Xiaoning Liu

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.

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.

Latticed pentamode acoustic cloak.

We report in this work a practical design of pentamode acoustic cloak with microstructure. The proposed cloak is assembled by pentamode lattice made of a single-phase solid material. The function of rerouting acoustic wave round an obstacle has been demonstrated numerically. It is also revealed that shear related resonance due to weak shear resistance in practical pentamode lattices punctures broadband feature predicted based on ideal pentamode cloak. As a consequence, the latticed pentamode cloak can only conceal the obstacle in segmented frequency ranges. We have also shown that the shear resonance can be largely reduced by introducing material damping, and an improved broadband performance can be achieved. These works pave the way for experimental demonstration of pentamode acoustic cloak.

Microstructural designs of plate-type elastic metamaterial and their potential applications: a review

Elastic metamaterials are of growing interest due to their unique effective properties and wave manipulation abilities. Unlike phononic crystals based on the Bragg scattering mechanism, elastic metamaterials (EMMs) are based on the locally resonant (LR) mechanism and can fully control elastic waves at a subwavelength scale. Microstructural designs of EMMs in plate-like structures have attracted a great deal of attention. In this paper, the recent advances in the microstructural designs of LR-based EMM plates are reviewed. Their potential applications in the fields of low frequency guided wave attenuation, wave manipulation and energy trapping at a subwavelength scale, and structural health monitoring are discussed.

Broadband solid cloak for underwater acoustics

Application of transformation theory to underwater acoustics has been a challenging task because highly anisotropic density is unachievable in water. A possible strategy is to exploit anisotropic modulus rather than density, while has not been experimentally demonstrated. We present an annular underwater acoustic cloak designed from particular graded solid microstructures. The geometry tailored microstructures mimics meta-fluid with highly anisotropic modulus through substantially suppressed shear wave. Transient wave experiments are conducted with the cloak in a designed 2D underwater waveguide system and proved excellent cloaking performance for enclosed target over broadband frequency 9-15 kHz. This finding paves the way for controlling underwater acoustics using the structured anisotropic modulus meta-fluid.

Design of arbitrary shaped pentamode acoustic cloak based on quasi-symmetric mapping gradient algorithm.

Due to solid and broadband nature, pentamode acoustic cloak is more promising for engineering applications. A simple algorithm based on an elasticity equation is proposed to obtain quasi-symmetric mapping gradient and in turn the characteristic stress for arbitrary shape cloaks. A high degree of symmetry of the obtained mapping gradient and nearly perfect cloaking effect of the designed pentamode cloaks are confirmed by numerical examples. The proposed method paves the way to design more complicated transformation devices with pentamode materials.

Analytical formulation of a discrete chiral elastic metamaterial model

By embedding appropriately designed chiral local resonators in a host elastic media, a chiral metamaterial with simultaneously negative effective density and bulk modulus can be achieved. In this work, an two dimentional (2D) ideal discrete model for the chiral elastic metamaterial is proposed. The discrete dynamic equation is derived and then homogenized to give the continuous description of the metamaterial. The homogenization procedure is validated by the agreement of the dispersion curve of the discrete and homogenized formulations. The form of homogenized governing equations of the metamaterial cannot be classified as a traditional Cauchy elastic theory. This result conforms the conscience that the Cauchy elasticity cannot reflect the chirality, which is usually captured by higher order theory such as the non-centrosymmetric micropolar elasticity. However when reduced to a (2D) problem, the existing chiral micropolar theory becomes non-chiral. Based on reinterpretation of isotropic tensors in a 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. This 2D chiral micropolar theory constitutes a hopeful macroscopic framework for the theory development of chiral metamaterials.

Wave propagation in tunable lightweight tensegrity metastructure

Lightweight metastructures are designed consisting of prismatic tensegrity building blocks which have excellent strength-to-weight ratio and also enable unique compression-torsion coupling. A theoretical model with a coupled axial-torsional stiffness is first developed to study the band structures of the proposed lightweight metastructures. Then, various unit cell designs are investigated for bandgap generations at desired frequency ranges. Broadband full-wave attenuation is found in the tensegrity metastructure with special opposite-chirality. Furthermore, tunable stiffness in the prismatic tensegrity structure is investigated and ‘small-on-large’ tunability is achieved in the metastructure by harnessing the geometrically nonlinear deformation through an external control torque. Prestress adjustment is also investigated for fine tuning of the band structure. Finally, frequency response tests on the finite metastructures are preformed to validate their wave attenuation ability as well as their wave propagation tunability. The proposed tensegrity metastructures could be very useful in various engineering applications where lightweight and tunable structures with broadband vibration suspension and wave attenuation ability are in high demand.

Two-dimensional water acoustic waveguide based on pressure compensation method

A two-dimensional (2D) waveguide is a basic facility for experiment measurement due to a much more simplified wave field pattern than that in free space. A waveguide for airborne sound is easily achieved with almost any solid plates. However, the design of a 2D water acoustic waveguide is still challenging because of unavailable solids with a sufficient large impedance difference from water. In this work, a new method of constructing a 2D water acoustic waveguide is proposed based on pressure compensation and has been verified by numerical simulation. A prototype of the water acoustic waveguide is fabricated and complemented by an acoustic pressure scanning system; the measured scattered pressure fields by air and aluminum cylinders both agree quite well with numerical simulations. Most acoustic pressure fields within a frequency range 7 kHz-15 kHz can be measured in this waveguide when the required scanning region is smaller than the aluminum plate area (1800 mm × 800 mm).