Low-frequency Band Gaps Research Articles

A new inerter-based acoustic metamaterial MRE isolator with low-frequency bandgap

Abstract Acoustic metamaterials are capable of generating vibration bandgaps at specific frequency ranges, which makes them have good applications in the field of vibration isolation. To further broaden the vibration bandgaps, both magnetorheological elastomer (MRE) and graded stiffness are employed to enhance the bandgap properties. However, lowering the vibration bandgap is usually accompanied with excessive reduction of the structure stiffness. Except for reducing the stiffness, increasing the mass of the acoustic metamaterial can also lower the bandgap. In this research, a novel inerter-based acoustic metamaterial MRE isolator (IAM-MREI) was designed and prototyped. Inerters not only can generate large equivalent mass, but also are discovered to be able to greatly lower and broaden the vibration bandgap of the IAM-MREI with a brand-new mechanism, which cannot be achieved only with extra equivalent mass. The effects of the inerters on the overall performance of the IAM-MREI was thoroughly investigated and validated both theoretically and experimentally. The evaluation experiments confirmed that the IAM-MREI possesses a low frequency vibration bandgap and can provide great vibration isolation performance.

Design and Application of a Lightweight Plate-Type Acoustic Metamaterial for Vehicle Interior Low-Frequency Noise Reduction

To reduce the low-frequency noise inside automobiles, a lightweight plate-type locally resonant acoustic metamaterial (LRAM) is proposed. The design method for the low-frequency bending wave bandgap of the LRAM panel was derived. Prototype LRAM panels were fabricated and tested, and the effectiveness of the bandgap design was verified by measuring the vibration transmission characteristics of the steel panels with the installed LRAM. Based on the bandgap design method, the influence of geometric and material parameters on the bandgap of the LRAM panel was investigated. The LRAM panel was installed on the inner side of the tailgate of a traditional SUV, which effectively reduced the low-frequency noise (around 34 Hz) during acceleration and constant-speed driving, improving the subjective perception of the low-frequency noise from “very unsatisfactory” to “basically satisfactory”. Furthermore, the noise reduction performance of the LRAM panel was compared with that of traditional damping panels. It was found that, with a similar installation area and lighter weight than the traditional damping panels, the LRAM panel still achieved significantly better low-frequency noise reduction, exhibiting the advantages of lightweight, superior low-frequency performance, designable bandgap and shape, and high environmental reliability, which suggests its great potential for low-frequency noise reduction in vehicles.

Enhanced low-frequency band gap of nonlinear quasi-zero-stiffness metamaterial by lowering stiffness coupling

Enhanced low-frequency band gap of nonlinear quasi-zero-stiffness metamaterial by lowering stiffness coupling

Investigating the robustness of interface topological modes in rods

Topological phononic crystals and metamaterials are structures that can present waveguiding and energy concentration phenomena, which can be of interest in structural dynamics for energy harvesting and passive vibration and noise control. The periodicity of the typical phononic crystals and metamaterials is broken for these structures, which need to present at least two crystal lattices with different topological characteristics. Thus, the topological invariant, such as the Zak phase, which defines the topological characteristic, must be computed. A rod metastructure exhibiting two low-frequency band gaps, each with a topological interface mode, was designed. It has bolt sets whose weights generate variability, which was modeled and inferred. In order to increase variability along the rod metastructure, washers were included or removed. Experiments were performed to validate the simulations. It was observed that the variability of the topological mode in the first band gap is more robust considering its mode shape, natural frequency, and energy concentration at the interface than the second interface mode, at higher frequency. As variability increases, the robustness of the energy concentration at the interface and of the mode shape of both topological modes decreases. The same behavior was observed for the natural frequencies of the topological modes.

Topological interface states in deep-subwavelength phononic beams with acoustic black hole configurations

We present deep-subwavelength phononic beams engineered with unit cells incorporating acoustic black hole (ABH) configurations. The ABH design enables the realization of topological interface states (TISs) within the first band gap at low frequencies, where the lattice constant (a) is far smaller than the wavelength (λ) of the controlled wave. Manipulating the ABH configuration and breaking the unit-cell symmetry allow us to control Zak phases for the topological beams. Two topologically distinct phononic beams are interconnected to produce the TIS within their low-frequency band gaps. Through numerical and experimental demonstrations, we confirm the existence of TISs at frequencies ranging from 4.3 to 8.5 Hz using the designed topological beams of which a/λ is less than 1/20. We also offer the potential to further reduce the value of a/λ by rearranging the ABH unit cells.

