Metamaterial Rod Research Articles

Propagation characteristics of elastic longitudinal wave in a piezoelectric semiconductor metamaterial rod and its tuning

Elastic metamaterial structures have many distinct wave properties such as band gap structure and topological phase inversion. The coexistence and interaction of piezoelectricity and semiconductor behavior in piezoelectric semiconductor (PS) materials endow metamaterials with some new physical effects. We investigate the propagation characteristics of elastic longitudinal waves in a metamaterial rod made of n-type PS material and piezoelectric (PE) dielectric material. Based on one-dimensional rod model, we present the transfer matrixes for the PS and PE phases as well as the interfacial transfer matrix of unit cell. The analytical dispersion relations of the considered PS-PE metamaterial rod are obtained by utilizing Bloch's theorem. Numerical results show that band gap structures of the metamaterial rod are dependent on the initial electron concentration, length ratio of PE phase, interfacial condition, and capacitor connected with the PE phase. The selection of certain initial electron concentration, length ratio of PE phase, and capacitor can lead to the appearance of topological phase inversion, highlighting the potential for controlling and manipulating the wave propagation properties of PS metamaterial structures. This paper provides a theoretical guidance on the development of smart devices based on PS metamaterial structures. The novel combination of piezoelectricity and semiconductor behavior in these materials opens up new avenues for designing and engineering advanced devices with tailored wave properties and functionalities.

Inverse Design of Linear and Nonlinear Cylindrical Metamaterial Rod

Continuum elastic metamaterials can be used to reduce system-generated 2nd harmonics and they should also pass the fundamental harmonics during nonlinear ultrasonic testing. Linear metamaterials are designed based on the bandgap structure of the periodic layered materials showing contrast in acoustic impedances. Design parameters such as widths of the periodic layered elastic materials are calculated by a parametric sweep by solving eigenvalue problems, and the transfer matrix method. Most of the design studies assume infinitely long periodic elastic layers, but in practice length of metamaterial is limited by the reduction in fundamental amplitude of input short pulse. Though the linear metamaterials are designed for nonlinear ultrasonic applications, considering geometric and material nonlinearity of the layered elastic materials which contributes to harmonic scattering, the sensitivity of widths of layered materials to amplitudes of the 2nd harmonics, along with the linear interference is the most realistic modeling approach. In this study, linear and nonlinear metamaterials are designed using shape optimization techniques by solving transient finite element studies considering realistic geometric and material models. Gradient-free algorithms such as co-ordinate search and Nelder Mead are used during optimization. Effective design approaches are proposed and demonstrated to control longitudinal modes in a cylindrical rod.

Vibration Attenuation Optimization in a Rod With Different Periodic Piezoelectric Shunting Configurations

Wave propagation control in piezoelectric meta-materials has been extensively investigated in recent years due to its significant effects on elastic wave attenuation. In this work, a novel piezoelectric meta-material rod connected to three configurations of shunting circuits is proposed for broad band gaps. The numerical model is constructed to predict the band gap, attenuation constant, and vibration transmission. For larger attenuation within the band gaps, the shunting circuit parameters are optimized with a genetic algorithm. The result shows that the structure with the optimized parameters provides prominent vibration control ability. Both the attenuation constant and the width of the band gaps are enlarged.

Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

Waveguide metamaterial rod as mechanical acoustic filter for enhancing nonlinear ultrasonic detection

Nonlinear ultrasonic guided waves are among the most promising new tools for early stage damage detection owing to their high sensitivity and long-range propagation features. However, signatures from instrumentation, transducers, and couplant effects create false positives mixing with the material- or defect-induced nonlinearities, leading to inaccurate measurements. Here, we propose a novel technique using a waveguide metamaterial rod, which acts as a mechanical acoustic filter for suppression of higher harmonic components in the measured signal. The proposed waveguide metamaterial consists of an array of flat axisymmetric ridges arranged periodically on the surface of the rod. It is experimentally demonstrated that the higher harmonic components are filtered when the proposed metamaterial rod is placed at the transmission side, thus removing unwanted nonlinearities from the received signal in a pitch-catch configuration. Furthermore, the application of this method is demonstrated by detecting a discontinuity in the workpiece through its nonlinear response enhanced using the metamaterial. This technique is attractive for early stage material diagnosis in engineering, biomedicine, and health monitoring of critical engineering assets.

