Metamaterial Plate Research Articles

Metamaterial invisibility of a corner target with proportional integral active control

Wave invisibility in confined space has been proved practical significance in mechanical engineering and military fields. In this work, a flexural wave cloak of a corner-domain target in a metamaterial plate with proportional integral (PI) active control circuit is proposed. According to the double reflection principle and mechanical characteristic at the boundary, wave fields for a corner-domain target are defined as a collection of incident, scattering and three mirror domains. The unknown scattering mode coefficients are determined by the image method and boundary conditions. The dynamic stress concentration, scattering amplitude and scattering cross-section for the corner-domain target are obtained. The cloaking configuration is composed of multiple equally spaced concentric layers, which are filled with piezoelectric (PZT) patches. In addition, these PZT patches are connected to the active control circuit with proportional integral (PI) control module. The results indicate that the flexural wave cloak can reduce the dynamic stress concentration, scattering amplitude and scattering cross-section in corner domain. Compared to the original structure without PI active control, the effective frequency range of the active cloak can be extended by 20%.

Feynman’s method in chiral nanorod-based metamaterial nanoplasmonics

We propose a theoretical approach to some of the nanorod-based metamaterial implementations that does not depend on macroscopic electrodynamics. The approach is motivated by the fact that in actual experiments the incident electromagnetic wave encounters a metamaterial structure which is planar in its shape, contains a layer or two of artificially created building blocks, and therefore cannot be regarded as a three-dimensional continuous medium. This leads to a theoretical framework in which the phenomenological concept of refractive index loses its principled meaning, and the deeper concept of scattering is taking center stage. Our proposal and its mathematical realization rely heavily on Feynman’s explanation of the physical origin of the index of refraction and on his formula for the field of a plane of oscillating charges. We provide a complete proof of Feynman’s formula, filling in some steps that were missing in the original derivation, and then generalize it to the case of a finite disk, which may be relevant to the actual experiments involving laser beams. We then show how the formula can be applied to metamaterial nanoplasmonics by considering some subtle interference effects in uniform laser beams striking metamaterial plates. The first two effects use a single layer of aligned plasmonic nanorods, while the third uses a single layer of gyrotropic elements that may conveniently be described by the celebrated Born-Kuhn oscillator model. The considered effects can potentially be used in the development of quality standards for various metamaterial devices.

A metamaterial sandwich plate with spring-lever-mass resonators

Sandwich plates are widely used in practical engineering, including civil engineering, transportation, aerospace, and other industrial fields. However, characteristics of high specific stiffness and strength cause poor performance in the vibro-acoustic fields. Therefore, resonators are introduced into the core of sandwich plates to improve their performance on vibration isolation. This paper proposes a new metamaterial sandwich plate, multiple spring-lever-mass resonators are introduced into the sandwich plate to obtain the low-frequency band gaps. The band structure of the metamaterial sandwich plate with spring-lever-mass resonators is calculated by the finite element method with the Bloch-Floquet theorem, and the band gap of the unit cell is obtained. The transmission spectra of the proposed structure are investigated to verify the accuracy of prediction results. The results show that effective performance on low-frequency vibration isolation via the metamaterial sandwich plate with spring-lever-mass resonators can be achieved, and this study can provide valuable references for related research and potential applications on the manipulation of wave propagation.

Reduced relaxed micromorphic modeling of harmonically loaded metamaterial plates: investigating boundary effects in finite-size structures

In this paper, we propose an approach for describing wave propagation in finite-size microstructured metamaterials using a reduced relaxed micromorphic model. This method introduces an additional kinematic field with respect to the classical Cauchy continua, allowing to capture the effects of the underlying microstructure with a homogeneous model. We show that the reduced relaxed micromorphic model is not only effective for studying infinite-size metamaterials, but also efficient for numerical simulations and analysis on specimens of finite size. This makes it an essential tool for designing and optimizing metamaterials structures with specific wave propagation properties. The proposed model’s efficiency is assessed through numerical simulations for finite-size benchmark problems, and shows a good agreement for a wide range of frequencies. The possibility of producing the same macroscopic metamaterial with different but equivalent unit cell “cuts” is also analyzed, showing that, even close to the boundary, the reduced relaxed micromorphic model is capable of giving accurate responses for the considered loading and boundary conditions.

