Local Resonance Mechanism Research Articles

Multi-objective optimized design of two-dimensional multi-phase phononic crystals with materials self-selection

In this paper, the multi-objective optimization problem (MOOP) of selecting suitable materials from four materials for phononic crystals layouts is investigated based on an optimization method combined nondominated sorting-based genetic algorithm II (NSGA-II) and finite element method (FEM). Driven by different optimization objectives, the changes in the optimized structure compared to the seed structure are the change of the bandgap mechanism from a local resonance mechanism to a Bragg scattering mechanism, the change of the included materials from four to three, and the significant change in the location and extent of the pores and other materials, respectively. The obtained nondominated Pareto solution of MOOP can balance the bandgap and the structural mass, which provides the decision-maker trade-off to select the appropriate optimized solution. Compared with the single-objective optimization problem (SOOP), the MOOP not only obtains a nondominated solution close to the result of SOOP, but also obtains other nondominated solutions of MOOP, which proves the effectiveness of the optimization algorithm in this paper. The design method in this paper can be easily extended to select suitable materials from a wider variety of materials for bandgap optimization design of PnCs, which has very promising applications.

Research on the Vibration Reduction Design of Camshaft Swing Grinding Based on Local Resonance Mechanism

Research on the Vibration Reduction Design of Camshaft Swing Grinding Based on Local Resonance Mechanism

Multilayer coupled plate-type acoustic metamaterials for low-frequency broadband sound insulation

Acoustic metamaterials have been becoming a popular topic for the better sound insulation at low frequency than traditional materials. However, due to the local resonance mechanism, this excellent performance can only be demonstrated in narrow frequency bands. Therefore, multilayer coupled plate-type acoustic metamaterials (MPAM) are proposed in this paper. The structure consists of a large plate-type acoustic metamaterial (PAM) with periodic square metamaterial units and double-layer fibers with different densities. According to finite element study on the insertion loss (IL) of the MPAM, the governing physical mechanism of the MPAM was analyzed according to the sound pressure level distributions and the vibration modes of the PAM layer. In addition, large-scale MPAM samples with a size of 506 mm*506 mm were manufactured, the reverberation and anechoic chamber was employed to verify the sound insulation performance. It can be concluded from the test results that the IL peak originate from the anti-resonance of the PAM layer rather than the weight of the materials. Compared to the structures without PAM layer, in the range of 360 Hz−950 Hz, the IL is increased by 5 dB at least and up to 17 dB at most. The influences of the incident angles, the frame density and the coverage rate of the PAM layer on the IL are disscussed. The proposed MPAM structure, analytical techniques and test results may be helpful for the engineering application of acoustic metamaterials.

Tapered resonator-based phononic crystal: Avoided level crossings, robust self-collimation, and bi-refringence

In search of novel phononic crystals to effectively control the propagation of elastic waves, we propose a new single-material phononic crystal (PnC) with unit cells containing tapered resonators (TRs). The thickness of the circular taper radially decreases outward from the center. The device modulates dispersion of the wave by a local resonance mechanism and by slowly varying the group velocity of elastic waves. The TRs are layered on the top of a conventional PnC slab with a square arrangement of air holes. The band structure of the PnC is theoretically studied and a comparison is drawn between the avoided level crossings and the symmetry-protected ordinary degeneracies. In the absence of a bandgap, the zero group velocity at the band maximum restricts the waves from propagating. Moreover, the design shows anomalous dispersion phenomena such as self-collimation and bi-refringence, which are rare in conventional PnCs. We trace the origins of these phenomena by analyzing equifrequency contours associated with relevant frequencies. We show that the self-collimation effect persists even with a small variation in the angle of incidence and a perturbative hole at the center of each of the TRs. Within the classical limit, the scale invariance of the elastic wave equation makes the device useful in both the low frequency ultrasonic and the high frequency phononic regime.