Surface Waves in a Nonlinear Metamaterial Rod

AbstractWe consider propagation of surface Transverse Electric (TE) waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear surface TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

Bridging-Coupling Phenomenon in Linear Elastic Metamaterials by Exploiting Locally Resonant Metachain Isomers

Elastic and acoustic metamaterials are man-made structures designed to control and manipulate waves through band gaps. The generalized bandwidth of metamaterials with locally resonant (LR) band gaps is usually narrow, limiting their applications in noise and vibration control. On the other hand, nonlinear metamaterials with dipolar resonances can present a broad chaotic band with low amplitude resonances due to bridging coupling, which is only observed under sufficiently large excitation amplitudes. In this work, we show that bridging-coupling phenomenon can also be observed in linear metamaterials with dipolar resonance, producing a special pass band with low amplitude resonances at low frequencies without excitation amplitude dependence. Such phenomenon emerges in a modified resonant metachain with zigzag interconnections and is based on the isomerism of traditional metamaterials. Although this modified isomer preserves the static stiffness and mass density (i.e., static performance) of the original metamaterial, its dispersive behavior presents interesting properties (i.e., branches with negative mass features and overlapping of opposite group velocity), resulting in an overall negative effective mass between the LR band gaps that is responsible for the remote interaction and the enhanced wave performance. In addition to the theoretical discussions, the bridging coupling is experimentally observed in a three-dimensional printed elastic metamaterial rod supporting longitudinal waves. The design can be extended to elastic bending, acoustic and electromechanical media, as well as to systems with periodicity in two and three dimensions (i.e., plates and solids). Therefore, the findings of this work open avenues to investigate the bridging-coupling phenomenon in linear systems as well as to explore the properties of metamaterial isomers.

Elastic metamaterial rod for mode filtering in ultrasonic applications

The proposed 1D elastic metamaterial rod finds application in non-destructive evaluation, as a filter in the transduction side, where only the torsional and flexural modes need to be generated by isolating longitudinal modes. In this Letter, this is achieved by obtaining a wide bandgap in low-frequency ultrasound regime. The novelty of the proposed design arises from the use of a high impedance mismatch between the materials selected for the rod. The proposed concept is demonstrated and verified with numerical simulations. The effectiveness of the proposed technique is confirmed by comparing the results obtained from the rod made of a single material.

Guest Editorial: Non‐Destructive Testing

Guest Editorial: Non‐Destructive Testing

Wave-canceling acoustic metarod architected with single material building blocks

Preventing elastic waves from traveling down thin structures is a subject of great interest from the point of view of both physics and applications. It represents a problem—mirrored by the case of light in waveguides—that has broad implications. To completely prohibit sound waves in a given frequency range in rods, for example, all axially propagating acoustic eigenmodes must exhibit strong damping. Here, we demonstrate experimentally and by simulation a metamaterial rod made from a single material that can simultaneously shut out all elastic-wave polarizations, namely longitudinal, flexural, and torsional modes, in a band in the sub-kHz range. We first bond five acrylic building blocks together to make a subwavelength resonator and then fix an array of these inside an acrylic tube to form a cylindrical metarod that inhibits sound transmission in the metamaterial bandgap frequency range. Applications include vibration control and earthquake mitigation.

1J2-1 Perfect-bandgap acoustic metamaterial rod based on a single material

1J2-1 Perfect-bandgap acoustic metamaterial rod based on a single material

Stochastic wave finite element quadratic formulation for periodic media: 1D and 2D

Abstract Periodic structures have properties of controlling mechanical waves. These solutions are used in aircraft, trains, submarines, space structures, where high level of robustness has to be ensured in presence of uncertainty in the numerical models. The paper presents a stochastic formulation for the Bloch analysis of periodic structures, based on the quadratic 1D and 2D forms of the Wave Finite Element method. In 1D case, numerical examples of periodic rod and metamaterial rod systems are considered; for the 2D case, homogeneous and periodic plates are considered. In both cases, the effect of uncertainties on wavenumber variation is studied. The accuracy and performance of the developed method is compared with Monte Carlo Simulation (MCS) results. It is found that the uncertainties affects the wavenumber scattering. Maximum variation of wavenumber occurs at the band gap edge frequencies and trends are increasing in higher frequency. In terms of computational cost, the presented formulation offers advantages over MCS. The obtained computational cost savings can be a remarkable achievement for the optimization and reliability study under uncertainties of complex structures.

