Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Effects of core position of locally resonant scatterers on low-frequency acoustic absorption in viscoelastic panel

Locally resonant sonic materials, due to their ability to control the propagation of low-frequency elastic waves, have become a promising option for underwater sound absorption materials. In this paper, the finite element method is used to investigate the absorption characteristics of a viscoelastic panel periodically embedded with a type of infinite-long noncoaxially cylindrical locally resonant scatterers(LRSs). The effect of the core position in the coating layer of the LRS on the low-frequency(500 Hz–3000 Hz) sound absorption property is investigated. With increasing the longitudinal core eccentricity e, there occur few changes in the absorptance at the frequencies below 1500 Hz, however, the absorptance above 1500 Hz becomes gradually better and the valid absorption(with absorptance above 0.8) frequency band(VAFB)of the viscoelastic panel becomes accordingly broader. The absorption mechanism is revealed by using the displacement field maps of the viscoelastic panel and the steel slab. The results show two typical resonance modes. One is the overall resonance mode(ORM) caused by steel backing, and the other is the core resonance mode(CRM) caused by LRS. The absorptance of the viscoelastic panel by ORM is induced mainly by the vibration of the steel slab and affected little by core position. On the contrary, with increasing the core eccentricity, the CRM shifts toward high frequency band and decouples with the ORM, leading to two separate absorption peaks and the broadened VAFB of the panel.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Wide-band underwater acoustic absorption based on locally resonant unit and interpenetrating network structure

The interpenetrating network structure provides an interesting avenue to novel materials. Locally resonant phononic crystal （LRPC） exhibits excellent sound attenuation performance based on the periodical arrangement of sound wave scatters. Combining the LRPC concept and interpenetrating network glassy structure, this paper has developed a new material which can achieve a wide band underwater strong acoustic absorption. Underwater absorption coefficients of different samples were measured by the pulse tube. Measurement results show that the new material possesses excellent underwater acoustic effects in a wide frequency range.Moreover, in order to investigate impacts of locally resonant units,some defects are introduced into the sample. The experimental result and the theoretical calculation both show that locally resonant units being connected to a network structure play an important role in achieving a wide band strong acoustic absorption.

Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. Sánchez-Dehesa （Phys. Rev. B 67 14 4301（2003））, it is shown that there exists an error of about 50% in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

Oblique incidence properties of locally resonant sonic materials with resonance and Bragg scattering effects

A locally resonant sonic material （LRSM） is an elastic matrix containing a periodic arrangement of identical local resonators （LRs）, which can reflect strongly near their natural frequencies, where the wavelength in the matrix is still much larger than the structural periodicity. Due to the periodic arrangement, an LRSM can also display a Bragg scattering effect, which is a characteristic of phononic crystals. A specific LRSM which possesses both local resonance and Bragg scattering effects is presented. Via the layered-multiple-scattering theory, the complex band structure and the transmittance of such LRSM are discussed in detail. Through the analysis of the refraction behavior at the boundary of the composite, we find that the transmittance performance of an LRSM for oblique incidence depends on the refraction of its boundary and the transmission behaviors of different wave modes inside the composite. As a result, it is better to use some low-speed materials （compared with the speed of waves in surrounding medium） as the LRSM matrix for designing sound blocking materials in underwater applications, since their acoustic properties are more robust to the incident angle. Finally, a gap-coupled LRSM with a broad sub-wavelength transmission gap is studied, whose acoustic performance is insensitive to the angle of incidence.

Analysis of underwater decoupling properties of a locally resonant acoustic metamaterial coating

This paper presents a semi-analytical solution for the vibration and sound radiation of a semi-infinite plate covered by a decoupling layer consisting of locally resonant acoustic metamaterial. Formulations are derived based on a combination use of effective medium theory and the theory of elasticity for the decoupling material. Theoretical results show good agree- ments between the method developed in this paper and the conventional finite element method （FEM）, but the method of this paper is more efficient than FEM. Numerical results also show that system with acoustic metamaterial decoupling layer exhibits significant noise reduction performance at the local resonance frequency of the acoustic metamaterial, and such performance can be ascribed to the vibration suppression of the base plate. It is demonstrated that the effective density of acoustic metamaterial decoupling layer has a great influence on the mechanical impedance of the system. Furthermore, the resonance frequency of locally resonant structure can be effectively predicted by a simple model, and it can be significantly affected by the material properties of the locally resonant structure.