In-plane vibration characteristics of metamaterial plates with locally resonant microstructures

In-plane vibration characteristics of metamaterial plates with locally resonant microstructures

Research progress on terahertz achromatic broadband polarization wave plates

The electromagnetic wave in the terahertz region shows many promising characteristics, such as non-ionization, “fingerprint” spectrum, sensitivity to weak resonance, strong penetration to non-polar substances, and so on. This study reviews the recent achievements of terahertz achromatic broadband polarization wave plates. The key parameters to evaluate the performance of terahertz polarized wave plates are described briefly. The relevant works, and benefits and drawbacks of terahertz wave plates based on diverse materials and designs, notably metamaterial wave plates, are summarized based on unique material attributes and design methodologies. Additionally, the current state of the terahertz achromatic broadband wave plate is generalized, along with the role of metamaterial in the design of terahertz wave plate, the innovative interdisciplinary path of terahertz metamaterial polarization is explained, and future research prospects are explored.

Vibro-acoustic performance of graded piezoelectric metamaterial plates

This work investigates the vibro-acoustic performance of graded piezoelectric metamaterial plates. A piezoelectric layer with electrodes segmented in a regular lattice is attached over a rectangular, simply-supported panel to realize the electromechanically coupled metamaterial plate, rendering a geometrically periodic structure. The grading is achieved in the electric domain, as each unit cell’s inductive shunt resonant frequency can be tuned independently. We investigate two first-order grading patterns based on linear variations along one and both dimensions of the plate and evaluate their impact on vibration attenuation, sound power, kinetic energy, and acoustic radiation efficiency. The graded metamaterial plates outperform the periodic locally resonant counterparts in vibration and radiated sound power attenuation. Moreover, sound radiation efficiency may increase within the attenuation band for steep grading patterns related to the vibration localization phenomenon. The results show that piezoelectric metamaterial plates with reconfigurable properties are an interesting alternative for enhanced vibro-acoustic performance.

Acoustic cloaking design based on penetration manipulation with combination acoustic metamaterials

The acoustic wave transmission manipulation ability is the most important performance for the acoustic metamaterials. To manipulate the acoustic transmission, the combination acoustic metamaterials structures are involved, and the two-directional acoustic penetration cloaking scheme are constructed. The combination acoustic metamaterials include chiral metamaterials and self-collimation metamaterials, the acoustic wave transmission path are manipulated to bypass from the acoustic scattering target in the penetration cloaking, and the target scattering stealth problem are effectively solved. In the end, the acoustic transmission manipulation performances are verified by numerical analysis with a finite-width acoustic metamaterial structure plates. The results provide technical support for design and application for acoustic transmission manipulation with acoustic metamaterials.

Dynamic responses of functionally graded origami-enabled auxetic metamaterial sector plate induced by mechanical shock: Application of innovative machine learning algorithm

For the first time, in the current work, the quasi-3D new refined theory (Q3D-NRT) is used to analyze the dynamic reactions of functionally graded (FG) annular sector plates made of graphene origami (GOri)-enabled auxetic metal metamaterials to the mechanical shock loading. The auxetic property of the annular plates is effectively controlled by graphene content and GOri folding degree that is graded across the thickness direction of the annular plates in a layer-wise manner, as Poisson’s ratio and other material properties are position-dependent and can be estimated by genetic programming-assisted micromechanical models (MM). Hamilton’s concept is used to find the structure’s governing equations. The differential quadrature technique and the Laplace transform are used at design sites to solve the time-varying equations of motion. The system response is translated from the Laplace domain to the time domain using a modified version of the Dubner and Abate approach. To investigate the impact of different geometrical and physical factors on the dynamic reactions of the annular sector plates, thorough parametric research is conducted. The findings of the present mathematical modeling are compared with those of the earlier publications and also with those of the machine learning approach. Utilizing this learning strategy, differential equations may be solved with very cheap computer costs while also overcoming formulation complexity. It needs a valid dataset from experimental or numerical analysis to use machine learning techniques. This dataset was compiled using the study’s numerical findings. Additionally, the machine learning approach demonstrates the capacity to deliver findings with a high degree of accuracy when predicting the mechanical characteristics of the existing structure under novel loading and boundary circumstances.

