Resonant Band Gap Research Articles

A smart fluorescent colorimetric dual-response sensing for the determination of tetracycline antibiotics

This work synthesized the ethylenediamine-doped puffer fish skin carbon dots using biomass as a green precursor. Three tetracycline antibiotics (TCs) were detected fluorescence and colorimetrically using carbon dots as probes; on this basis, hydrogels were used to carry out visual identification and quantification. In the presence of TCs, the nitrogen-doped carbon dots (N-CDs) displayed a quenching impact on fluorescence because of fluorescence resonance energy transfer (FRET), dynamic quenching, and band gap transition. As a result, it was possible to identify the precise concentrations of tetracycline (TC), oxytetracycline (OTC), and chlortetracycline (CTC). The assay has great biocompatibility, which was supported by cytotoxicity, a wide linear range (0.5–500 M), a low detection limit (0.15 M), and outstanding selectivity. With a high recovery rate, the approach has been successfully used to identify TCs in food and water samples such milk, honey, and tap water.

Rogue waves as modulational instability result in one-dimensional nonlinear triatomic acoustic metamaterials

In this study, a triatomic acoustic nonlinear metamaterial was modelled. It is a network of identical periodic unit cells made up of three different masses. These masses interact with connections modelled by springs whose stiffnesses are linear and nonlinear. Handling the motion equations of nth unit cell, the semidiscrete approximation method is used to extract the three-component coupled nonlinear Schrödinger equations. The dispersion relationship was determined. The results showed that the dispersion relation of the one-dimensional triatomic chain contained an acoustic branch and two optical branches. The dispersion curves show that the proposed acoustic metamaterial exhibits two local resonance bandgaps independent of spatial periodicity. The spectral range and frequency bandgap are related to the mass of the three atoms in the original cell. Based on the theory of linear stability analysis, modulation instability is the condition for the existence of rogue waves. Analytically, it is shown that modulational instability and rogue wave phenomena are strongly influenced by variations in the nonlinearity, dispersion, and diffraction terms, which contain the values of the masses and stiffnesses.

Quasi-full bandgap generating mechanism by coupling negative stiffness and inertial amplification

Current research on mechanical metastructures cannot achieve extremely wide and low bandgaps because of engineering constraints, such as size, stability, and weight. To isolate vibration in both ultralow and middle-high frequency ranges, we propose a new bandgap merging mechanism that coordinates the Bragg and locally resonant bandgaps to form a quasi-full bandgap, starting from zero frequency. In the proposed mechanism, negative stiffness and inertial amplification are introduced to overcome the mass and stiffness limitations, allowing us to tune the lower boundary of the locally resonant bandgap and the cut-off frequency of the Bragg bandgap. The quasi-full bandgap can be achieved analytically by determining certain parameter conditions. Here, the dispersion curves become two horizontal lines independent of the wave vectors with frequencies always zero and another constant. A damping mechanism is introduced to lower the resonance peak below 0 dB for full-band vibration attenuation. To prove the bandgap tunability at large wave amplitude, the nonlinear dispersion relation of the proposed metastructure is solved with the Harmonic Balance Method. Numerical simulations and experiments are also conducted to confirm the results. In general, the proposed bandgap merging mechanism may provide a route for controlling time-varying, ultralow, and wide-frequency vibrations.

Tuning Fork Seismic Metamaterial for Low-Frequency Surface Wave Attenuation with Locally Resonant Band Gaps

Tuning Fork Seismic Metamaterial for Low-Frequency Surface Wave Attenuation with Locally Resonant Band Gaps

Analysis of bending waves and parametric influence on band gaps in periodic track structure

Vibration of railway tracks generated due to rail-wheel interaction is a key research concern. A rail with equally spaced supports can be regarded as a periodic structure. Such a structure possesses unique property of band gap because of that they act as vibro-acoustic filters. Here, the propagation behavior of vertical and lateral bending waves is studied in a periodic ballastless track structure. Bloch-Floquet theorem is used to formulate the dispersion relations for the propagation of two types of waves which is validated by corresponding finite element model. The results show coexistence of both resonance and Bragg type band gaps they are owing to locally resonant units and spatial periodicity in the track. Furthermore, the study also explores the impact of track parameters, such as pad stiffness and sleeper spacing, on the properties of these band gaps.

