Metamaterial Plate Research Articles

Topological elastic wave transport and manipulation in three-dimensional metamaterials stacked with sandwich plates

Topological metamaterials demonstrate unprecedented wave manipulation abilities with topologically protected robustness, which have been extensively investigated in one-dimensional (1D) and two-dimensional (2D) mechanical systems, but less explored in three-dimensional (3D) systems. In this study, a 3D topological mechanical metamaterial with periodically stacked sandwich metamaterial plates is proposed to achieve 2D topological surface wave transport in a relatively low-frequency range. An innovative chiral compression-torsion coupling core is employed on the sandwich metamaterial plate to lower the band frequency. Analogous to the quantum valley Hall effect, the two-fold topological nodal line is lifted by breaking the spatial inversion symmetry, opening a topological band gap. By supercell analysis, the topological interface state is demonstrated to appear at the interface of two topologically different domains, and the topological boundary state can also be excited under appropriate free or fixed boundary conditions. Taking advantage of the 3D periodicity, the wave propagation based on both topological interface states and boundary states is examined in both 2D flat plates and 3D structures, realizing 1D topological waveguide and 2D topological surface wave transport respectively. It is found that mode symmetry matching is crucial for constructing the topological wave transport with both interface and boundary states. Leveraging the dependence of boundary states on boundary conditions, this work innovatively presents route-switchable and layer-selective wave manipulation by controlling boundary conditions without complicated structure design, enriching the strategies for tunable elastic wave manipulation. Besides, the topologically protected surface wave transport is demonstrated by introducing defects and disorders. These findings provide new insights into the topological transport of elastic waves in 3D mechanical metamaterials and contribute to the development of intelligent and robust devices for various purposes, such as vibration mitigation, energy harvesting, and signal sensing.

Application of machine learning algorithm and Carrera unified formulation in thermal buckling analysis of a functionally graded graphene origami enabled auxetic metamaterial sandwich plate with an auxetic concrete foundation

This study presents a comprehensive thermal buckling analysis of sandwich plates composed of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) face sheets on an auxetic concrete foundation, using Carrera’s unified formulation (CUF) as the theoretical framework. FG-GOEAM materials are emerging as advanced composites, combining exceptional mechanical resilience, tunable auxetic behavior, and high thermal stability, making them suitable for extreme environments. By employing CUF, a powerful and adaptable modeling approach, this work accurately captures the complex mechanical interactions within the FG-GOEAM sandwich structure under thermal loads, incorporating both material gradation and auxetic properties. To further enhance the precision and efficiency of this thermal buckling analysis, a deep neural network (DNN) is developed as a machine learning algorithm to predict critical temperature differences, based on a dataset generated through mathematics simulation. The DNN model demonstrates excellent predictive capability, validated by close alignment between its estimates and CUF results, thus reducing computational costs while maintaining high accuracy. Parametric studies are conducted to assess the effects of material gradation, aspect ratios, and foundation properties on thermal buckling performance. The results highlight the superior thermal stability of FG-GOEAM structures and the potential of DNNs to serve as reliable, computationally efficient tools for advanced structural analysis. This study provides a novel, integrated framework for high-fidelity thermal buckling prediction in complex auxetic composites, paving the way for broader applications in engineering fields requiring lightweight, thermally stable structures.

Sound transmission characteristics of piezoelectric metamaterial plates with resonant shunt circuits

Abstract In this study, a comprehensive investigation is conducted into the sound transmission characteristics of piezoelectric metamaterial plates, which feature five distinct resonant shunt circuits. To begin with, the intrinsic equations that pertain to piezoelectric materials, along with their equivalent models under external circuit conditions are established. Subsequently, the sound transmission loss of the plate and its corresponding equivalent bending stiffness model are constructed. Five resonant shunt circuits are employed, encompassing a basic resonant shunt circuit, one with series/parallel capacitance, and another with series/parallel negative capacitance. Ultimately, the influence of these diverse shunt circuits and their respective parameters on the sound insulation capabilities of piezoelectric metamaterial plates is comprehensively calculated and analyzed. Research results show that the inductance and resistance within the resonant shunt circuit influence the sound transmission characteristics exhibited by the piezoelectric metamaterial plate. Irrespective of whether the capacitance is configured in parallel or series within the resonant shunt circuit, the low-frequency sound transmission loss of the piezoelectric metamaterial plate experiences a notable modification. The effect of negative capacitances in the resonant shunt circuit on the sound transmission loss of the plate exhibits a contrasting pattern compared to the influence of the capacitances within the resonant shunt circuit on the sound transmission loss.