Active band gap control of magnetorheological meta-plate using frequency feedback control law

An innovative special class of magnetorheological metamaterial is proposed to achieve a tunable band gap using a new frequency feedback control law. By using the frequency feedback control law, the active band gap can intelligently track the external excitation frequency. The active control function of the band gap is realized using an intelligent local resonator embedded in the plate. Such a local resonator consists of a mass and a magnetorheological elastomer (MRE) driven by an external magnetic field. The local resonator and metamaterial plate are modeled analytically, and an analytical expression is derived to predict the band gap region. The effect of the external magnetic field on vibration attenuations is analyzed by the Galerkin method. Subsequently, a closed-loop frequency feedback control strategy is used to actively adjust the band gap according to the excitation frequency. Based on this frequency feedback control strategy, the effective band gap range of the metamaterial plate can be largely widened. The effect of damping of the MRE on broadband vibration reduction is also investigated, and the results show that the damping of the MRE plays an important role in the control of the band gap of the magnetorheological metamaterial.

Dual-Function Cloak of Edge Target in Metamaterial Plate with Active Intelligent Control

Wave invisibility has attracted great attention because of its significant influences on mechanical, acoustic, and many other fields, and it has a great potential application to practical engineering. In this work, a dual-function cloak is proposed in which there is an edge object with an intelligent control system in an elastic wave metamaterial plate. Based on the image and scattering cancellation methods, the scattering mode coefficients are derived. The effects of material and structural parameters on dynamic stress concentration and scattering amplitude are investigated. The cloaking configuration consists of concentric layers of piezoelectric (lead–zirconate–titanate [PZT]) patches, which are connected with the intelligent control system. The theoretical and experiment results show that the dual-function cloak can effectively reduce the dynamic stress concentration and scattering amplitude. Compared to the range from 100 to 450 Hz for the original structure without a control system, the effective frequency range of the intelligent cloak can be extended from 100 to 500 Hz. The present design with both strength enhancement and invisibility of the edge target is expected to provide new ideas for the development of mechanical metamaterials and novel structures.

Broadband low-frequency sound insulation of a metamaterial plate with inertial amplification

The recent development of Inertia Amplification (IA) acoustic metamaterial (AMM) opens a new venue for insulating low-frequency sound waves. This differs from conventional approaches that rely excessively on the structural density of the insulator and, therefore, lead to prohibitively heavy structures. The IA-AMM acquires a large effective density and a broad flexural bandgap by amplifying the inertia of many small mass elements periodically distributed in its unit cells, thus holding great promise as an effective yet lightweight solution for low-frequency sound insulation. This paper explores this possibility through numerical and experimental investigations. A semi-analytical model of an IA-AMM plate is developed by combining analytical equations characterizing the kinematics of an IA mechanism and FEM equations governing the vibration of the host plate. Based on this model, sound transmission characteristics of the plate under various sound incidences are analyzed with different amplification angles. By comparing with a locally resonant AMM plate, we found that the IA-AMM plate's sound transmission losses (STLs) are significantly and systematically improved over a wide frequency range of 116–544 Hz. To understand the underlying physics, the band diagram of the IA-AMM plate is calculated, which indicates the formation of a flexural bandgap covering the frequencies of the improved STL. The velocity contour of the plate at the center frequency of this bandgap also reveals much-suppressed vibration velocity amplitudes and a dipole-like sound radiation directivity, further explaining the observed enhancement of the sound insulation ability. Numerically predicted improvement of sound insulation is finally confirmed by experiments.