High-fidelity dynamics of piezoelectric covered metamaterial Timoshenko beams using the spectral element method

Piezoelectric metamaterial beams have received enormous research interest for the applications of vibration attenuation and/or energy harvesting in recent years. This paper presents a generic modelling approach for predicting the high-frequency dynamics of piezoelectric metamaterial beams. The spectral element method (SEM) is used to derive the dynamic stiffness matrix of a composite piezoelectric beam segment. Boundary condition implementations are demonstrated. Both band structure and transmittance analyses are realized. Several case studies for piezoelectric metamaterial beams configured in different geometric/electrical forms are carried out. The corresponding finite element (FE) models are built for verification, and a comparison study with the transfer matrix method (TMM) is conducted. For the uniform configurations, an almost indistinguishable difference is noted between the theoretical and FE results. For the stepped configurations, only minor discrepancies are observed in the high-frequency responses. The improved robustness and stability of the SEM method compared to the TMM method are demonstrated. A further discussion has been provided to explain the cause of the high-frequency discrepancies: sudden changes in the cross-section of the beam result in the stress concentration effect and reduce the bending stiffness at the junction connection. Finally, the value of the high-fidelity modelling approach is reflected through a parametric-based optimization study towards merging the Bragg scattering and locally resonant band gaps in an example piezoelectric metamaterial beam to achieve a wide band gap.

Quasi-static band gaps in metamaterial pipes with negative stiffness resonators

A novel configuration of periodically supported pipes with negative stiffness resonators (NSRs) at midspans is investigated in this paper. By leveraging the expanded bandwidth and enhanced damping effects offered by the NSRs, as well as the quasi-static (QS) band gaps of periodically supported pipes, this configuration enables the realization of ultrawide QS band gaps. The Floquet-Bloch theorem and Finite Element Method (FEM) are employed to determine the dispersion relationship of the infinite periodic pipe, elucidating the wave propagation characteristics. The band formation mechanism is revealed by conducting a comparative analysis with other systems in which unit cells only comprise periodic supports or NSRs. By analyzing the dispersion relationships, the effects of critical parameters on the transition and interplay between Bragg and local resonance (LR) band gaps are investigated. The results reveal that, with increasing absolute values of the negative stiffness ratio or mass ratio at a constant resonant frequency, the LR band gap created by NSRs eventually transforms into a wide QS band gap. The study further extends to metamaterial pipes of finite length, where FEM simulations are carried out using ANSYS to confirm the physical band-gap properties observed in the periodic systems. The advantage of the wave attenuation bandwidth introduced by NSRs is demonstrated by comparing the results with those obtained by traditional types of resonators. With the same added mass, the system with NSRs exhibits a substantially wider LR band gap than the traditional resonators. Finally, owing to the damping magnification mechanism of NS elements, when a reasonable amount of damping is introduced, the proposed system shows superiority in achieving ultrawide QS band gaps through band-gap merging over pipe systems with suspended resonators.

Resonance reduction for linked train cars moving on multiple simply supported bridges

The dynamic interaction of a moving train over a series of railway bridges with equal spans can result in a coupled vibration problem of wave transmission between two periodic structures. Dual resonance occurs when both systems vibrate in phase and the train travels at a resonant speed. The objectives of this paper are to (1) develop an active pitching resonator (APR) to attenuate resonance waves in a train; (2) study the dispersion relation for pitching motion control of periodically linked train cars; (3) investigate the key parameters that affect the dispersion band gaps of wave attenuation in a train; (4) present an active vibration cancellation method to enhance the control performance of the APR; and (5) demonstrate the effectiveness of using the optimal APRs to reduce resonance of a moving train. Through dispersion analysis, the optimum APR can not only shift the target frequency level away from resonance of a moving train, but also create a wide resonance band gap to reduce wave transmission in the train. Finally, the effectiveness of the optimum APR unit in reducing the resonance and attenuating the waves of a train travelling over multiple-span simple beams is demonstrated by dynamic finite element analysis of the train-bridge interaction.

