Frequency Band Gaps Research Articles

Retuning the disordered periodic structures by sorting unit cells: Numerical analyses and experimental studies

Periodic structures feature frequency band gaps in which the propagation of certain waves will be attenuated. Therefore, they are widely applied in the vibration control of structures. The premise of this theory is that the structure should be perfectly periodic. However, this must be broken more or less due to inevitable deviations, leading structures to disorder. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Moreover, the disorder pattern plays an important role in such a performance change. In this paper, we study the influence of the disorder patterns and explore a general permutation to retune the disordered periodic structures which means to reduce the deviation of the dynamic characteristics between the nominal and disordered structures. This research is conducted through three stages. In the first stage, a diatomic lumped-mass model is used. We study the implication of the disorder and propose a sorting strategy inspired by global sensitivity analysis (GSA). In the second stage, the sorting strategy is corroborated with numerical simulations by a finite element (FE) model of beam. We use the wave finite element method (WFEM) to calculate the band gaps. A thousand samples are generated randomly to test the sorting strategy and the contrarian strategy. In the third stage, the sorting strategy is verified by an experimental structure of beam. We set up an experimental system and scheme to measure and analyze the effects of the strategy for 5 groups of experiments. We show that vibration suppression may deteriorate statistically due to disorder for periodic structures. Specifically, vibration mitigation is most sensitive to the deviation in the first unit cell from the excitation. Inspired by this finding, a retuning strategy is proposed for the first time, i.e. the unit cell with the smallest deviation should be arranged in the position nearest to the excitation. The results in all stages show that the strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures.

Second Harmonic Generation in 1D Nonlinear Plasma Photonic Crystals

AbstractIn this paper, a 1D nonlinear plasma photonic crystal (NPPC) structure composed of polarized ferroelectric crystals and nonlinear plasma periodic alternation is proposed. The transfer matrix method is employed to analyze the second harmonic generation (SHG) problem of this structure. In the designed NPPCs, the fundamental wave (FW) operates in the gigahertz (GHz) band and the nonlinear plasma is controlled by an external high‐intensity control wave (CW). Numerical simulations are performed to investigate the effects of different incident angles and external CW intensities on the total conversion efficiency (T‐con) of the second harmonic wave (SHW). Additionally, the internal electric field distribution and incident light intensity within the nonlinear structure are analyzed. The importance of the relationship between the FW frequency and photonic band gap (PBG) in enhancing SHG is summarized. The results demonstrate that the optimal structure can be obtained by changing the structural parameters, such that the FW and SHW are tuned to the edge of the PBG. At this point, the electromagnetic field density is large, the group velocity is small, the local field is enhanced, and the nonlinear optical interaction is increased, resulting in a significant increase in the T‐con of the SHW.

Edge and corner states in two-dimensional finite phononic crystals: Simulation and experimental study

We investigate the mechanical vibration transmission in two-dimensional infinite and finite phononic crystals (PCs). The infinite PC consists of a periodic structure formed by square plates connected to the center of each of their nearest neighbors through a tiny beam. Numerical simulations using finite elements show a wide full bandgap for frequencies between 27 kHz and 32 kHz, approximately. Acoustic resonant spectroscopy was used to measure the PC frequency spectra for the different vibrations, using a finite PC consisting of 8 by 8 cells, which was designed with the same configuration as the infinite one. Experimental results corroborate the existence of a full complete bandgap predicted by the numerical method. However, the width was significantly reduced due to the appearance of edge and corner states. The border states were obtained numerically using a supercell. The measured wave amplitudes and the simulated ones present a great similarity. Some states appear located at the corners of the finite PC demonstrating that zero-dimensional states can also appear in two-dimensional phononic crystals.

Broadband vibration attenuation study and wave propagation analysis of extended arrow tetragonal lattice structure

In order to reduce vibration and noise with wide frequency, a new extended arrow tetragonal lattice topology is proposed. The band gap characteristics are discussed by combining the finite element method and Bloch’s theorem. The generation principle of band gap is explained by vibration mode analysis. By topological optimization of the structure, band gap has obvious optimization effect. The propagation characteristics of elastic waves with a specific frequency in the structure are studied from the point of view of energy. Finally, the band gap frequency range is compared with the transmission function, and the stress cloud diagram is analyzed. The research shows that the structure has good band gaps and can play a good role in vibration and noise reduction. Through the topological design of the structure, the band gap frequency range of the structure is optimized, which provides a new design idea for wide frequency vibration attenuation.

