Frequency Range Of Band Gap Research Articles

Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators

Vibration propagates in the form of elastic waves. The tuning of elastic waves is of great significance for vibration and noise reduction. The elastic metamaterials (EMs), which can effectively prohibit elastic wave propagation in the band gap frequency range, have been widely studied. However, once the structures of the EMs are determined, the band gap is also determined. In this paper, a discrete nonlinear elastic metamaterial is proposed. The harmonic balance method is used to derive the nonlinear dispersion relation combined with Bloch’s theorem. The low frequency band gap near the linear natural frequency of local resonators is obtained. The theoretical results show that the nonlinearity will change the starting and ending frequencies of the band gap. In addition, amplitude can also influence the band gap. This means that the amplitude can be changed to achieve the tunability of elastic waves in nonlinear elastic metamaterials. Finally, the theoretical results are verified by numerical simulation, and the results are in good agreement with each other.

Design of periodic arched structures integrating the structural nonlinearity and band gap effect for vibration isolation

In this study, a Roman-bridge-inspired metamaterial for vibration isolation is proposed that simultaneously realizes a geometrical nonlinear structure and band gap effect, through the arrangement of periodic materials in a semicircular arched structure. Finite element analysis and band diagram analysis are performed to verify the effect of the periodic arch-structured metamaterial by calculating the transmissibility and band gap frequency range of cuboid, arched and periodic arched models. Based on the calculation results, the relationship between the geometrical parameters of the periodic arch structure and band gap frequency are analyzed, and an empirical correlation is formulated for the generation of a training database for a machine learning optimization model. The geometrical parameters of the metamaterial were optimized using the machine learning model based on an autoencoder architecture with supervised learning. An optimized metamaterial with a band gap area at three target frequencies is generated by the trained neural network, and the effectiveness of the optimized structure is validated by both numerical analysis and a frequency response test.

Bandgap and Vibration Suppression Mechanisms of Novel Star‐Shaped Hybrid Metamaterials

Herein, a novel star‐shaped hybrid acoustic metamaterial structure is proposed. Based on Bloch's theorem and the finite element method, the bandgap characteristics and the bandgap formation mechanism of different combinations of structures are first analyzed. Then, the propagation characteristics of elastic waves in Model C2 are studied with focus on equal frequency contours, phase velocity, and group velocity. And the attenuation of elastic waves in the finite size structure of Model C2 illustrates that the elastic waves are effectively suppressed in the bandgap frequency range, which further confirms the perfect correspondence between the bandgap and the vibration attenuation region. Finally, the influence of structural parameters on the bandgap is analyzed, as well as the change of the bandgap when the structure undergoes large deformation, which can realize the tunability and flexibility of the bandgap. This study provides important clues for the design of vibration isolators and metamaterials, and shows the good engineering application potential of the structure for vibration isolation.

Analysis of noise attenuation for offshore platform silencer in duct with flow

Recently, the NORSOK standards, which regulate noise and vibration on offshore platforms, were strengthened by prohibiting the use of glass wool for environmental and safety reasons. In addition, the use of sound-absorbing materials in panels and silencers was prohibited. Therefore, developing a silencer that does not use sound-absorbing materials is necessary. In this study, a bandgap expressed by acoustic characteristics of a periodic structure was applied to develop a silencer without sound-absorbing materials. The bandgap is formed in a frequency range in which propagation of acoustic waves is suppressed by setting a specific distance between single units based on periodic structural theory. The designed silencer evaluates the noise attenuation effect of the periodic structure based on a fluid-structure coupling finite-element equation for a plane wave in a stationary medium. In addition, the silencer model was selected by analyzing the regenerated noise originating from the periodic structure in the flow duct. This flow noise is used to analyze the propagation of sound waves based on the FW-H equation. This is achieved by employing the Lighthill acoustic analogy to predict the flow-induced sound pressure. Furthermore, compressed air was injected at the end of the duct in the flow noise experiment to perform measurements. The results from the acoustic and flow noise experiments were compared to confirm the effect of the flow in the duct on noise generation. Moreover, the flow noise analysis based on the flow velocity elucidated the effect of the periodic structure on the flow. In addition, the analysis results were used to investigate its performance of the silencer with the periodic rod arrangement considering the flow noise in the duct and predict its acoustic characteristics in the bandgap frequency range.