Topologically tunable local-resonant origami metamaterials for wave transmission and impact mitigation

Origami metamaterials can control the propagation and energy transmission of elastic waves via the flexible design of microstructure topology, which has great application prospects in the field of structural impact resistance. In this paper, by integrating the Bloch theorem and the local resonance (LR) mechanism, a tunable hybrid origami metamaterial (HOM) is proposed to achieve low-frequency and broad bandgaps (BGs) for realizing wave transmission and impact mitigation. The elastodynamic wave equation of the HOM is established based on the Mindlin plate theory and discretized with the higher-order spectral elements, and band structures of the HOM are obtained through the semi-analytical periodic spectral plate (PSP-SAFE) methods. Effective dynamic properties of the HOM are numerically calculated to explain wave transmission behavior. Interestingly two complete BGs in the low-frequency range are found, and the proposed metamaterial can broaden the low-frequency bandgaps by coupling the polarization BGs and local resonance BGs. The influences of three significant parameters on two complete BGs within the region of interest are then discussed. Furthermore, the wave mitigation capacity of locally resonant HOM is investigated under impact pulses. It is noted that the reaction peak force of the HOM possesses an approximately 25.7% better reduction than that of origami structures with no mass inclusion. Especially when the external excitation frequency is consistent with local-resonance BGs, the transmission rate shows dramatically decrease due to the dramatic dissipation of energy in space. The locally resonant hybrid origami metamaterial shows promising potential for applying low-frequency wave attenuation and impact mitigation.

Emergence of negative-dispersion passbands below the ring frequency of a piezoelectric meta-shell

The local-resonance (LR) mechanism is usually employed to induce bandgaps in the scope of metamaterials. On the contrary, we investigate LR passbands in this paper, which are located below the ring frequency of a piezoelectric meta-shell shunted with resonant circuits. The flexural wave properties of the meta-shell are investigated analytically through dispersion relations, and also verified by numerical results. It is observed that the piezoelectric shunting could induce longitudinal bandgaps above the ring frequency, while passbands below the ring frequency. Interestingly, negative dispersions may appear in this longitudinal passband when negative bending rigidity is induced through the piezoelectric bending effect, implying that the group velocity of flexural wave is opposite to its phase velocity. We demonstrate such rigidity-correlated dispersion behaviors through energy flow analysis based on the Poynting vector. It is also revealed that the curvature of shells impacts the width of negative-dispersion passbands, with the smaller radius leading to narrower passbands. Since the curvature couples in-plane vibrations and out-of-plane vibrations, it facilitates flexural-wave passbands below the ring frequency as well by introducing the piezoelectric tensional effect, but with dispersions maintaining positive. Moreover, we find that if the piezoelectric shunting induces the bending effect and the tensional effect simultaneously, their interplay at the overlap frequency range may create negative-dispersion passbands above the ring frequency, whereas cancels the impacts with each other below the ring frequency. The results in this research break the limitation that flexural wave propagation below ring frequencies of shells is conventionally not allowed in the longitudinal direction. It also offers the opportunity to implement unprecedent wave properties related to negative dispersions, such as negative refraction and superlensing, with single-negative curved metamaterials.

An engineering feasible metastructure: Ring-spring-resonator based sandwich metabeam for vibration attenuation

Local resonance mechanisms have attracted a great deal of attention due to their bandgap property. In this paper, an engineering feasible ring-spring-resonator based metabeam (RSR-B), consisting of wire rope isolators and mass blocks, was designed based on the mechanism of two-stage vibration system and local resonance. Three kinds of metabeams were prepared and their vibration attenuation properties were investigated theoretically, numerically and experimentally. These metabeams are easily made and have many advantages in vibration attenuation over ordinary vibration isolation beams. The first and second metabeams are both merely manufactured by one kind of ring-spring-mass resonators, which means the monotonic and narrow bandgap. Considering the arrangement form of resonators, two kinds of resonators are combined to form the third metabeam, which has an obviously widened bandgap, completely covering the bandgaps of the first and the second metabeams.