The propagation characteristics of flexural wave in periodic ballast track

The vertical vibration band gap characteristics of the ballast track were investigated in this paper. The rail was simplified as a beam with double layer of periodic supports. The dispersion characteristics were studied considering the rail as Timoshenko beam, using the plane wave expansion method. The eigenvalue equation of the Timoshenko beam with complex boundary conditions, which was a problem for the traditional plane wave expansion method, has been solved using special mathematical solution of matrix inversion. The band gap of the flexural waves in periodic track structure was confirmed by the rail vibration transmission characteristics obtained from the experiments. The physical significance of band gap frequency was analyzed in detail in this paper. In addition, we give a more accurate prediction model of Bragg band gap frequency of periodic track structure compared previous studies. The band gap of the flexural waves in periodic track structure was confirmed by the rail vibration transmission characteristics obtained from the experiments. The influence of temperature force on the band gap characteristics of the flexural waves was also analyzed, and a sensitivity index of temperature force was given as a result. The results indicate that the square of the band gap frequency has a linear relation with the longitudinal temperature force, which is different from the previous research.

Band gaps in an acoustic metamaterial composed of resonator with elastic support

In this paper, the band gaps in a mass-spring structure composed of resonator with elastic support are investigated. The band structure, effective parameters, and transmission spectra of the acoustic metamaterials are calculated numerically. The numerical results show that the elastic support and resonator in the structure generate the first and the second band gap, respectively. The effective parameters are analyzed to reveal the nature of this phenomenon and calculated to obtain the edge frequencies of band gaps. The transmission spectra are in accordance with the complex band structure. It is found that the attenuation factor is non-zero in band gap, and it determines the shape and magnitude of transmission ratio in band gap. The influences of the structural parameters on the band structure and attenuation factor are investigated numerically. Numerical results show that the band structure can be modulated by changing the structural parameters, and the topological structure will be changed when those parameters change greatly.

Harnessing chiral buckling structure to design tunable local resonance metamaterial for low-frequency vibration isolation

This paper proposes a tunable local resonance metamaterial with chiral buckling structures for low-frequency vibration isolation. The unit cell consists of the inner and outer buckling stiffness structure, basic structure, and local resonator. The bistability of three kinds of unit cells with different initial shapes of beams is investigated and compared via the elliptic integral method and finite element analysis. Then, their axial stiffness in different states is studied. The dynamic responses of the metamaterial with simple unit cells and hybrid supercells are theoretically derived and analyzed by Bloch's theorem and transfer coefficient method. Theoretical, numerical, and experimental results demonstrate that the unit cell with initially convex downward beams has strong bistability and determinate deformation modes. The axial stiffness of the unit cell in two stable states differs by an order of magnitude. Changing some specific parameters broadens the gap in the axial stiffness between the two stable states. The axial negative stiffness characteristics and rotation effect of the unit cell have the potential for energy dissipation and tensile-torsion material. The metamaterial with simple unit cells has tunable and wide band gap and low-frequency vibration isolation via the stable states switching of the inner and outer buckling stiffness structures. The metamaterial with hybrid supercells can further broaden the band gap width and lower the band gap frequency, which has up to 16 different band gap characteristics.

Design of a Functionally Graded Material Phonon Crystal Plate and Its Application in a Bridge

In order to alleviate the structural vibrations induced by traffic loads, in this paper, a phonon crystal plate with functionally graded materials is designed based on local resonance theory. The vibration damping performance of the phonon crystal plate is studied via finite element numerical simulation and the band gap is verified via vibration transmission response analysis. Finally, the engineering application mode is simulated to make it have practical engineering application value. The results show that the phonon crystal plate has two complete bandgaps within 0~150 Hz, the initial bandgap frequency is 0.00 Hz, the cut-off frequency is 128.32 Hz, and the internal ratio of 0~100 Hz is 94.13%, which can effectively reduce the structural vibration caused by traffic loads. Finally, stress analysis of the phonon crystal plate is carried out. The results show that phonon crystals of functionally graded materials can reduce stress concentration through adjusting the band gap. The phonon crystal plate designed in this paper can effectively suppress the structural vibration caused by traffic loads, provides a new method for the vibration reduction of traffic infrastructure, and can be applied to the vibration reduction of bridges and their auxiliary facilities.

Vibration attenuation performance of isolator based on locally resonant phononic crystal via train load

A locally resonant phononic crystal isolator (LRPCI) that the external ring vibrators attached to the central connectors through the rubber is designed, and it is installed to attenuate vibration under the track of rail transit. The energy band structure of the isolator is calculated by the finite element method, and its bandgap range is from 49.7 Hz to 104.9 Hz. The transmission loss and the equivalent mass density are further calculated to verify the accuracy of the bandgap, and they are perfectly corresponding to the bandgap. Then, the vehicle-rail-floating slab track-tunnel multibody dynamic model is built to analyse the vibration attenuation performance of the floating slab track installed the LRPCI and steel spring isolator under the train load. The results show that the LRPCI has a low frequency bandgap and can reduce the low frequency vibration, and the vibration isolation performance of the LRPCI is better than that of the steel spring isolator. The LRPCI has a low frequency bandgap, which can isolate the vibrations caused by wheel-rail interaction, and further reduce the impact of vibrations on surrounding buildings and the environment.