Composite metastructure with tunable ultra-wide low-frequency three-dimensional band gaps for vibration and noise control

Low-frequency vibration and noise control present enduring engineering challenges that garner extensive research attention. Despite numerous active and passive control solutions, achieving multiple ultra-wide attenuation regions remains elusive. Addressing vibration and noise control across a multidirectional broad low-frequency spectrum, three-dimensional metastructures have emerged as innovative solutions. This study introduces a novel three-dimensional composite metastructure featuring multiple ultra-wide three-dimensional complete band gaps. The research emphasizes the design strategy of elastic ligaments to achieve multiple ultra-wide attenuation regions spanning from 0.7 to 40 kHz. The band structures are elucidated through modal analysis and further substantiated by an analytical model based on a spring-mass chain with an additional resonator. The underlying physical mechanism for the formation of multiple ultra-wide band gaps is revealed through novel vibration modes from finite element analyses. Furthermore, we demonstrate that the distribution and the relative width of the ultra-wide band gaps can be tuned by modifying the geometric parameters of the metastructure. Utilizing additive manufacturing, prototypes are fabricated, and low-amplitude vibration tests are conducted to evaluate real-time vibration attenuation properties. Consistency is observed among theoretical, numerical, and experimental results. The proposed structure shows significant potential for high-performance meta-devices aimed at controlling noise and vibration across an extremely wide low-frequency spectrum.

Longitudinal wave propagation in a practical metamaterial lattice

A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Bandgap Control of Local Resonance Sandwich Meta-Plate with Cantilevered Archimedean Spiral Beam-Mass Resonators

In order to attenuate the various low-frequency vibrations that may cause structural fatigue and damage, impact human health and affect work efficiency, this paper presents a novel local resonance metamaterial sandwich meta-plate structure containing a cantilever spiral beam-mass resonator, and investigates vibration reduction effects of it within the obtained low-frequency bandgap range. For this purpose, a theoretical model of the low-frequency resonator being composed by a cantilever Archimedean spiral beam and cylindrical mass is established. The natural frequency of it is calculated by solving the Euler-Lagrange equation of the resonator. The accuracy and reliability of the theoretical model are verified through COMSOL simulation. The stress distribution of five types of cantilever spiral beam mass resonators (i.e. Archimedes spiral, triangle spiral, square spiral, pentagon spiral and hexagon spiral) and different cross-sectional shapes (rectangular, square, circular, diamond and triangular) are analyzed. Then, a unit cell model of a sandwich meta-plate with a cantilever Archimedean spiral beam resonator is selected. Hamilton’s principle is used to deduce the bandgap range under infinite periods, and the theoretical solutions are also verified. The parameter optimization of the substrate plate and resonator are also studied. Moreover, the effects of the various structural variables on the bandgap range are systematically explored. Finally, the dynamic responses of the sandwich meta-plate composed of [Formula: see text]-unit cells under different excitation frequencies, boundary conditions and structural damping are analyzed.

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.

Tunable low-frequency broadband band gap in nonlinear locally resonant metamaterial inspired by sarcomere structure

Since traditional locally resonant metamaterials (LRMs) cannot achieve a broadband band gap in the low-frequency band, the suppression and isolation of low-frequency broadband vibration has always been a difficult problem in the field of vibration control. Therefore, in this paper, inspired by the structure of the sarcomere, a novel nonlinear LRM is proposed, aiming to open a wider band gap in the low-frequency band. Firstly, a statics model of the nonlinear local resonator (LR) is established to explore the mechanical nonlinear characteristics of the structure with different geometric parameters. And the inflection point fitting method is used to approximate the nonlinear statics model of nonlinear LR. Then a dynamics model was established, the nonlinear dispersion relationship of the infinite periodic system was obtained by Bloch's theorem and l-P perturbation method. And an analytical investigation of the theoretically calculated band gap is conducted through the band gap ratio and relative band gap width. In addition, according to the influence of different structural parameters on the real and imaginary parts of the wave vector, the regulation rules and mechanisms for nonlinear LRM to open low-frequency broadband band gaps are revealed. Finally, the Runge-Kutta method was used to numerically calculate the vibration transmissibility curve of the nonlinear LRM composed of a limited number of nonlinear LRs. And the correctness of the theoretically calculated band gap was verified. The research results provide theoretical support for the application of nonlinear LRMs in the suppression and isolation of low-frequency broadband vibrations.