Vibration Characteristics of Elastic Metamaterial Rod

This paper investigates the free vibration and steady forced vibration of elastic metamaterial rods. Firstly, the elastic metamaterial rod is equivalent to the effective medium rod based on the effective medium theory. Then the free vibration and steady forced vibration method of the effective medium rod are established from the classical theory, and with this method we can explored the difference characteristics between the elastic metamaterial rod and the natural media rods. The results show that the effective medium rod has some strange phenomenon such as the same shape of different natural frequencies, the accumulation of natural frequencies near the lower band and the loss of natural frequency. This work is expected to help the vibration control of the elastic metamaterial for finite structure.

Low-frequency band gaps in a metamaterial rod by negative-stiffness mechanisms: Design and experimental validation

A metamaterial rod with resonators containing negative-stiffness (NS) mechanisms is proposed for generating very low-frequency bandgaps. The underlying principle employs the NS mechanism (a pair of mutual repelling permanent magnet rings) to partially or totally neutralize the stiffness of the positive-stiffness element (two coil springs) of the resonator and thus to achieve an ultralow, even zero, stiffness, which enables a significant shift of the bandgap from a high frequency to a low one. Experiments on the restoring force feature of the resonator and the bandgap of the metamaterial rod are carried out, which provide sufficient evidence to validate the proposed concept for substantially lowering bandgaps in locally resonant metamaterials. This study opens a potential path to manipulate elastic waves within a very low-frequency range.

Symmetric surface waves along a metamaterial dielectric waveguide and a perfectly conducting cylinder covered by a metamaterial layer


 
 
 Existence of symmetric complex waves in a metamaterial dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric layer of metamaterial, a metamaterial Goubau line, is proved. Analytical investigation and numerical solution of dispersion equations reveal several important properties of running waves inherent to open metal-metamaterial waveguides which have not been reported for waveguides filled with standard media.
 
 

Vibration band gaps for elastic metamaterial rods using wave finite element method

Band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators are investigated. New techniques to analyze metamaterial systems are using a combination of analytical or numerical method with wave propagation. One of them, called here wave spectral element method (WSEM), consists of combining the spectral element method (SEM) with Floquet–Bloch׳s theorem. A modern methodology called wave finite element method (WFEM), developed to calculate dynamic behavior in periodic acoustic and structural systems, utilizes a similar approach where SEM is substituted by the conventional finite element method (FEM). In this paper, it is proposed to use WFEM to calculate band gaps in elastic metamaterial rods with spatial periodic distribution and periodically attached local resonators of multi-degree-of-freedom (M-DOF). Simulated examples with band gaps generated by Bragg scattering and local resonators are calculated by WFEM and verified with WSEM, which is used as a reference method. Results are presented in the form of attenuation constant, vibration transmittance and frequency response function (FRF). For all cases, WFEM and WSEM results are in agreement, provided that the number of elements used in WFEM is sufficient to convergence. An experimental test was conducted with a real elastic metamaterial rod, manufactured with plastic in a 3D printer, without local resonance-type effect. The experimental results for the metamaterial rod with band gaps generated by Bragg scattering are compared with the simulated ones. Both numerical methods (WSEM and WFEM) can localize the band gap position and width very close to the experimental results. A hybrid approach combining WFEM with the commercial finite element software ANSYS is proposed to model complex metamaterial systems. Two examples illustrating its efficiency and accuracy to model an elastic metamaterial rod unit-cell using 1D simple rod element and 3D solid element are demonstrated and the results present good approximation to the experimental data.