Single-step detection of toxic airborne metallic nanoparticles using Goos–Hänchen effect in photonic Bragg grating structures

A real-time photonic crystal sensor is suggested for the detection of airborne heavy metal nanoparticles (HMNPs). The sensor consists of a sandwiched sampling cell between two stacks of alternating TiO2 and Si-Ge layers, forming the core of the device. The sensor’s performance is based on monitoring changes in both the intensity and phase of a probe beam as it propagates through the core. By analyzing the fluctuations in intensity, central frequency, and full width at half maximum (FWHM) of the resonant mode within the transmittance spectrum bandgap, or by monitoring the phase changes at the angle of maximum transmittance that may result in a remarkable Goos–Hänchen (GH) shift in transmittance, the sensor can identify the pollutant nanoparticles. Tuning the thicknesses of the slabs and the number of unit cells in the photonic crystal can dynamically shift the resonant mode and bandgap edges, allowing for easy adjustment of the sensor’s responsivity. Furthermore, the optical response of the sensor can be tuned through external parameters such as the incident angle of the probe light or an externally applied electric field. Additionally, the sensor exhibits sensitivity not only to changes in the extent of the sample but also to the shape of the present HMNPs. These characteristics make the proposed configuration cost-effective, user-friendly, and suitable for HMNPs detection without the need for complex sample preparation, data analyses or additional tools/accessories.

Tunable elastic wave modulation via local phase dispersion measurements of a piezoelectric metasurface with signal correlation enhancement

Tunable piezoelectric metasurfaces have been proposed as a means of adaptively steering incident elastic waves for various applications in vibration mitigation and control. Bonding piezoelectric material to thin structures introduces electromechanical coupling, enabling structural dynamics to be altered via tunable electric shunts connected across each unit cell. For example, by carefully calibrating the inductive shunts, it is possible to implement the discrete phase shifts necessary for gradient-based waveguiding behaviors. However, experimental validations of localized phase shifting are challenging due to the narrow bandgap of local resonators, resulting in poor transmission of incident waves and high sensitivity to transient noise. These factors, in combination with the difficulties in experimental circuitry synthesis, can lead to significant variability of data acquired within the bandgap operating region. This paper presents a systematic approach for extracting localized phase shifts by taking advantage of the inherent correlation between the incident and transmitted wavefronts. During this procedure, matched filtering greatly reduces noise in the transmitted signal when operating in or near bandgap frequencies. Experimental results demonstrate phase shifts as large as −170° within the locally resonant bandgap, with an average 28% reduction in error relative to a direct time domain measurement of phase, enabling effective comparison of the dispersive behavior with corresponding analytical and finite element models. In addition to demonstrating the tunable waveguide characteristics of a piezoelectric metasurface, this technique can easily be extended to validate localized phase shifting of other elastic waveguiding metasurfaces.

A metamaterial for low-frequency vibration damping

The local resonant phononic crystal structure is significantly smaller than the control wavelength so it is of major importance for controlling the sound field in the low-frequency band. However, lightweight and small local resonant phononic crystal structures still present a great challenge. In this paper, we propose a metamaterial for low-frequency damping. The band structures and eigenmodes are calculated using the finite element method, and the generation mechanism of the resonant band gap is analyzed. The results show high transmission losses in the band gaps of 26.8–30.8 Hz and 33.7–180.1 Hz. In addition, the effect of geometric parameters on the bandgap frequency is discussed, and the control of the low-frequency bandgap can be achieved by adjusting the geometric parameters. The results of the study provide a new design idea for obtaining phononic crystal structures with low-frequency band gaps.

New optical dispersion models for the accurate description of the electrical permittivity in direct and indirect semiconductors

We propose new optical dispersion models to describe the imaginary part of the electrical permittivity of dielectric and semiconductor materials in the fundamental absorption region. We work out our procedure based on the well-known structure of the semi-empirical Tauc–Lorentz dispersion model and the band-fluctuations approach to derive a five-parameter formula that describes the Urbach, Tauc and high-absorption regions of direct and indirect semiconductors. Main features of the dispersion models are the self-consistent generation of the exponential Urbach tail below the bandgap and the incorporation of the Lorentz oscillator behavior due to electronic transitions above the fundamental region. We apply and test these models on optical data of direct (MAPbI3, gallium arsenide and indium phosphide), indirect (gallium phosphide and crystalline silicon), and amorphous hydrogenated silicon semiconductors, accurately describing the spectra of the imaginary part of the electrical permittivity. Lastly, we compare our results with other similarly inspired dispersion models to assess the optical bandgap, Urbach tail and oscillator central resonance energy.

