carpet cloak and waveguide with arbitrary cross sections are provided to validate the proposed method. The proposed method is very simple compared with other quasi-conformal methods based on grid generation tools.

Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices

In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However, when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in the 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation, which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is applied for the homogenization of a triangular chiral lattice, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are verified by the exact solution of the discrete model.

Investigation of the negative-mass behaviors occurring below a cut-off frequency

Negative-mass phenomena occurring below a cut-off frequency are examined using both theoretical and experimental methods. The paper begins with an investigation of a mass–spring structure, the effective mass of which is shown to be negative below a specific frequency. Due to the decaying nature of lattice waves in the negative-mass system, the transmission drop induced by negative effective mass is demonstrated experimentally. Further investigation is conducted for a rectangular solid waveguide with clamped boundary conditions. It is shown that the lowest bandgap mode of the clamped waveguide can be attributed to negative effective mass below a cut-off frequency. Based on this observation, elastic metamaterials made of a steel grid filled with styrene butadiene rubber are designed and fabricated. Both the simulation and experimental analyses demonstrate that the designed metamaterials have negative effective mass below a cut-off frequency.Negative mass phenomena occurring below a cut-off frequency is examined by both theoretical and experimental methods. The paper begins with the investigation on a mass-spring structure, the effective mass of which is shown to be negative below a specific frequency. Due to the decaying nature of lattice waves in the negative-mass system, the transmission drop induced by negative effective mass is demonstrated experimentally. Further investigation is conducted for a rectangular solid waveguide with clamped boundary conditions. It is shown that the lowest bandgap mode of the clamped waveguide can be attributed to negative effective mass below a cut-off frequency. Based on this observation, elastic metamaterials made of the steel grid filled by styrene butadiene rubber are designed and fabricated. Both simulation and experimental analyses demonstrate that the designed metamaterial have negative effective mass below a cut-off frequency.

Superlensing effect of an anisotropic metamaterial slab with near-zero dynamic mass

A metamaterial slab of anisotropic mass with one diagonal component being infinity and the other being zero is demonstrated to behave as a superlens for acoustic imaging beyond the diffraction limit. The underlying mechanism for extraordinary transmission of evanescent waves is attributed to the zero mass effect. Microstructure design for such anisotropic lens is also presented. In contrast to the anisotropic superlens based on Fabry-Perot resonant mechanism, the proposed lens operates without the limitation on lens thickness, thus more flexible in practical applications. Numerical modeling is performed to validate the proposed ideas.

Nonsingular two dimensional cloak of arbitrary shape

We propose a general method to circumvent the singularity (infinitely large values of material parameters) of arbitrary two dimensional (2D) cloaks. The presented method is based on the deformation view of the transformation design method. It is shown that by adjusting the principle stretch out of the cloaking plane, 2D cloaks of arbitrary shapes without singularity can be constructed. It is also demonstrated that the method based on the equivalent dispersion relation and the design method for nonsingular 2D cloak from mirror-symmetric cross section of a three dimensional (3D) cloak can be derived from the proposed theory. Examples of a cylindrical electromagnetic cloak and an arbitrary shaped 2D electromagnetic cloak without singularity are provided to demonstrate the method.

Pattern Transformation of Heat-Shrinkable Polymer by Three-Dimensional (3D) Printing Technique

A significant challenge in conventional heat-shrinkable polymers is to produce controllable microstructures. Here we report that the polymer material fabricated by three-dimensional (3D) printing technique has a heat-shrinkable property, whose initial microstructure can undergo a spontaneous pattern transformation under heating. The underlying mechanism is revealed by evaluating internal strain of the printed polymer from its fabricating process. It is shown that a uniform internal strain is stored in the polymer during the printing process and can be released when heated above its glass transition temperature. Furthermore, the internal strain can be used to trigger the pattern transformation of the heat-shrinkable polymer in a controllable way. Our work provides insightful ideas to understand a novel mechanism on the heat-shrinkable effect of printed material, but also to present a simple approach to fabricate heat-shrinkable polymer with a controllable thermo-structural response.

Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: membrane model.

Membrane-type acoustic metamaterials (MAMs) have demonstrated unusual capacity in controlling low-frequency sound transmission/reflection. In this paper, an analytical vibroacoustic membrane model is developed to study sound transmission behavior of the MAM under a normal incidence. The MAM is composed of a prestretched elastic membrane with attached rigid masses. To accurately capture finite-dimension rigid mass effects on the membrane deformation, the point matching approach is adopted by applying a set of distributed point forces along the interfacial boundary between masses and the membrane. The accuracy and capability of the theoretical model is verified through the comparison with the finite element method. In particular, microstructure effects such as weight, size, and eccentricity of the attached mass, pretension, and thickness of the membrane on the resulting transmission peak and dip frequencies of the MAM are quantitatively investigated. New peak and dip frequencies are found for the MAM with one and multiple eccentric attached masses. The developed model can be served as an efficient tool for design of such membrane-type metamaterials.