Theoretical and Experimental Investigations on the Ultra-Low-Frequency Broadband of Quasi-Static Metamaterials

This paper proposes an I-shaped radial elastic metamaterial with ultra-low-frequency broadband characteristics and studies the propagation characteristics of elastic waves in their quasi-static state. Through the calculation of the dispersion relationship, the frequency response function, and the eigenmode displacement field, it is found that the ultra-low-frequency wide band gap can be generated in the quasi-static metamaterial. The wide band gap is mainly caused by modal transitions. The equivalent mass–spring model reveals the modal changes of the I-shaped radial elastic metamaterial under the surface constraints. Furthermore, by studying the directional vibration displacement field of the finite period structure, it is demonstrated that the mechanism of the ultra-low-frequency broadband (0<Reduced frequency(Ω)<0.20) is the local resonance mechanism. Subsequently, the influence of the geometric and the material parameters on the location and width of the band gap is explored numerically. Finally, based on the model, through the hammer modal experiment, it is proven that the quasi-static structure yields an ultra-low-frequency stop band of 0.1–1012 Hz. The research conclusions can be applied to mechanical engineering fields such as ultra-low-frequency vibration reduction.

Q-Factor Enhancement of Coupling Bragg and Local Resonance Band Gaps in Single-Phase Phononic Crystals for TPOS MEMS Resonator.

This paper presents a type of single-phase double “I” hole phononic crystal (DIH-PnC) structure, which is formed by vertically intersecting double “I” holes. By using the finite element method, the complex energy band curve, special point mode shapes, and different delay lines were calculated. Numerical results showed that DIH-PnC yielded ultra-wide band gaps with strong attenuation. The formation mechanism is attributed to the Bragg-coupled local resonance mechanism. The effects of the pore width in DIH-PnC on the band gaps were further explored numerically. Significantly, as the pore width variable, the position of the local resonance natural frequency could be modulated, and this enabled the coupling between the local resonance and the Bragg mechanism. Subsequently, we introduced this DIH-PnC into the thin-film piezoelectric-on-silicon (TPOS) resonator. The results illustrated that the anchor loss quality factor () of the DIH-PnC resonator was 20,425.1% higher than that of the conventional resonator and 3762.3% higher than the of the cross-like holey PnC resonator. In addition, the effect of periodic array numbers on was researched. When the reached 1.12 × 106, the number of the period array in DIH-PnC only needed to be 1/6 compared with cross-like holey PnC. Adopting the PnC based on the coupling Bragg and local resonance band gaps had a good effect on improving the of the resonator.

Static mechanical properties and stress wave attenuation of metaconcrete subjected to impulsive loading

To mitigate shock wave propagation, a conventional engineered aggregate (EA) consisting of solid core coated with relatively soft material was designed to be tuned at targeted frequencies based on the local resonance mechanism. Previous studies demonstrated that metaconcrete consisting of conventional engineered aggregates (EAs) exhibited favourable attenuation performance of impulsive loading effects on structures. However, it was also found that the existence of the soft coating on conventional EA caused a reduction in the compressive strength of metaconcrete. In this study, a new type of EA by adding a relatively stiff shell outside the soft layer of the conventional EA was developed to overcome the issue of strength reduction whilst keeping its favourable wave attenuation properties. Quasi-static mechanical properties of metaconcrete consisting of conventional and newly developed EAs were examined through standard compression tests. The dynamic responses of the cylindrical metaconcrete specimens subjected to non-destructive and destructive impulsive loadings were also tested to investigate its wave attenuation capacity. The failure processes and the failure modes of metaconcrete made of different types of EAs under destructive tests were compared. It was found that adding a stiffer shell to the conventional EAs can improve the mechanical properties of metaconcrete while still keeping its good performance in mitigating stress wave propagation under both destructive and non-destructive loads.

New metamaterial mathematical modeling of acoustic topological insulators via tunable underwater local resonance

This study presents a new type of active underwater local resonance metamaterial mathematical model for topologically protected acoustic wave propagation. The underwater acoustic metamaterial consists of arrays of core cylinders coated with soft shells periodically located in a water environment. An efficient but simple computational model is established to analytically predict the system band behavior. Compared to a system with only Bragg scatters, two double Dirac cones (DDCs) are observed in the dispersion curve due to the local resonance mechanism. The result obtained from numerical analysis shows great consistency with analytical prediction. By tuning structural parameters, the four-fold degeneracy is realized at the center of the irreducible Brillouin zone, i.e., the Γ point. It leads to the generation of two dipolar states and two quadrupolar states. Motivated by the theoretical prediction, locations of the cylinders are tuned and the closing-reopening phenomenon of bandgaps in both higher frequency region and lower region is observed with topologically protected phase transition. Besides, it is found that two frequency domains for topologically protected interface modes (TPIMs) occur. It provides potentials for two passive working frequency ranges without structural reconstruction or active tuning of the system. The effects of temperature on TPIM behavior are also demonstrated. Both working frequencies of TPIMs can be easily tuned to different ranges without influencing the quality of TPIMs. Besides, robustness and defect-immune properties of the topologically protected wave propagation are exhibited. With temperature control, this smart system can be performed as an acoustic metamaterial switch device.