Topological interface and corner states of flexural waves in metamaterial plates with glide-symmetric holes

This study investigates the topological localization and propagation of flexural waves in metamaterial plates with perforated holes exhibiting glide symmetry. The dispersion relations of flexural waves in this mechanical system exhibit four-fold Dirac degeneracies at the M point of the Brillouin zone. By properly adjusting the rotation angles of the perforated holes, these degeneracies can be lifted up to create omnidirectional bandgaps, enabling nontrivial topological phases. Both numerical and experimental results demonstrate multiple topological states of flexural waves in the developed elastic metaplates, including dual-band helical interface states and anisotropic interface/corner states. The simple perforated metaplates with glide-symmetric holes provide novel, manufacturable platforms for the flexible manipulation of topological flexural waves, greatly facilitating potential applications such as energy harvesting and signal enhancement.

Vibration analysis of multilayer graphene origami-enabled metamaterial plates

Vibration analysis of multilayer graphene origami-enabled metamaterial plates

Multi-functional periodically heterogeneous structures for energy harvesting and vibration attenuation-effects of piezoelectricity and shunting circuits

Abstract We explore a kind of metamaterial plate structures intended for simultaneous energy harvesting and vibration control. These structures are designed using a periodically perforated piezoelectric plate (the matrix) with elastic inclusions situated in the holes and serving for the resonators. The design options comprise two- and three-phase configurations related to the mechanical connection between the matrix and inclusions. By introducing a singularity—the focal spot created as a defect in the perfectly periodic structure and using the theory of super-cell, an enhanced piezoelectric energy harvester is obtained. It is observed that such a meta-structure serves as a dual-purpose system: efficiently capturing vibrational energy at a focal spot while maintaining the overall vibration attenuation throughout the structure. The band gap analysis based on the Bloch’s wave decomposition theory shows that by concentrating energy and halting vibration propagation, approximately 10 times energy harvesting enhancement and a remarkable 100 dB reduction in vibrations are achieved simultaneously. Besides the passive response of these meta-structures, we consider its extension by an external electric circuit (EC). Such modified configurations enable to exploit ‘actively’ the piezoelectric plate property to transmit the mechanical response between two, or more distant locations. Due to nonlocal interactions introduced by means the controllable EC, we consider optimization of the EC impedance to reduce the vibrations at a selected location of the whole structure without any external energy supply. The computational study discovers perspectives and benefits of designing such active self-powered meta-structures.

Magnetorheological metamaterials for active broadband tuning of vibration attenuation

We propose a class of magnetorheological metamaterial plates with tunable band gaps achieved by means of a frequency-feedback control law. This approach allows for the intelligent tracking of excitation frequencies that enables an active control of band gap bounds. The active control mechanism is implemented through intelligent local resonators integrated into a main structure which comprise a mass and a magnetorheological elastomer (MRE) sensitive to an external magnetic field. The influence of the external magnetic field on vibration attenuation is examined using the Galerkin method. Next, a closed-loop frequency feedback control strategy is employed to dynamically adjust the band gap in response to excitation frequencies. This strategy significantly broadens the effective band gap range of the metamaterial plate. Besides, we studied the effect of MRE damping on broadband vibration reduction, underscoring its pivotal role in the band gap control for our magnetorheological metamaterials.

Rainbow trapping and piezoelectric energy harvesting of flexural waves in a gradient metamaterial waveguide

Metamaterials have provided a new way of controlling classic waves to achieve applications in space. In this work, we construct the gradient waveguide in two-dimensional elastic metamaterial plate to achieve rainbow trapping of flexural waves and then realize piezoelectric energy harvesting. Based on the band gap of flexural waves, the waveguide is formed by the introduction of line defects into the perfect metamaterial plate. The gradient waveguide is designed through the investigation of dispersion curves of guided waves for different geometrical parameters. The elastic flexural waves at different frequencies in the gradient waveguide separate, stop and hence are amplified in different positions. That is, the rainbow trapping is observed. To convert mechanical energy into electrical energy, piezoelectric patches are attached in the proposed metamaterial waveguide. Compared with a reference harvester (i.e., a homogeneous plate without metamaterial structure), the output power from the metamaterial energy harvester is significantly amplified. Besides, the proposed metamaterial harvester exhibits the capacity of multi-frequency energy harvesting.

Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method

Several types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps. In most of these structures, bandgaps are determined by their geometric configurations and material properties. This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate. The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results. In this method, the feedback voltage is related to the displacement of a resonator and the excitation frequency. By applying a feedback voltage on the piezoelectric fiber-reinforced composite (PFRC) layers attached to a cantilever-mass resonator, the natural frequency of the resonator can be adjusted. It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap. Based on this frequency-displacement feedback control strategy, the bandgap of the metamaterial plate can be effectively adjusted, and the vibration of the metamaterial plate can be significantly suppressed.