Tapered rainbow metabeam for wideband multimode acoustic blocking based on quadruple-mode resonators

We construct a rainbow metamaterial for multimode sound blocking over a broad range of sub-kHz frequencies in the form of a tapered rectangular cross section beam of machined cells based on elements that can, on average, simultaneously attenuate the majority of the possible elastic-wave polarizations. Using aluminum, we construct a five-cell structure containing sub-wavelength planar resonators with interconnected ribs, which couple to compressional, in-plane shear, flexural, and torsional vibrations. Backed up by numerical simulations, we verify that this tapered structure can, on average, strongly attenuate acoustic modes over the frequency range of the combined metamaterial bandgaps, that is over a frequency range representing ∼50% around ∼0.7 kHz. Applications include vibration isolation.

Mitigation of seismic waves using graded broadband metamaterial

In recent years, researchers have shown interest in blocking low-frequency vibrations with the aid of metamaterials due to their inherent wave-filtering properties. However, proposing a practical metamaterial layout remains a challenge, taking into consideration the size, shape, and availability of metamaterial components. This study proposes a new configuration that can increase the range of the attenuation frequency. The configuration focuses on the capability of graded metamaterials in filtering a wide range of wave frequencies that can be generated by low-amplitude waves. To find the best configuration with the widest bandgap, square periodic sections using different materials including steel, rubber, concrete, tungsten, and carbon fiber-reinforced polymer were considered. Unit cells with two layers of materials were examined numerically to determine the attenuation zones and the effect of material properties and core size on the bandgap width and frequency range. Furthermore, the performance of the unit cells in a soil medium under the low-amplitude low-frequency surface and bulk waves is evaluated in the frequency domain using finite element analysis, in which the metamaterial is embedded periodically in a soil medium with different configurations, including a graded distribution. The results show that having an array of unit cells spaced periodically can decrease the transmission of the wave to the protected zone located after the array, and the application of grading can increase the attenuation zones to filter frequencies as low as 4.5 Hz and up to 29 Hz.

Numerical study and topology optimization of vibration isolation support structures

Lightweight design and harmful vibration isolation of supporting structures are the most common design contents in practical engineering, but they are often difficult to be considered together. Phononic crystals have the characteristics of elastic wave bandgaps, which can effectively isolate the vibration within the bandgap frequency range. The integrated coupling design of vibration isolation and structure support by topology optimization is studied in order to make the obtained macro structure with periodic characteristics have both high support structure stiffness and lower frequency vibration isolation bandgaps. Taking a two-dimensional cantilever beam with multiple periodic substructures in the length direction for example, the finite element method and an improved multi-objective genetic algorithm are used to realize the topology iterative change of the substructure mesh, the solution of the substructure band structure and the natural frequency of the cantilever beam. Maze algorithm is used to avoid invalid operation in optimization process and the mesh generation strategy combining coarse mesh and fine mesh is taken to improve the operation efficiency. Two optimization objective functions reflecting the overall support stiffness and relative bandgap width of the cantilever beam are set. The topology design of the substructure with transverse symmetry constraints and bisymmetric constraints are carried out, respectively. The topology optimized structures with bandgaps of different mechanisms are obtained from the Pareto front of the numerical results.

Configuration-controllable porous metamaterial and its bandgap characteristics: Experimental and numerical analysis

Metamaterials that can tune the bandgap by controlling the configuration have prospects for the security of engineering structures. A configuration-controllable metamaterial is developed in this study to achieve effective vibration reduction, and its bandgap characteristics are investigated through experiments and numerical analysis. The metamaterial specimen is designed and fabricated using silicone rubber. A corresponding experimental platform is constructed to achieve a controllable configuration of the metamaterial. Subsequently, the vibration transmission of the specimen with different deformations is tested. The commercial software COMSOL is used to simulate finite-element dynamic models of the unit cell, and the entire structures of the metamaterial is established to analyze their bandgaps and frequency response characteristics. Both the numerical and experimental results demonstrate that the configuration change can significantly affect the bandgap characteristics. With increasing compression, the existing low-frequency bandwidth of the metamaterial narrow, whereas the high-frequency bandwidth broadens. When the metamaterial deformation is larger, a new bandgap appears at a lower frequency. In addition, the effects of the geometric parameters on the bandgaps are revealed. It shows that the frequency range, width and number of bandgaps of the developed metamaterial can be effectively adjusted through configuration control.