Prey Impact Localization Enabled by Material and Structural Interaction in Spider Orb Webs

AbstractSpider webs are mechanical systems able to deliver an outstanding compromise between distinct requirements such as absorbing impacts and transmitting information about vibration sources. Both the frequency information and amplitude of input signals can be used by the spider to identify stimuli, aided by the mechanical filtering properties of orb webs. In this work, a numerical model based on nonlinear stress–strain constitutive relations for spider silk is introduced to investigate how the spider orb web allows spiders to detect and localize prey impacts. The obtained results indicate how the orb web center relative transverse displacements, produced by local resonance mechanisms, are used for precise localization, while nonlinear stress stiffening effects improve prey sensing. Finally, it is also shown that, although beneficial, a large number of radial threads may not be necessary for prey localization.

Vibration-reduction optimization of the point-supporting floating-slab track based on local resonance mechanism

With the continuous increase of subway operating mileage, the problem of subway vibration has become more and more significant. Nowadays, the point-supported floating-slab track is recognized as the best method to control track vibration, which is mainly designed based on the mass-spring-damping theory. How to further improve the vibration control ability of the point-supported floating-slab track? In this paper, a new type of rubber point-supported floating slab track is designed based on the local resonance theory. Through calculation and dynamic test, it is obtained as follows: (1) The band gap of the point support structure by local resonance type depends on the two vertical vibration modes. (2) As the elastic modulus of the cladding layer increases, the bandwidth of the band gap of the corresponding structure increases significantly. (3) The increase of the vibrator density can increase the bandwidth, while reducing the start and stop frequencies, which is beneficial to attenuate the resonance of the floating-slab track. (4) The cushion material parameters of point support structure by local resonance type 2 will not affect the band gap. The increase in sleeve density will reduce the band gap, which is not conducive to vibration reduction. Local resonance type floating-slab track will be the development direction of track vibration-reduction measures in the future.

Multi-parameter independent manipulation for flexural wave by notched metasurface

There are two severe limitations of current flexural wave metasurface based on local resonance mechanism or modal conversion method: low transmittance and only a single manipulation parameter. Inspired by the interaction between notches and flexural waves, we propose a high transmittance and multi-parameter independent manipulation metasurface composed of an array notches. Firstly, based on the phase shift accumulation method, a full 2π phase shift is achieved by modulating four notch parameters independently. Secondly, the refraction and focusing metasurfaces are designed based on the generalized Snell's law and compared with the simulation results. Finally, the designed focusing metasurfaces is validated by corresponding experiments. The four metasurfaces have a good performance for broadband flexural wave focusing, and the numerical and experimental focal lengths are in great agreement with the theoretical values. The notched metasurface provides an innovative way to manipulate flexural waves without resonators, which can be used in the applications of energy harvesting, waveguide design and ultrasonic detection.

Impact mitigation performance of hybrid metamaterial with a low frequency bandgap

Elastic metamaterials exhibit a significant potential in wave attenuation and impact mitigation application owing to their unusual dynamic performance. This work is aimed at investigating the properties and impact mitigation performance of a novel hybrid metamaterial (HMM) fabricated using 3D printing based on a selective laser sintering (SLS) technology. This HMM consists of periodic mass inclusions integrated with a conventional reentrant frame, producing a local resonance mechanism and negative Poisson's ratio properties. Dispersion characteristics and vibration modes are numerically demonstrated, and the results indicate three wide bandgaps in low frequency ranges induced by the local resonance mechanism. The wave attenuation capacity of the HMM is explored numerically and experimentally, and it proves that the bandgap of the HMM can be flexibly tailored by adjusting geometrical configuations of HMM. A comprehensive comparison between the wave mitigation capacity of HMM and the base reentrant structure is established computationally under different modulated unit impact pulses. When the bandgap overlap ratio is 42.5%, HMM can reduce the transmitted peak force by a factor of 2.17 and the root mean square (RMS) value of the reaction force by a factor of 1.59, highlighting the role of bandgap overlap ratio in enhancing the impact mitigation performance of HMM. Furthermore, an impact test indicates that the HMM shows an approximately 22.6% better mitigation performance under the same impact energy than that of a conventional reentrant structure. These results confirm the potential application of the proposed hybrid metamaterial in impact mitigation and noise control.