The mechanism of adjusting the low-frequency ultra-wide band gap within lightweight spherical superstructue

Conventional resonant structures can be effective in obtaining broadband, but it is still a challenge to design small-sized and lightweight acoustic metamaterials with a low-frequency ultra-wideband. This paper proposes a new approach of designing a lightweight spherical localized resonance superstructure with adjustable stiffness ratio, and the mechanism of adjusting the low-frequency ultra-wide forbidden band is revealed. Then, the correlation between the zero value of its dynamic equivalent mass and the stiffness ratio of the system is studied. It is found that not only is the upper bound of the negative mass effectively broadened, but also the lower bound is successfully lowered only by adjusting the stiffness ratio of the sphere. Most importantly, based on the regulation mechanism with adjustable stiffness ratio, the lower boundary of the band gap is lowered from 171 Hz to 141 Hz, and the upper boundary is increased from 445 Hz to 710 Hz. Therefore, the low-frequency ultra-wideband of 141–710 Hz is obtained only by adjusting the stiffness ratio of the system and the Finite Element Method, which is highly consistent with theoretical analyses. Obviously, the mechanism of obtaining the low-frequency wideband through adjusting the stiffness ratio not only provides a novel idea for adjusting the low-frequency ultra-wideband, but also provides theoretical guidance for the developing the small-size and lightweight acoustic devices, so it would have potential application in the field of vibration and noise reduction.

Easy to fabricate 3D metastructure for low-frequency vibration control

As a burgeoning category of elastic metamaterials, 3D metastructures have garnered significant research attention for manipulating low-frequency acoustic and elastic waves. Bandgap engineering allows for the control of these waves across a subwavelength ultrawide frequency range. However, the manufacturing of these 3D structures poses a challenge, necessitating additional support materials for 3D-printed components, creating difficulties in mass production. In this study, we propose a novel lightweight 3D metastructure design that is easy to fabricate and provides a low-frequency subwavelength bandgap. We replaced conventional struts supporting heavy mass inclusions in typical designs with modified arch beams. This structural modification enables the easy and self-supporting manufacturing of 3D metastructure unit cells without the need for extra support material. Utilizing magnets and steel masses with bolts as hard inclusions, the magnet facilitates the quick assembly of the 3D metastructure, potentially facilitating mass manufacturing in practical applications. The wave dispersion and bandgap properties of the metastructure are investigated numerically, and experimental vibration tests are performed on the 3D-printed and assembled parts. The experimental results and numerical findings demonstrate robust vibration attenuation at low frequencies by the proposed 3D metastructure. The suggested, easy-to-fabricate 3D-metastructure design holds potential applications in low-frequency elastic-wave manipulation, including noise and vibration control.

Optimization of novel plate acoustic metamaterials and modulation of the low-frequency bandgap

Based on the local resonance mechanism, five new acoustic metamaterial plate structures with low-frequency bandgaps are proposed in this paper. The two new structures obtained by heuristic structural design are capable of suppressing vibrations over a large frequency range in the low-frequency range of 0-400 Hz, which is promising for practical applications. The mechanism of bandgap generation is found to be a shift in the form of local resonance. Among the three original models, model C has the smallest transmission coefficient T min of −154.6. Analysis of the group and phase velocity diagrams reveals that the change in frequency has a great influence on the energy transfer, speed and direction of the wave in the structure. The heuristic structural design allows the mass block of model B1 to undergo angular state changes, which ultimately realizes the regulation of the bandgap position and the total bandgap width within a certain range. It is also found that the variation of the bandgap properties has a certain regularity with the change of the structural parameters.

Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation

Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation

Uncovering Pattern-Transformable Soft Granular Crystals Induced by Microscopic Instability

Abstract Upon compression, some soft granular crystals undergo pattern transformation. Recent studies have unveiled that the underlying mechanism of this transformation is closely tied to microscopic instability, resulting in symmetry breaking. This intriguing phenomenon gives rise to unconventional mechanical properties in the granular crystals, paving the way for potential metamaterial application. However, no consistent approach has been reported for studying other unexplored transformable granular crystals. In this study, we present a systematic approach to identify a new set of pattern-transformable diatomic granular crystals induced by microscopic instability. After identifying the kinematic constraints for diatomic soft granular crystals, we have generated a list of feasible particle arrangements for instability-induced pattern transformation under compression. Instead of computationally intensive finite element models (FEMs) with continuum elements, we adopt a simplified mass-spring model derived from granular contact networks to efficiently evaluate these feasible particle arrangements for pattern transformation. Our numerical analysis encompasses quasi-static analysis and microscopic/macroscopic instability analyses within the framework of linear perturbation. Subsequently, the pattern transformation of the identified particle arrangements is confirmed through quasi-static analyses employing detailed finite element (FE) simulations with continuum elements. Additional numerical simulations with continuum elements reveal that the pattern transformations of particle arrangements are significantly influenced by the initial void volume and some transformed granular crystals may exhibit strong low-frequency directional phononic band-gaps, which were not observed in the initial granular crystals.