Multifunctional metamaterials for simultaneous sound absorption and flexural vibration isolation

Controlling the noise and vibration simultaneously in some engineering scenes is extremely essential to eliminate harmful effects on the humans and equipments. To overcome this challenge, a multifunctional metamaterial plate with both airborne sound absorbtion and flexural vibration isolation simultaneously is investigated theoretically, numerically, and experimentally. The plate consists of a host plate and a Helmholtz resonator, where Helmholtz resonance is used to absorb sound waves and its external solid domain plays as role of a local resonator to isolate the flexural vibrations. The theoretical models were established to characterize the mechanism of the sound absorption and vibration isolation. The experimental results demonstrated that the proposed metamaterial plate can achieve perfect sound absorption at 649 Hz and a flexural wave band gap at 289–470 Hz. Besides, although the sound absorption and vibration isolation functions are integrated in the same component, our theory identifies several critical geometrical parameters which can manipulate the absorption peak and the flexural wave bandgap, allowing us to design its frequency of multiple functions as desired. This work provides a promising solution for noise and vibration reduction in engineering.

Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Optimization of novel plate acoustic metamaterials and modulation of the low-frequency bandgap

Based on the local resonance mechanism, five new acoustic metamaterial plate structures with low-frequency bandgaps are proposed in this paper. The two new structures obtained by heuristic structural design are capable of suppressing vibrations over a large frequency range in the low-frequency range of 0-400 Hz, which is promising for practical applications. The mechanism of bandgap generation is found to be a shift in the form of local resonance. Among the three original models, model C has the smallest transmission coefficient T min of −154.6. Analysis of the group and phase velocity diagrams reveals that the change in frequency has a great influence on the energy transfer, speed and direction of the wave in the structure. The heuristic structural design allows the mass block of model B1 to undergo angular state changes, which ultimately realizes the regulation of the bandgap position and the total bandgap width within a certain range. It is also found that the variation of the bandgap properties has a certain regularity with the change of the structural parameters.

Guided elastic wave propagation in elastic metamaterial plate with periodic array of interfacial crack-like voids

Abstract A special kind of elastic metamaterials with periodic unit-cells composed of two layers with internal crack-like voids situated at the interfaces between two neighboring sub-layers is studied. To investigate experimentally guided waves propagation in EMMs with arrays of voids, several specimens with periodic arrays of crack-like voids have been manufactured using additive manufacturing techniques. The elastic waves have been excited by a rectangular piezoelectric transducer bonded at the surface of the specimen, while the wave-fields on the surface of the EMM specimen are measured by a laser Doppler vibrometer. The dispersion characteristics are investigated using the matrix pencil method and band-gaps are observed experimentally.

Elastic birefringent metamaterials and quarter-wave plate

The elastic matrices of extremal metamaterials have one or more zero eigenvalues, allowing energy-free deformation modes. These elastic metamaterials can be well approximated by manufactured microstructures. They can exhibit an unprecedented capacity to manipulate bulk and surface waves, which are unavailable with conventional solids due to the easy deformation modes, as already exemplified by pentamode materials (PMs). In this paper, we theoretically investigate a direct one-to-one correspondence of birefringent metamaterial and quarter-wave plate between optical and elastic waves based on a carefully designed quadramode material (QM). This QM metamaterial allows only two transverse wave modes, eliminating mode conversion due to the presence of the longitudinal mode. The characteristics of the elastic birefringent metamaterial and elastic quarter-wave plate are demonstrated by both homogenized and corresponding discrete models. A free space elastic wave isolator, analogous to a diode in electronics, is also proposed, which can effectively protect upstream sources or systems from back-reflected noise or interference. An additional benefit of the discrete model is also revealed for its working frequency tunability through deformation. This work provides the first study on elastic birefringent metamaterials and tunable elastic quarter-wave plate, which may stimulate applications of extremal elastic metamaterials for controlling elastic wave polarization.

Non-linear dynamics and bandgap control in magneto-rheological elastomers metamaterials with inertial amplification

Sandwich plate structures are extensively utilized in engineering due to their favorable stiffness-to-weight ratio. Nonetheless, these lightweight thin-walled structures frequently encounter challenges related to inadequate low-frequency vibration performance, which significantly restricts their applications, particularly in the realm of precision instruments which is sensitive to vibration. This study introduces an innovative design of an active nonlinear metamaterial, to achieve tunable broadband low-frequency bandgaps for sandwich plates. The nonlinear oscillator incorporates an inertia amplification mechanism (IAM), Euler-buckled beams, mass elements, and magneto-rheological elastomers (MREs), which are modulated via external magnetic fields to adjust the material's stiffness dynamically. Employing Hamilton's principles and the plate wave expansion method (PWE), the dispersion relations for the metamaterial plate are derived, elucidating the dispersion surfaces and the band structures within its sandwich-like plates.The dynamical equations of the metamaterial plate are formulated and validated through numerical simulations using the Galerkin method, confirming the theoretical predictions. The results demonstrate effective control over low-frequency and broadband bandgaps under low mass ratio conditions through strategic manipulation of the inertia amplification factor and magnetic flux. The study extensively explores the nonlinear dynamic responses of the metamaterial, highlighting the significant impact of excitation amplitudes on the amplitude-dependent bandgaps.