Bandgap mechanism and vibration reduction property of wave-resistance sleeper with negative effective mass density

Based on the capability of controlling low-frequency elastic waves in solids with subwavelength size, locally resonant phononic crystals have potential applications in track vibration reduction. By periodically embedding 3D locally resonant unit cells (LRUCs) in a concrete matrix, a wave-resistance sleeper with a negative effective mass density is proposed, and the generation mechanism of the bandgap and parameter sensitivity are studied. Furthermore, the vibration mitigation performance of the wave-resistance sleeper applied to the ballastless track is analyzed. The results show that the local resonance of the LRUC results in negative responses in the wave-resistance sleeper to the vibration excitation, and a bandgap is generated in this frequency range. By changing the elastic modulus of the coating or the core density, the boundary frequencies of the bandgap of the wave-resistance sleeper can be effectively adjusted, and the bandwidth can be expanded by increasing the ratio of core radius to coating thickness, or by increasing the filling fraction, and adopting a thinner steel spherical shell. The bandgap of the wave-resistance sleeper was verified by test results. Based on the local resonance mechanism, the wave-resistance sleeper can effectively prohibit vibrations at multiple design frequencies from transmitting to the track bed.

Investigation of novel 3D-printed diatomic and local resonant metamaterials with impact mitigation capacity

A novel dual local resonance metamaterial chain, at a low frequency regime (<200 Hz), is designed and fabricated using selective laser sintering technology for characterization of wave attenuation and impact mitigation, consisting of a main structure and cantilever-in-mass resonators as a periodic sub-structure. The dispersion characteristics and mode polarization of metamaterial chains with various resonators are studied using a mass-spring model and finite element modelling simulation. The results clearly demonstrate the bandgap of the dual resonance system is extended by both the local resonance and diatomic resonance mechanisms. A parametric study is established to optimize the bandgap ratio, revealing that the bandgap of the design can be shifted by changing the stiffness ratio between two resonators in the sub-structure. The wave attenuation in the frequency domain obtained from impact modal tests exhibits a good agreement with computational results. In particular, the dynamic load attenuation capacities of the metamaterial chains under different impact durations are studied using impact mitigation tests, which show that the dual resonance design has the best attenuation performance under impact force, where the transmission rate is driven down to 0.2, compared with 0.48 for the design without resonators.