Novel mm-Wave Oscillator Based on an Electromagnetic Bandgap Resonator

This letter introduces a novel millimeter (mm)-wave oscillator concept based on an electromagnetic bandgap (EBG) resonator (also called a photonic crystal resonator). To realize an ultralow phase noise monolithic microwave integrated circuit (MMIC) oscillator, an EBG resonator is developed by introducing a periodic structure into an ultrahigh resistivity silicon wafer to create an EBG which confines a localized resonant mode with a reduced mode dielectric filling factor of 47%. The measured results of the resonator demonstrate an unloaded Q-factor of 108300 can be achieved at 45 GHz. Measured oscillator phase noise levels of −91.5, −121.5, and −133 dBc/Hz are obtained at offset frequencies of 1, 10, and 100 kHz, respectively.

Investigation of a magnetorheological elastomer metamaterial sandwich beam with tunable graded stiffness for broadband vibration attenuation

Metamaterials with local resonance show promising application prospects in low-frequency vibration attenuation. However, with the drawback of narrow band gap, such potential is greatly limited. In order to broaden the local resonant band gap, a semi-active graded magnetorheological elastomer (MRE) metamaterial sandwich beam (GMREMSB) with real-time tunable graded stiffness was proposed and investigated in this study. For theoretical calculation, a mass-spring model was established for the GMREMSB. Then the calculated band gap and transmissibility using Timoshenko beam theory and spectral element method were compared. An experimental test was also conducted for verification. The results show that the bandwidth of the proposed GMREMSB can be widened by the graded stiffness arranged in ascending order. The experimental band gap of the GMREMSB under the graded current of 0.0–0.5–1.0 A is 6.4 Hz wider than the band gap of the periodic structure with the single current of 0.0 A and is 5.0 Hz wider than that of 1.0 A. The growth rate reaches 15.06% and 11.39%, respectively.

Finite-amplitude nonlinear waves in inertial amplification metamaterials: Theoretical and numerical analyses

The motivation of this study is to understand the unique characteristics of finite-amplitude elastic wave propagation in an inertial amplification (IA) system coupled with a Duffing resonator and leverage the unique opportunities offered by the IA mechanism and nonlinearities to achieve the modulation of elastic waves. Based on the assumption of the perturbation method, the effective range of the wave amplitude was investigated, which is usually ignored. Meanwhile, the obvious phenomenon of bandgap transition (between the single resonance bandgap and hybrid bandgap) is observed with varying IA levels. In particular, we demonstrated a new phenomenon of negative wave propagation and an obvious standing-wave mode in this system. Here, an analytical investigation of the amplitude-dependent and IA-dependent nonlinear dispersion is conducted based on the perturbation approach. Numerical simulations using the time-domain finite element method and Gaussian pulse excitation were performed to validate the nonlinear dispersion and negative motion of the wave packet. The research results can be used to tune wave propagation in metamaterials and provide ideas for the design of metamaterials, which can be used in practical circumstances for different energy transfer needs.

A Design of Auxetic Metamaterial with Locally Resonant Bandgaps Using Topological Optimization

In the past two decades, auxetic metamaterials have shown their potential in many fields such as energy absorption and vibration mitigation. Many mechanisms have been proposed to guide the design of their microstructures. More recently, structural optimization methods, especially topology optimization, have been employed for the design and optimization of metamaterials. In this paper, topology optimization was employed with the SIMP method and MMA optimizer for the design of auxetic metamaterials. The negative Poisson’s ratio was verified by numerical simulation. Bandgap study was also conducted on the optimized layout and it showed that the optimization also achieved auxetic metamaterials with two narrow locally resonant bandgaps in addition to broadening and lowering the bandgap of the initial configuration.

Mode purification for multimode Lamb waves by shunted piezoelectric unimorph array

Guided wave-based nondestructive testing and structural health monitoring methods have been developed to exhibit attractive potentials and best prospects for rapid and sensitive detection of defects or damage in engineering structures. Different modes of guided waves can provide different sensitivities of damage detection. However, the multimode and mode conversion nature of guided waves poses significant challenges to mode purification of received signals. This study aims to design a metamaterial-based smart transducer for mode purification of Lamb waves in a plate, which can filter out an undesired mode of the Lamb wave to enhance sensing and actuating signals of a dominated mode. The smart transducer consists of a periodic array of shunted piezoelectric unimorphs with staggered polarization directions and is bonded on the surface of a host plate. Numerical and experimental results show that a local resonance bandgap for an anti-symmetric Lamb wave, rather than a symmetric Lamb wave, can be obtained and tuned through the shunting inductance circuit. Within such mode bandgap, the wave control for propagating a specific mode of the Lamb wave can be further realized, i.e., the mode of the Lamb wave is purified. The design presented herein offers enhanced capabilities in controlling guided wave propagation for engineering applications and nondestructive testing techniques.