New floating slab track isolator for vibration reduction using particle damping vibration absorption and bandgap vibration resistance

• A new floating slab track vibration isolator is developed using particle damping vibration absorption and bandgap vibration resistance. • Using the low-frequency vibration reduction effect of non-obstructive particle damping (NOPD), the attenuation of resonance peaks in the begin of bandgap frequency range is realized. • A coupled train-floating slab track-bridge dynamic model is established to investigate the vibration isolation capability. The environmental vibrations caused by rail transit continue to increase in importance. Even though there are a variety of efficient vibration reduction measures, there is still room for further improvement by trying new, effective vibration control mechanisms. In this paper, a new floating slab track vibration isolator is developed using particle damping vibration absorption and bandgap vibration resistance. Using the low-frequency vibration reduction effect of non-obstructive particle damping (NOPD), the particulate material is added to the outer ring vibrator to participate in vibrations, and the attenuation of resonance peaks in the begin of bandgap frequency range is realized. The energy loss factor and damping ratio of particle damping for different particle sizes are analyzed using a discrete element model. A finite element model with integrated particle damping effect is also formulated and the bandgap behavior of phononic crystal vibration isolator (PCVI) with additional particle damping is analyzed. The effect of particle damping is assessed by calculating the force transmission spectrum. In order to the investigate vibration isolation performance of the combined NOPD-PCVI when subjected to excitation from trains running at different speeds, a coupled train-floating slab track-bridge dynamic model is established. The results show that the NOPD-PCVI offers better vibration isolation than a steel-spring vibration isolator and the traditional PCVI (T-PCVI) in the frequency band of 50–150 Hz. The energy dissipation provided by particle damping and the bandgap damping of phononic crystals reduce the vertical accelerations of the bridge deck in the bandgap frequency band. Specifically, the total vertical accelerations of the bridge deck equipped with NOPD-PCVIs is reduced by 15.3 dB compared to steel springs, and 5.6 dB compared to T-PCVIs, respectively.

Characterization of millimeter wave photonic crystal circulator with a ferrite sphere

In this work, a millimeter wave circulator based on photonic crystals (PCs) with a ferrite sphere is constructed and experimentally characterized. A ferrite sphere can be manufactured through compressed-air puffing method with low cost and high precision, and the symmetrical structure can also simplify the assembly. In photonic crystal waveguide (PCW), the waveguide mode and bandgap frequency range are analyzed to better understand the device design based on PCW. The gyromagnetic ferrite sphere and impedance matcher (consisting of two Teflon cylinder gaskets and two metallic triangular pedestals) provide excellent performance for circulator. The measured isolation and insertion loss within the operation band 24 ∼ 28 GHz is better than 15 dB and 1.5 dB, respectively.

Flexural wave mitigation in metamaterial cylindrical curved shells with periodic graded arrays of multi-resonator

This paper aims to present a theoretical model of flexural wave bandgaps in locally resonant cylindrical curved shell and investigates a technique for broadband wave mitigation using a metamaterial cylindrical curved shell. Firstly, cartesian coordinates are converted to cylindrical coordinates in the cylindrical curved shell structure to construct periodic conditions in the circumferential direction. Then, governing equations are derived by using the extended Hamilton principle, and plane wave expansion (PWE) method is implemented to calculate the band structures of acoustic metamaterial cylindrical curved shells with different multi-resonator parameters. In addition, a periodic graded arrays technique is also utilized to broaden the frequency range of bandgap. Lastly, finite element method (FEM) is used to calculate the band structures and vibration transmission characteristics to verify the accuracy of PWE results. The results disclose that the proposed structure has a good attenuation effect on flexural wave and the periodic graded arrays technique can effectively splice bandgaps of each resonator to enlarge frequency range of the flexural wave mitigation. Hence, the proposed structure can be used to achieve a good attenuation effect on flexural wave in the future.

Tunable acoustic waveguide based on a magnetorheological fluid filling

A novel phononic crystals (PnCs) structure that comprises periodically arranged hollow pillars filled with magnetorheological fluid (MRF) is fabricated by three-dimensional printing. The dispersion relations and transmission characteristics of the PnCs filled with MRF are numerically calculated using the finite element method and verified by experiment. Additionally, straight and bent type waveguides are fabricated. The results show that the MRF filling can control the frequency range at the bandgap and passband of the PnCs plate. The bandgap frequency range shifts to a lower frequency when an external magnetic field is applied.