Broadening bandgaps in a multi-resonant piezoelectric metamaterial plate via bandgap merging phenomena

Locally resonant metamaterials usually have narrow bandgaps, which significantly limits their applications in realistic engineering environments. In this paper, an optimization method based on the genetic algorithm is proposed to broaden bandgaps in multi-resonant piezoelectric metamaterial through the merging of multiple separated bandgaps. Using the effective medium theory, the equivalent bending stiffness and dispersion relationship of a metamaterial plate are first obtained. Then, the criteria for determining the bandgap ranges for the two cases with and without damping are provided and analyzed. Furthermore, based on the bandgap merging phenomena, an optimization method for widening the bandgap is proposed based on the genetic algorithm. By investigating the bandgap widening effects in cases without and with damping, it is found that, when there is no damping, the bandgap can only be slightly widened; while after introducing damping into the transfer functions, the bandgap can be significantly widened by more than 200%. The bandgap widening effects are verified by comparing with finite element simulation results.

Design of elastic metamaterial plate and application in subway vibration isolation

Design of elastic metamaterial plate and application in subway vibration isolation

Low-Frequency Flexural Wave Acoustic Insulation Characteristics of a Double-Layer Metamaterial Plate

The effects of geometric parameters and constituent material parameters on the flexural wave bandgap of a locally resonant double-layer metamaterial plate are investigated using the finite element method. Reasonable parameters are obtained through optimization; then, a double-layer plate made of ABS material with added aluminum mass blocks is designed. The results show that it can open the low-frequency (112--124 Hz) flexural wave bandgap at a subwavelength size. The metamaterial plate is modeled as an equivalent spring-mass system, and the frequency range with negative density for the equivalent dynamic mass is consistent with the width of the flexural wave bandgap. The bandgap generation mechanism is further elucidated. Sound insulation performance of double-layer metamaterial panels verified in an acoustic chamber. The maximum amplitude of STL is achieved at the 112 Hz point in the bandgap frequency range, which indicates that the low-frequency bandgap can effectively reduce vibration and noise. These results demonstrate that this novel double-layer metamaterial plate has wide applications in engineering.

Identifying Factors Influencing the Properties of Vibroacoustic Metamaterials Using Three Different Acoustic Methods

Vibroacoustic metamaterials offer an approach for the targeted damping of unwanted structural vibrations and noise by integrating periodically arranged resonators into a matrix of bulk material. Fabrication using the laser bed powder fusion process allows the targeted integration of bulk resonators and powder depots, leading to an extension of the designable damping properties. Herein, the adaptation of acoustic methods is focused on the characterization of the properties of metamaterial plates. The investigated vibroacoustic metamaterial plates are made of polyamide PA1.2, combining material and structural damping. The vibration behavior of the plates over a range of frequencies using acoustic impedance measurements in a custom‐built measurement tube is investigated and it is compared with structural dynamics experiments using an electrodynamic shaker. The measurements allow for the identification of stop bands (frequency range with high damping) and influencing factors such as metamaterial design, mass, powder amountand surface on the frequency‐dependent damping properties. The adapted technique investigated in this work provides an experimental platform to characterize the complex interplay of acoustic metamaterial design and holds promise for scaling up metamaterial technology for industrial applications due to its simplicity, small space requirement, and low cost.

Double-panel metamaterial with multi-resonator for broadband sound insulation

Currently, double-layer panels are usually filled with damping and sound-absorbing materials, which can effectively reduce the intensity of sound waves and enhance the sound insulation capability in the mid to low frequency range. Although this method can improve the peak and valley values in sound insulation to a certain extent, it still struggles to meet stricter design standards and requirements. This paper proposes a double-layer metamaterial plate with multi-resonator (DLMPMR) to fulfill sound insulation requirements through modifications to the double-layer plate structure. Firstly, the mathematical model pertaining to the sound insulation of DLMPMR is derived utilizing on the transfer matrix method and subsequently verified by the finite element analysis approach. Secondly, the influence mechanism of diverse structural parameters on the sound insulation performance of DLMPMR is studied. It is explored that the sound transmission loss (STL) of DLMPMR can be improved by adjusting the structural parameters to enhance the resonance of the structure across a broader frequency range and shifting the resonance frequencies to lower ranges. Finally, the sound insulation capability of the structure is verified through the reverberant fully anechoic chamber. The results demonstrate that the structure exhibits acoustic performance surpassing the mass law in the range of 220-5000 Hz. The proposed metamaterial, owing to the light weight and thinness, demonstrates promising potential for various applications in noise control engineering.