Bending and buckling analysis of functionally graded graphene origami metamaterial irregular plates using generalized finite difference method

Bending and buckling behavior of graphene origami(GOri) metamaterial irregular plates (octagonal star plates, cordiform plates, a quarter of annular plates and a quarter of annular plates with a hole) under different boundary conditions are investigated based on the higher-order shear deformation theory. The metamaterial by adding GOri to copper matrix in the form of gradient arrangement as reinforcement material has the properties of negative Poisson's ratio (NPR) and compressive, flexural as well as fracture toughness beyond traditional materials that are independent of the topology/architecture of the structure. The governing equations of irregular plate structures are deduced with Hamilton’s principle. Generalized finite difference method, which is a meshless method based on Taylor series expansion and moving least squares approximation, is adopted to solve the numerical solutions. The accuracy and convergence of the proposed method are verified by numerical examples. Numerical experiments show that with the increase of GOri weight fraction, the central bending deflection of irregular plate structures decreases as the folding degree of GOri rises from 20% to 80% and the temperature changes from 300 K to 400 K, the opposite conclusions can be drawn for the buckling. The research on the bending and buckling behavior of irregular plate structures in this paper has important theoretical value for its future application in aerospace engineering field.

Characteristics of band gaps of a metamaterial plate with membrane-type resonators based on the energy approach

Local resonance metamaterials have garnered substantial interest in recent years due to their potential to effectively control low-frequency noise and vibration. This study proposes a new metamaterial plate with double mass membrane-type resonators (DMMRs). Combining polynomial fitting and virtual spring method, the natural characteristics of the resonator and the dispersion surfaces of the metamaterial plate are obtained. Results show the proposed metamaterial plate exhibits multiple band gaps, resulting from the cancellation of shear forces in the plate by the reaction forces generated by the first two resonances of the resonators. Parametric analysis is performed to obtain the variation patterns of the band gaps, where approximate models of the resonator are adopted to explain the effects of the parameters. It is found that the occurrence and width of the two band gaps are closely related to the mass ratio between the masses on the resonator and the substrate plate. Furthermore, finite element analysis is conducted to verify the effectiveness of the theoretical derivation, as well as the suppression effect of the metamaterial plate. The findings demonstrate the advantages of the metamaterial plate in vibration control and band gap tuning. The study provides guidance for the design and analysis of elastic wave metamaterials.

Determination of vibration energy flow-controlling regions in a piezoelectric metamaterial plate with temperature rise

In this study, vibration energy flow (VEF)-controlling regions in a piezoelectric metamaterial plate were determined using the structural intensity method. A finite element model was developed to derive the motion equation of a piezoelectric metamaterial plate in which the stiffness matrix depends on the temperature rise and input voltage. A VEF analysis model was developed to investigate the influence of temperature rise and input voltage on the VEF magnitude and direction based on the structural intensity method. In the numerical calculations, the bandgaps of the finite piezoelectric metamaterial plate agreed well with the band structures, which verified the effectiveness of the finite element model. In the present VEF analysis model, the structural intensity method was developed to investigate the influences of temperature rise and input voltage on the VEF magnitude and direction, and a new representation, called the divergence representation, was proposed to obtain the specific locations of sinks and sources in some complex structures. The numerical results showed that the magnitude of VEF increased with temperature rise or input voltage. The influence of the input voltage on the VEF direction may be offset by the temperature rise, and vice versa. To better analyze the influence of these two parameters, temperature-rise and input voltage-controlling regions were first analyzed. The input voltage played a more important role in controlling the direction of VEF than the temperature rise in the input voltage-controlling region and vice versa.

Using Structural Intensity Approach to Study the Energy Attenuation in Metamaterial Plate

Metamaterials have been extensively studied because of their bandgap characteristics, which can be used in vibration isolation. Current studies on the effect of vibration attenuation in metamaterials mainly focus on vibration amplitude, velocity, and acceleration. The structure intensity is a more effective approach to evaluating vibration. In this study, the structural intensity method is adopted to describe the vibration suppression effect of elastic metamaterial plates. The energy flow density in the stop band and the passband in the metamaterial plate can be obtained, and the mechanism for the vibration blocking of the metamaterial plate in the stop band is revealed. The study demonstrates that the power flows around the vibration source, which is calculated by the loop integral of structure intensity around the vibration source, can be used to describe the attenuation and transmission characteristics of vibration.