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 ventilation barrier for low-frequency sound insulation

This paper proposes a ventilation barrier for low-frequency sound insulation with a double-opening Helmholtz’s periodic structure. The energy band characteristics of the unit structure and the sound transmission loss of the ventilation barrier are calculated using the finite element method. The research results show that the ventilation barrier exhibits excellent sound insulation in the range of 323–803[Formula: see text]Hz, and the sound insulation band is consistent with the bandgap of the unit structure. In order to reveal the sound insulation mechanism, we have performed a modal analysis of the unit structure. Further, the effects of different dimensional parameters on the structural bandgap are analyzed by changing the structure. The results show that extending the length of the structure inlet or outlet can effectively reduce the start frequency of the low-frequency bandgap, thus achieving the regulation of the sound insulation band. The proposed low-frequency sound insulation ventilation barrier has a simple structure with great application prospects. In addition, the proposed ventilation barrier provides a new idea for noise control in low-frequency ventilation environments.

On seismic isolation of soil-meta-foundation-structure systems

Meta-materials are engineered composites with physical properties that can introduce frequency band gap regions suitable for wave manipulation and filtering. This study investigates the seismic behavior of soil–structure systems with a meta-foundation designed using alternatively repeated layers of concrete and rubber. First, the frequency band gaps of the meta-foundation were derived using the Floquet-Bloch theory. The frequency band gaps for different meta-foundation configurations with infinite and finite numbers of unit cells were presented. Then, a two-dimensional (2D) plane-strain finite element simulation was proposed to study the isolation performance of meta-foundations on or embedded in soil half-space. Finally, two four-story steel structures with different dynamic characteristics were modeled under different input motions. The results show that direct embedment of meta-foundations in soil may break periodicity, requiring special treatments on the side boundaries of the foundation. Moreover, the numerical results show considerably enhanced structural performance for the meta-foundation system with a reduction up to 95.1% and 97.9% for the maximum horizontal acceleration and inter-story drift, respectively, compared to the non-isolated system. The results also indicate enhanced soil response under the meta-foundation and acceptable structural performance outside the band gap frequencies compared to the non-isolated system.

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.

A Novel Unit Cell for Low-Frequency Vibration Suppression Through Meta-Plates: Modeling, Optimization and Testing

Exceptional properties of emerging of unconventional metamaterials including phononic/sonic crystals such as bandgap frequency have made them pertinent in various applications. In this paper, a novel single-phase optimized unit cell is proposed via genetic algorithm interfaced with the FE method. The unit cell parameters are fine-tuned according to two different objective functions over the low-frequency range of 2[Formula: see text]kHz to achieve the widest and maximum bandgaps summation for the in-plane and out-of-plane modes. For the in-plane propagation, almost 1681[Formula: see text]Hz bandgaps summation and a wide 635[Formula: see text]Hz frequency bandgap are obtained. Besides, there have been 1311[Formula: see text]Hz and 368[Formula: see text]Hz bandgap for the other case. Then, the meta-plates acquired through the investigations with finite arrangements are computed numerically and experimentally to mitigate longitudinal and bending wave propagation. It is found that the structures have high-performance capability to suppress the low-frequency vibrations inside the specified area and can substantially attenuate the propagation of elastic waves.

Innovative structural design of chiral lattices with low frequency wide multiple band gaps and vibration suppression

In order to achieve low-frequency vibration and noise reduction, this paper proposes an innovative structure based on the four-ligament chiral structure. The band gap characteristics and the principle of band gap generation are numerically analyzed by using the finite element method. By optimizing the proposed structure, the band gap is obviously transferred to the low frequency. The propagation characteristics of elastic waves with a specific frequency on the passband in the proposed structure are studied. Finally, the calculated band gap frequency range is compared with the finite element simulation results, and the two correspond perfectly. The research shows that the proposed structure has a good bandgap frequency range, which can play a good role in suppressing vibration transmission, and by improving the chiral structure of the basic four ligaments, the bandgap frequency range of the structure can be transferred from a high frequency to low frequency, which provides ideological guidance and scheme for the structural design of metamaterial that suppress low-frequency waves.