Impact vibration properties of locally resonant fluid-conveying pipes

Fluid-conveying pipe systems are widely used in various equipments to transport matter and energy.Due to the fluid–structure interaction effect,the fluid acting on the pipe wall is easy to produce strong vibration and noise,which have a serious influence on the safety and concealment of the equipment.Based on the theory of phononic crystals,this paper studies the vibration transfer properties of a locally resonant(LR)pipe under the condition of fluid–structure interaction.The band structure and the vibration transfer properties of a finite periodic pipe are obtained by the transfer matrix method.Further,the different impact excitation and fluid–structure interaction effect on the frequency range of vibration attenuation properties of the LR pipe are mainly considered and calculated by the finite element model.The results show that the existence of a low-frequency vibration bandgap in the LR pipe can effectively suppress the vibration propagation under external impact and fluid impact excitation,and the vibration reduction frequency range is near the bandgap under the fluid–structure interaction effect.Finally,the pipe impact experiment was performed to verify the effective attenuation of the LR structure to the impact excitation,and to validate the finite element model.The research results provide a technical reference for the vibration control of the fluid-conveying pipe systems that need to consider blast load and fluid impact.

Negative Poisson’s ratio locally resonant seismic metamaterials vibration isolation barrier

In recent decades,the application of seismic metamaterials to protect civil infrastructures being free of the damage of earthquakes has been attracting extensive attention.Specifically,the proposed locally resonant seismic metamaterials provide the probability of isolating the low-frequency seismic wave using a small-size isolation barrier.However,in previous studies,the energy absorption properties of locally resonant seismic metamaterials remain one of the least understood aspects of isolation.Benefit from the fascinating energy absorption characteristic of negative Poisson ratio(NPR)metamaterial,we creatively design a new seismic metamaterial structure by assembling the locally resonant seismic metamaterial and NPR metamaterial,to isolate seismic waves.The sound cone technique combining the transmission spectrum is employed to identify the surface wave from the hybrid waves.The generation mechanism of frequency bandgap and the isolation effectiveness of the proposed seismic metamaterial are discussed in detail.The results indicate that the generation of ultra-low and ultra-wide frequency bandgap with the range of 0.65 Hz–18.9 Hz is attributed to the locally resonant and energy absorption of the proposed seismic metamaterial structure and the excellent isolation effect is achieved by transforming the surface wave into the bulk wave.The frequency bandgap narrows as the distance increases between each resonator.In addition,the mechanical properties of the NPR bearing,such as the Poisson ratio,mass density,and elastic modulus,have remarkable impact on the frequency bandgap,especially on the upper bound frequency.In practical engineering,the NPR bearing with a low Poisson ratio,small mass density,and high elastic modulus is suggested for the design of the NPR locally resonant seismic metamaterial structures.Time domain analysis for the practical seismic wave verifies that the proposed seismic metamaterial has a promising application in isolating ultra-low and ultra-wide seismic waves,with the isolation effectiveness larger than 70%.This work contributes a new locally resonance seismic metamaterial design idea for isolating and adjusting the low-frequency seismic wave.

Research on embedded locally resonant metamaterials used for vibration attenuation of thin-walled workpieces in mirror milling

The shell composed of large-scale parts is the essential component of mechanical structures in the aerospace,shipping,and railway industries.These workpieces are characterized by thin walls and weak rigidity,thus requiring an effective technology for high-performance machining.Accordingly,an embedded locally resonant metamaterial with double resonators is proposed and combined with the magnetic follow-up support technology to attenuate the vibration of thin-walled parts for the first time.The band structures and parametric adjustment laws are systematically investigated and validated by analytical calculation and finite element method,which proves the proposed model is broadband,lightweight,and flexible in low frequencies.Its characteristics,as well as the relatively simple structure,are unique advantages for thin-walled structure milling.Finally,mirror milling experiments have been performed to assess the slave module with the proposed substructure.From the results,the root mean square amplitude of the thin-walled workpiece with the combined device decreases by nearly 9%,which means that the performance has been improved by the combined device.Furthermore,this work provides an integrated and efficient solution for vibration suppression in thin-walled parts milling,which extends locally resonant metamaterials to practical engineering fields and helps to improve the status quo of mirror milling from the perspective of metamaterials.