Wide Rayleigh waves bandgap engineered metabarriers for ground born vibration attenuation

The present study proposes two types of engineered resonant metabarrier designs for ground born vibration attenuation at subwavelength frequency region. By establishing analytical and full-scale 3D numerical models, the effectiveness of metabarrier in attenuating incoming Rayleigh surface waves in the earthquake frequency range of interest is investigated. The metabarrier designs are comprised of a cylindrical steel mass encapsulated inside a hollow concrete setup mounted with low-stiffness rubber bearings. The interaction of surface ground motion caused by the propagation of Rayleigh waves with the vertical resonant mode of metabarriers result in the trapping and/or mode conversion of Rayleigh waves into bulk shear waves that propagate deep into the ground. This so-called wave hybridization or the local resonance phenomena induces an extremely wide low frequency bandgap from both designs that is found effective in attenuating incoming Rayleigh waves at the deep-subwavelength scale. By varying the height and arrangement types of resonant metabarriers, the seismic metawedge phenomena are also investigated. In the bandgap frequency range, the Rayleigh waves attenuation is validated by performing a full-scale 3D numerical frequency response analysis including an actual earthquake record (Imperial Valle-1940 El-Centro) based time history analysis. The findings reported indicate such metabarriers can be embedded into the ground surrounding civil infrastructures to be protected from earthquake hazards.

Pentamode metamaterials with ultra-low-frequency single-mode band gap based on constituent materials

An effective method for realizing ultra-low-frequency single-mode band gap in pentamode metamaterials is proposed based on constituent materials. Results show that the decreasing ratio E/ρ (stiffness/mass density) of constituent material can significantly lower the frequency range of single-mode band gap. By merely replacing the constituent material from Al to rubber, the center frequency f c of single-mode band gap can be reduced nearly 600 times (from 3621 Hz to 6.5 Hz), while the normalized bandwidth Δf/f c and the ratio of bulk modulus B to shear modulus G of pentamode structure keep substantially stable. The nonlinear fitting demonstrates that the relation between f c and E/ρ satisfies the logarithmic function. The two-component pentamode structure is designed to further explore the ultra-low-frequency single-mode band gap. The effects of thick-end diameter D of double-cone, diameter D 0 and material type of additional sphere, on single-mode band gap of two-component system are analyzed. This work is attractive for several ∼Hz acoustic/elastic wave regulations using pentamode metamaterials.

Phononic metastructures with ultrawide low frequency three-dimensional bandgaps as broadband low frequency filter

Vibration and noise control are among the classical engineering problems that still draw extensive research interest today. Multiple active and passive control techniques to resolve these problems have been reported, however, the challenges remain substantial. The recent surge of research activities on acoustic metamaterials for vibration and noise control are testimony to the fact that acoustic metamaterial is no longer limited to pure theoretical concepts. For vibration and noise control over an ultrawide frequency region, 3-D metastructures emerge as a novel solution tool to resolve this problem. In that context, the present study reports a novel proposal for 3-D monolithic phononic metastructures with the capability to induce low frequency ultrawide three-dimensional bandgaps with relative bandwidth enhancements of 157.6% and 160.1%. The proposed monolithic metastructure designs consist of elastic frame assembly that is connected with the rigid cylindrical masses. Such structural configuration mimics monoatomic mass-spring chain where an elastic spring is connected with a rigid mass. We develop an analytical model based on monoatomic mass-spring chain to determine the acoustic mode frequency responsible for opening the bandgap. The wave dispersion study reveals the presence of ultrawide bandgaps for both types of metastructures. The modal analysis shows distribution of vibration energy in the bandgap opening (global resonant mode) and closing (local resonant mode) bounding edges. We further analyze the band structures and discuss the physical concepts that govern such ultrawide bandgap. Vibration attenuation inside the bandgap frequency range is demonstrated by frequency response studies conducted by two different finite element models. Thanks to additive manufacturing technology, 3-D prototypes are prepared and low amplitude vibration test is performed to validate the numerical findings. Experimental results show the presence of an ultrawide vibration attenuation zone that spreads over a broadband frequency spectrum. The bandgaps reported by the proposed metastructures are scale and material independent. The research methodology, modelling and design strategy presented here may pave the way for the development of novel meta-devices to control vibration and noises over a broadband frequency range.

Microstructure-dependent Band Gaps for Elastic Wave Propagation in a Periodic Microbeam Structure

A new model for producing band gaps for flexural elastic wave propagation in a periodic microbeam structure is developed using an extended transfer matrix method and a non-classical Bernoulli–Euler beam model that incorporates the strain gradient, couple stress and velocity gradient effects. The band gaps predicted by the new model depend on the three microstructure-dependent material parameters of each constituent material, the beam thickness, the unit cell length and the volume fraction. A parametric study is conducted to quantitatively illustrate these factors. The numerical results reveal that the first band gap frequency range increases with the increases of the three microstructure-dependent material parameters, respectively. In addition, the band gap size predicted by the current model is always larger than that predicted by the classical model, and the difference is large for very thin beams. Furthermore, both the unit cell length and volume fraction have significant effects on the band gap.