Evaluation of the seismic response of frames implemented with metamaterials

This research aims at introducing a new idea in the design of frames to eliminate or suppress the transmission of waves through the structure in a certain designated range of frequencies that is called hereinafter as frequency band gap. To achieve this goal, we apply a concept from the mechanics of metamaterials to the investigated structural system by proposing a new beam-column connection in a multistory 2D frame. Modal and harmonic analysis are carried out for both the new proposed frame and the ordinary one in order to investigate the response of both systems. A thorough time history analysis is applied, also we demonstrate the response of the new proposed model under the loading of 9 different earthquake loads and a comparison between the resulted displacement and base shear is performed. Furthermore, a realization of the new connection is demonstrated. Results, comparison, and discussion are presented. The results show that the new proposed frame exhibits the calculated frequency band gap and the effect of seismic waves with frequencies within the bandgap frequency range was significantly mitigated. The novelty of this research is the ability of the new proposed idea to generate and tailor a frequency band gap in order to prevent the transmission of waves in this range of frequencies through the structural system itself. Consequently, the bandgap range of frequencies for each structure can be tuned depending on the seismic risk of its region on the global scale. This new feature could have a great impact and significant application to mitigate the effects of seismic waves on a structure.

Design of Linear Magnetic Field Sensor Based on Periodically Magnetized Cold Plasma

We have analyzed the impact of a linear magnetic field on the photonic band gaps exhibited by bulk cold plasma, under external square-wave-like periodic magnetic field of fixed magnitude, conceived as an extrinsic photonic crystal. Here photonic band gaps are determined using transfer matrix method (TMM). Here, the impact of an additional linear magnetic field is determined on the band gaps of plasma photonic crystal with constant magnitude of square like periodic magnetic field, for normal incidence. We determine how the additional and magnetic magnetic field affects the photonic band structure (PBS) and reflectance for such extrinsic photonic crystal. It is noted that, as we increase the additional applied magnetic field, the central frequency of band gaps is shifted toward higher frequency regions in GHz. The band edge increases linearly with the applied magnetic field. The shifting in lower band edge less as compared to upper edge. Sensor is a device which detect the stimuli and give output, and many physical parameters can be measured by sensors. The shifting of band edges can be utilized in design of magnetic field sensor. Here shifting in band gaps by variation in the additional applied magnetic field are determined. The larger value of sensitivity gives a good result for sensing-based application. This analysis is based on the band gaps of extrinsic photonic crystal, and can be employed in design of magnetic field sensor with good sensitivity. Moreover, it can find applications in tunable optical devices.

Nonlinearity enhanced wave bandgaps in metamaterial honeycombs embedding spider web-like resonators

Wave propagation in metamaterial honeycombs endowed with periodically distributed nonlinear resonators is addressed. The linear and nonlinear dispersion properties of the metamaterial are investigated. The nonlinear wave propagation equations obtained via a projection method and the Floquet–Bloch theorem are attacked by the method of multiple scales to obtain in closed form the nonlinear manifolds parametrized by the amplitudes, the frequency, and the wave numbers. The effects of the nonlinearity on the frequency bandgaps are thoroughly investigated and the optimization problem of the resonators nonlinearity towards increased bandgap size is tackled to provide a significant practical framework for the design of nonlinear metamaterials.

Low Frequency Attenuation Characteristics of Two-Dimensional Hollow Scatterer Locally Resonant Phonon Crystals.

The finite element method (FEM) was applied to study the low frequency band gap characteristics of a designed phonon crystal plate formed by embedding a hollow lead cylinder coated with silicone rubber into four epoxy resin short connecting plates. The energy band structure, transmission loss and displacement field were analyzed. Compared to the band gap characteristics of three traditional phonon crystal plates, namely, the square connecting plate adhesive structure, embedded structure and fine short connecting plate adhesive structure, the phonon crystal plate of the short connecting plate structure with a wrapping layer was more likely to generate low frequency broadband. The vibration mode of the displacement vector field was observed, and the mechanism of band gap formation was explained based on the spring mass model. By discussing the effects of the width of the connecting plate, the inner and outer radii and height of the scatterer on the first complete band gap, it indicated that the narrower the width of the connecting plate, the smaller the thickness; the smaller the inner radius of the scatterer, the larger the outer radius; and the higher the height, the more conducive it is to the expansion of the band gap.

Effects of randomness and piezomagnetic coupling on the appearance of stop-bands in heterogeneous magnetorheological elastomers

Phononic crystals (PCs) consist of a periodic arrangement of inclusions in a matrix material, and have garnered a great deal of interest owing to a phenomenon known as band gap frequencies in which particular frequency ranges are not able to propagate through the PCs. The aim of this work is to study the effects of magneto-elastic coupling and other parameters such as randomness in geometrical properties, volume fraction and size of inclusions on longitudinal wave propagation and, in particular, on the appearance of stop-band frequencies. The results indicate that the most important parameters deciding whether a frequency is in a stop-band or a pass-band are the randomness in geometrical properties and piezomagnetic coupling. It was observed that piezomagnetic coupling can lead to a widening of the first stop-band range for a periodic microstructure. Moreover, while randomness in particle size leads to a stop-band range and reduced wave transmission in the second pass region, randomness in particle position leads to removal of the pass band ranges compared to periodic structures. Additionally, the influence of piezomagnetic coupling becomes insignificant in fully random structures.