Bandgap formation and low-frequency structural vibration suppression for stiffened plate-type metastructure with general boundary conditions

Metastructures with unique mechanical properties have shown attractive potential application in vibration and noise reduction. Typically, most of the metastructures deal with the vibration bandgap properties of infinite structures without considering specific boundary condition and dynamic behaviors, which cannot be directly applied to the engineering structures. In this research, we design a Stiffened Plate-type Metastructure (SPM) composed of a plate with periodic stiffeners and cantilever beam-type resonators subjected to general boundary conditions for low-frequency vibration suppression. The effects of boundary conditions and the number and orientation of the stiffeners on Locally Resonant (LR) type bandgap properties in SPM are further investigated. An analytical modeling framework is developed to predict the bandgap formations and vibration behaviors of SPMs in finite-size configuration. The governing equations of the SPM reinforced by various arrangements of stiffeners are derived based on the first-order shear deformation theory and Hamilton’s principle, and a Fourier series combined with auxiliary functions is employed to satisfy the arbitrary boundary conditions. Finite element analysis and experimental investigations of vibration behaviors for the SPM are carried out to validate the accuracy and reliability of the present analytical model. For practical designs of the SPMs with specific boundary conditions, it is found that there exist optimal numbers of stiffeners and resonators which can produce the significant LR-type bandgap behaviors. Furthermore, various arrangements of stiffeners and resonators are explored for different boundary conditions by breaking the requirement of spatially periodicity. It is shown that for the designed SPM, the vibration modes of its host structure should be considered to widen the frequency range in which the resonators transfer and store energy, and hence improve the performance of low-frequency vibration suppression. The present work can provide a significant theoretical guidance for the engineering application of metamaterial stiffened structures.

Vibration isolation of mechatronic metamaterial beam with resonant piezoelectric shunting

Mechatronic metamaterials are of utmost significance in vibration isolation owing to their tunable bandgaps. However, their intricate mechanisms are always challenging for environmental changing. In this study, a mechatronic metamaterial beam shunted with inductor–resistor–capacitor (LRC) shunting circuits is discussed, with the aim of obtaining tunable bandgaps. The tunable bandgap can be effectively used to achieve low-frequency vibration isolation by changing the selection of circuit parameters. The mechatronic metamaterial beam model is established using Hamilton's principle and Kirchhoff's law, and the dispersion relationship is derived by applying the transfer matrix method. An experimental rig of a mechatronic metamaterial beam is used to validate the analytical methods. The experimental results support the analytical results. Mechatronic resonant and Bragg bandgaps shown in the frequency response curves (FRCs) can block vibration transmission, thus achieving vibration isolation within a certain frequency range. Parameters studies are conducted to illustrate how the mechanic and electric parameters affect the bandgaps. It is found that the electric parameters affect the position of the mechatronic local resonant bandgap in the FRCs. Thus, low-frequency isolation can be achieved by choosing the appropriate electric parameters.

Theoretical study on dispersion relations of chiral acoustic metamaterials considering mass-rotation

Low-frequency vibration affects the performance of equipment such as aircraft, ships, automobiles, etc., and the noise caused by vibration harms human health. Acoustic metamaterials can dampen elastic waves at specific frequencies due to their bandgaps. In this work, an acoustic metamaterial structure is designed with the introduction of chirality to obtain wider bandgaps. Considering the rotation of the structural parts, the periodic structure is equivalent to an ideal 6-DOF-model through the introduction of Bloch's theorem, analyzed its dispersion relationship and the influence of structural parameters theoretically, and the vibration characteristics of the structure are given with the help of FEM results. The results show that the designed structure has a local resonance bandgap of around 0.12 and the maximum transmission loss exceeds 40 dB. Parametric analysis of this structure shows that structures with different parameters have up to four bandgaps in total between the second and sixth dispersion curves, and the distribution of the bandgaps is centrosymmetric. Under some parameters, the total bandwidth reaches 83.5% of the total frequency range and reduced the normalized frequency of the first bandgap to lower than 0.07. Compared with existing structures, the newly designed structure has lower bandgap frequency and higher bandwidth, and its theoretical model has outfitted with high efficiency and accuracy. This research can provide theoretical guidance and reference for designing such kinds of acoustic metamaterials.