Numerical and Experimental Investigations on Tunable Low-frequency Locally Resonant Metamaterials

In this paper,a tunable locally resonant metamaterial is proposed for low-frequency band gaps.The local resonator composed of two pairs of folded slender beams and a proof mass is designed based on the theory of compliant mechanism.The design optimization on geometric parameters is carried out to fulfil the quasi-zero-stiffness property.The locally resonant metamaterial is formed by periodically arranged unit cells,and the transmittance of longitudinal wave is studied through three aspects:numerical predictions,finite element simulations and experimental tests.The variation trends revealed by these three methods match well with one another:the band gap moves to lower frequency and both its depth and width get smaller and smaller with the increase of pre-compression(Δ).The band gap overlays the frequency range of 73.10–92.38 Hz and 16.78–19.49 Hz atΔ=0mm andΔ=10mm,respectively,providing a wide range of tunability.Besides,the ultralow-frequency band gap can be achieved asΔapproaches 10 mm.This study may provide an avenue for achieving the tunable ultralow-frequency locally resonant band gap.

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation,which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits.Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant（LR）band gap（BG） with a much smaller transmission factor：（1） the structure is arrayed periodically while the resonant shunt circuits are aperiodic;（2） the resonant shunt circuits are periodic while the structure is aperiodic.The transmission factor curve is calculated,which is validated by the finite element method.Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.

Local resonant characteristics of a layered cylinder embedded in the elastic medium

Three kinds of resonant modes of a single layered circular elastic cylinder embedded in the elastic medium are analysed by considering the oscillation of the scatter＇s core, based on the fact that the core moves as a rigid body when the shell material is very compliant. The resonant frequencies of the single resonator acquired by our method are in good agreement with those calculated by the local interaction simulation approach （LISA） for the local resonant phononic crystal. Therefore, the local resonant characteristics of a single layered circular elastic cylinder can be used to evaluate the resonant frequencies of the phononic crystal. The effects of the geometrical and physical parameters of the shell and the core are also studied in details. This work is significant for designing the locally resonant phononic crystal based on the local resonant characteristics of the single resonator, and the resonant frequencies can be tuned by selecting the geometrical sizes and the materials.

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.

Modeling and analysis of gradient metamaterials for broad fusion bandgaps

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes,a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed.First,an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes,and a novel periodic structure unit model is constructed for vibration reduction.Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure,the material parameters,structural parameters,and the arrangement interval of the periodic structure unit are optimized.The finite element method(FEM)is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure.Then,the wave/spectrum element method(WSEM)and experimental test are used to verify the calculated results above.Lastly,the vibration attenuation characteristics of the structure under different conditions,such as rubber material parameters,mass ring material,and fluid-structure coupling effect,are analyzed.The results show that the structure can produce a complete bandgap of 46 Hz-75 Hz in the low-frequency band below 100 Hz,which can effectively suppress the low broadband vibration of the fluidconveying pipe.In addition,a high damping rubber material is used in the design of the periodic structure unit,which realizes the effective suppression of each formant peak of the pipe,and improves the vibration reduction effect of the fluid-conveying pipe.Meanwhile,the structure has the effect of suppressing both bending vibration and longitudinal vibration,and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe.The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

Layered metastructure containing freely-designed local resonators for wave attenuation

Combining periodic layered structure with three-dimensional cylindrical local resonators,a hybrid metastructure with improved wave isolation ability was designed and investigated through theoretical and numerical approaches.The metastructure is composed of periodic rubber layers and concrete layers embedded with three-dimensional resonators,which can be freely designed with multi local resonant frequencies to attenuate vibrations at required frequencies and widen the attenuation bandgap.The metastructure can also effectively attenuate seismic responses.Compared with layered rubber-based structures,the metastructure has more excellent wave attenuation effects with greater attenuation and wider bandgap.

Research Progress of Underwater Soundabsorbing Material

This article provides an overview of underwater sound-absorbing materials mainly applied with polyurethane matrix.It mainly elaborates on the underwater sound mecha-nism,commonly used underwater sound-absorbing materials and structures,as well as new underwater sound-absorbing material structures derived from local resonance pho-nonic crystals,such as phononic crystals,local resonance phonon wood piles,and meta-material sound-absorbing structures.This provides a broader development space and direction for the future development of underwater sound-absorbing materials.

Electro-mechanical coupling properties of band gaps in an with periodically attached “spring-mass” resonators

The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling Euler beam theory, nonlocal piezoelectricity theory and plane wave expansion (PWE) method. Three complete band gaps with the widest total width less than 10GHz can be formed in the proposed nanobeam by comprehensively comparing the band structures of three kinds of LR PC nanobeams with resonators attached or not. Furthermore, influencing rules of the coupling fields between electricity and mechanics,“spring-mass” resonator, nonlocal effect and different geometric parameters on the first three band gaps are discussed and summarized. All the investigations are expected to be applied to realize the active control of vibration in the region of ultrahigh frequency.