A review on seismic metamaterials: From natural toartificial structures

<p indent="0mm">In the recent three decades, the breath-taking discoveries of phononic crystals in conjunction with research advances in acoustic metamaterials have far-reaching implications in many science and engineering branches. These new discoveries can be traced to the fundamentals of wave manipulation and wave attenuation, etc., within a very wide frequency spectrum from ultrahigh electromagnetic wave frequency to very low seismic frequency ranges. Inspired by electromagnetic and photonic crystals, these newly designed artificial structures are able to control acoustic/elastic waves at relatively low frequency ranges. In periodic systems, Bloch waves are formed by reflection, refraction and scattering of De Broglie, electromagnetic/light and acoustic/elastic waves. These waves contain marvelous band structures which allow transmission or lead to attenuation. Frequency domains for transmission and attenuation correspond to passbands and stopbands, respectively. There exist many studies that materialize the idea of designing metadevices at will by utilizing wave band behaviors. Generally, the mechanism for forming stopbands contains two parts, i.e., Bragg scattering and local resonance, that can also be used to identify phononic crystals and acoustic metamaterials. Especially, a Bragg scattering type metamaterial prohibits waves with a wavelength of the same order as the lattice constant from propagating through the structure. It results in a large-scale structural dimension for a low frequency bandgap. Comparatively, local resonance type metamaterials allow the generation of bandgaps at low frequency ranges with relatively small dimensions as their properties rely primarily on the local resonance. The study of seismic wave propagation in civil engineering has been reinvigorated due to the new, exciting concept of seismic metamaterials. The spectacular designs provide new approaches to control seismic surface (Rayleigh and Love) and bulk (pressure and shear) waves for civil and structural engineers. This review traces the state-of-the-art developments of seismic metamaterials and establishes a link between photonic crystals at nano/micro scale and seismic metamaterials at macro scale. We present a survey of more recent developments in seismic metamaterials in terms of geometry, physics (i.e., the mechanism for forming stopbands) and experimental approaches which range from natural sources to artificial structures. A variety of mathematical and physics tools can be extended from photonic crystals to seismic megastructures, such as effective media theory, Brillouin zone, reciprocal space, rainbow trapping, etc. The development of finite element methods provides the possibility to simulate and analyze these complex artificial designs numerically. A school of forest trees as natural seismic metamaterials is a focal point in this review, which enables attenuation of seismic waves using natural resources and also inspires the discovery of seismic metasurfaces. For artificial structures, designs are generally made based on locations (i.e., metabarriers and metafoundations) or mechanisms (i.e., Bragg scattering and local resonance mechanism). Some metamaterial-like transformed urbanism or cities are also verified to work as seismic shielding or cloaking. Further, similar to experimental methods in other disciplines, scale model experiments and full-scale experiments have been explored to validate the efficiency of seismic metamaterials in wave attenuation. Although research in phononic crystals is moving towards extreme frontiers, metastructures working at low frequencies with stability, high bearing capacity, high ductility, wide bandgap and efficient attenuation zones remain substantial challenges. Besides soil-structure interactions, the combination of various components of seismic waves, ground conditions, soil properties, effects of groundwater table, structural nonlinearity or other ineluctable factors is yet to be fully considered. Ultimately, the emergence of seismic metamaterials broadens the horizons for seismic isolation and seismic vibration control. This review will help future researchers witness the continuous development of seismic metamaterials and comprehend the current challenges in this promising, potential and exciting research.

Closed-form bandgap design formulas for beam-type metastructures

Metastructures have received increasing attention because of their unique bandgap behavior that can be utilized to control vibration and noise of mechanical structures. This work is aimed to develop efficient formulas for bandgap estimation and design of flexural beam-type metastructures containing a periodic array of single-frequency force resonators. First, closed-form formulas are developed for a fast yet accurate estimation of the lowest two bandgaps, which may be formed by local resonance (LR) mechanism or Bragg scattering (BS) mechanism. Such formulas are shown to be more general than existing well-known closed-form formulas, which are only applicable to the case of deep-subwavelength LR-type bandgap. Second, closed-form formulas are proposed for a straightforward design of two particular cases of improved bandgaps compared with typical deep-subwavelength LR-type bandgap. One particular case is an ultra-wide near-coupled pseudo bandgap formed by strong interaction of the LR and BS mechanisms. Another particular case is an LR-type bandgap possessing significant attenuation performance at its bandgap center, and also having a broader effective width than the typical deep-subwavelength LR-type bandgap. Moreover, the broad applicability of the developed closed-form formulas is numerically verified by addressing bandgap design problems associated with simple and advanced multi-scale beam-type metastructures.

Vibration attenuation of finite-size metaconcrete: Mechanism, prediction and verification

To mitigate shock and vibration, metaconcrete with single-mass-coating resonators and double-mass-coating resonators was designed based on local resonance mechanism. The resonator is constructed by metallic ball coated with thin and soft rubber layer. Dynamic analysis method for finite-size metaconcrete is developed to predict the effective bands for vibration attenuation, which is verified by frequency-sweeping vibration experiment. Local resonance of the mass-coating system endows finite-size metaconcrete excellent vibration attenuation ability at the desired frequency band. Having two local resonation frequencies, double-mass-coating system effectively expands the vibration attenuation band from one to two and much wider compared with single-mass-coating system. The finite-size metaconcrete block designed in this research can dissipate 56.4% more energy than the common concrete block.