Analytical characterization of the dynamic response of viscoelastic metamaterials

The band-gap frequencies of elastic metamaterials are ideally determined by a metamaterial architecture; yet, in practical situations, are often dependent on the material damping in their constituent(s). The analysis of viscoelastic metamaterials requires however substantial computational resources and, except for oversimplified cases, is solely done numerically. Here, we propose an analytical procedure based on the spectral element method (SEM) to analyze bulk metamaterials with viscoelastic damping as continuous systems. Due to intrinsic limitations of the SEM to deal with complex geometries, we develop a procedure to build an approximate model based on SEM frame elements. The viscoelastic behavior is included by means of complex viscoelasticity moduli expressed by the generalized Maxwell mechanical model. We validate this approach by analyzing metamaterial plates and verify the findings experimentally. We demonstrate that our SEM-based analytical model can accurately capture wave transmission around the first band-gap frequencies. Therefore, our extension of the SEM approach to analyze three-dimensional meta-structures is promising to characterize wave propagation in realistic viscoelastic structures (with any type of linear viscoelastic behavior) in an accurate and computationally efficient way.

Topological transmission of elastic waves on a macroscopic pentamode metamaterial plate

In this paper, we devise a pentamode metamaterial plate exhibiting topological characteristics. By organizing pentamode metamaterial structural elements, topological boundary states are attained, effectively safeguarding propagation of elastic waves. Moreover, based on the numerical simulation model, we employ a polymer to fabricate a macro-scale specimen via additive manufacturing. Through assessing the vibrational response of the sample, we corroborate its topological attributes in governing elastic wave transmission. This discovery paves the way for a novel approach to manipulating acoustic/elastic waves employing pentamode metamaterials.

Flexural wave manipulation in perforated metamaterial plates with acoustic black holes interconnected by piezoelectric studs

Aiming at achieving lower and broader bandgaps (BGs) and stronger collimation effect, this research proposes a novel perforated metamaterial plate with acoustic black holes (ABHs) interconnected by piezoelectric studs for flexural wave manipulation. Based on the differential quadrature element method together with the first-order shear deformation plate theory, the governing equations of the metamaterial plate are derived. The proposed model is validated by comparing with finite element simulation results. Finally, the wave propagation characteristics including the BGs, equi-frequency contours (EFCs), and group velocities are obtained. The results reveal that the introduction of the stud embedded with piezoelectric patches brings wider complete BGs and stronger collimation effect at lower frequencies. The boundary frequencies and bandwidth of BGs and the preferential direction of wave energy flow are tunable by adjusting geometry parameters of the unit cell. The balance between ABH and piezoelectric effects should be kept to enhance the collimation by generating the caustic lobes. Utilizing the BG and self-collimation mechanism, flexural wave propagation can be manipulated by creating point or line defects in the metamaterial plates. This research provides guidance on the design of metamaterial structure with ABHs and piezoelectric material to achieve broadband vibration absorption and directional wave propagation.

Active Control Topological Valley Modes in Metamaterial Plates

Phononic crystals and metamaterials have a unique band structure that allows for the existence of topologically protected surface states. The topologically protected edge states can guide elastic waves without significant scattering or loss of energy. One of the most promising applications of topological insulators in wave guiding is in the field of acoustics, where they can be used to design highly efficient and robust acoustic wave guides. However, the high efficiency, precision, reconfigurability, and robustness of elastic waves remains challenging. The topological insulators provide a feasible method to design high-efficiency, robust, and low-backscattering waveguides. In this work, a novel design of hexagonal metamaterial plates composed of a base plate and piezoelectric patches is proposed. The hexagonal metamaterial plate can generate robust topologically protected edge waves via active control. The paths of the topologically protected edge waves can be tuned by adjusting the control parameters. The robustness and efficiency of the proposed hexagonal metamaterial plate are testified to by the numerical examples. These findings provide systematic theoretical guidelines for designing reconfigurable wave guides, elastic wave splitters, and novel elastic wave devices and hold great promise for the development of high-performance and versatile wave guide technologies with potential applications in a wide range of fields.