Ultra-wide low-frequency band gap in a tapered phononic beam

We propose a tapered phononic beam with a broad low-frequency band gap for flexural waves. A unit cell of the phononic beam consists of two identical uniform parts and a thickness- and width-varying part sandwiched between them. Thickness and width profiles and uniform beam length are controlled to change the shear and rotational stiffnesses of the phononic beam, changing the starting and ending frequencies of the first band gap. By identifying the effects of those geometrical parameters on band structures, we determine the parameter values that enable the phononic beam to yield an ultra-broad and ultra-low band gap from 3.6 Hz to 237.9 Hz with a small lattice constant of λ/25. For experimental realization, a finite phononic beam with three unit cells is fabricated by wire electric discharge machining and its displacement transmission is measured through impact hammer tests. Particularly low transmission of -35 dB to -10 dB is observed at the band-gap frequency range. We briefly present ongoing works to enhance the structural robustness of the phononic beam by changing geometrical parameters or material of a thin and narrow part.

Numerical simulation study on band gap characteristics of surface phononic crystal with spherical composite column

In the study of acoustic characteristics of micro-scale surface phononic crystal, the band gap characteristics below 100 MHz need to be further optimized. In this work, a piezoelectric surface phononic crystal with a composite column composed of nickel balls and epoxy backing is proposed. The finite element method is used to calculate the band gap characteristics and displacement vector field of the model. The influence of column radius on the band structure is studied, and meanwhile, the effect of the multi-layer composite column structure on the band gap is discussed via increasing the number of elements in the composite column, while the reason for the opening of the high-order band gap is analyzed in detail by combining the vibration mode. Furthermore, the temperature adjustability of the band gap is further studied. The results show that the spherical composite column deposition structure can open a wider complete band gap of surface acoustic wave in a lower frequency range than the existing inverse conical surface phononic crystal structure with the same lattice constant (Hsu J C, Lin F S <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.7567/JJAP.57.07LB01">2018 <i>Jpn. J. Appl. Phys.</i> <b>57</b> 07LB01</ext-link>). The restricted cavity mode is easily formed between the hard boundaries with the increase of column radius, which provides a possible way for low-order vibration modes to open high-order band gaps. There exist mode inheritance and energy coupling between adjacent modes, which leads the band gap to flatten and anti-flatten. Moreover, the real-time adjustment of band gap frequency by external temperature field can be realized via introducing the temperature-sensitive material epoxy resin into the structure. The band gap frequency range can be effectively reduced by increasing the number of composite cylinder layers, while the multi-vibrator structure can generate multipole resonance coupling with traveling wave and finally open a complete band gap between high-order frequency bands. This work provides a theoretical reference for analyzing the low-frequency band gap mechanism of micron-scale surface phononic crystal.

Electrostatic Wave Propagation in 1-D Magnetized Plasma Periodic Structures

The theory of electrostatic (or, more accurately, slow electric or quasi-electrostatic) waves propagation in 1-D magnetized plasma periodic structures, at frequencies below both the plasma and cyclotron frequencies, is presented using the transfer matrix method. It assumes that the applied static magnetic field is perpendicular to the surface of the plasma layers. The dispersion relation of the waves is obtained and it is shown to break up into bands of allowed and forbidden propagation, which are conspicuous in periodic structures. Furthermore, the transmittance behavior of the electrostatic waves as a function of frequency is studied. At a fixed value of the wavenumber, the frequency range of forbidden band gaps is found to become smaller by increasing the plasma width, while the forbidden band gaps become broader as external magnetic field increases.

Broadening bandgap of thermocrystal by tailoring air hole

Thermocrystal is a new type of artificial periodic crystal structure, which reduces the thermal conductivity of materials. The main factor affecting the thermal conductivity of thermocrystals is the coverage area between the bandgap frequency range and the thermal spectrum. In this letter, we found that, compared with the circular air hole, the elliptical air hole can significantly improve the thermal bandgap of thermocrystal, which will effectively reduce the thermal conductivity. Among them, the cross-shaped ellipse air hole can widen the thermal bandgap of thermocrystal to more than twice. This improves the efficiency of heat transfer by 62%.