Novel small-size seismic metamaterial with ultra-low frequency bandgap for Lamb waves

Seismic metamaterials (SMs) possess bandgap characteristics, enabling effective attenuation of seismic waves within a specific frequency range. However, small-sized SMs typically struggle to achieve a wide low-frequency bandgap. This paper proposes four types of SMs. The dispersion curves of these models were analyzed, and their vibration modes were studied to elucidate the bandgap mechanism. To investigate the influence of structural parameters on the bandgap, geometric variables are analyzed. Subsequently, the spectrum and acceleration time history curves of Lamb waves in a finite SM system are analyzed to verify the bandgap's authenticity. The designed structure exhibits a bandgap ranging from 1.24 Hz to 16.86 Hz, with a relative bandwidth as high as 172.6% and over 96% maximum vibration displacement attenuation of the El Centro seismic wave. The designed SMs effectively cover the 2 Hz seismic peak spectrum that leads to structural damage. They possess ideal relative bandwidth and excellent isolation performance, further advancing the engineering application of SMs.

Bandgap Calculation and Experimental Analysis of Piezoelectric Phononic Crystals Based on Partial Differential Equations.

Focusing on the bending wave characteristic of plate-shell structures, this paper derives the complex band curve of piezoelectric phononic crystal based on the equilibrium differential equation in the plane stress state using COMSOL PDE 6.2. To ascertain the computational model's accuracy, the computed complex band curve is then cross-validated against real band curves obtained through coupling simulations. Utilizing this model, this paper investigates the impact of structural and electrical parameters on the bandgap range and the attenuation coefficient in the bandgap. Results indicate that the larger surface areas of the piezoelectric sheet correspond to lower center bands in the bandgap, while increased thickness widens the attenuation coefficient range with increased peak values. Furthermore, the influence of inductance on the bandgap conforms to the variation law of the electrical LC resonance frequency, and increased resistance widens the attenuation coefficient range albeit with decreased peak values. The incorporation of negative capacitance significantly expands the low-frequency bandgap range. Visualized through vibration transfer simulations, the vibration-damping ability of the piezoelectric phononic crystal is demonstrated. Experimentally, this paper finds that two propagation modes of bending waves (symmetric and anti-symmetric) result in variable voltage amplitudes, and the average vibration of the system decreases by 4-5 dB within the range of 1710-1990 Hz. The comparison between experimental and model-generated data confirms the accuracy of the attenuation coefficient calculation model. This convergence between experimental and computational results emphasizes the validity and usefulness of the proposed model, and this paper provides theoretical support for the application of piezoelectric phononic crystals in the field of plate-shell vibration reduction.

Novel Frame-Type Seismic Surface Wave Barrier with Ultra-Low-Frequency Bandgaps for Rayleigh Waves

Seismic surface waves carry significant energy that poses a major threat to structures and may trigger damage to buildings. To address this issue, the implementation of periodic barriers around structures has proven effective in attenuating seismic waves and minimizing structural dynamic response. This paper introduces a framework for seismic surface wave barriers designed to generate multiple ultra-low-frequency band gaps. The framework employs the finite-element method to compute the frequency band gap of the barrier, enabling a deeper understanding of the generation mechanism of the frequency band gap based on vibrational modes. Subsequently, the transmission rates of elastic waves through a ten-period barrier were evaluated through frequency–domain analysis. The attentional effects of the barriers were investigated by the time history analysis using site seismic waves. Moreover, the influence of the soil damping and material damping are separately discussed, further enhancing the assessment. The results demonstrate the present barrier can generate low-frequency band gaps and effectively attenuate seismic surface waves. These band gaps cover the primary frequencies of seismic surface waves, showing notable attenuation capabilities. In addition, the soil damping significantly contributes to the attenuation of seismic surface waves, resulting in an attenuation rate of 50%. There is promising potential for the application of this novel isolation technology in seismic engineering practice.

Multi-frequency and low frequency bandgap characteristics of concentric ring cement-based locally resonant phononic crystal

Multi-frequency and low frequency bandgap characteristics of concentric ring cement-based locally resonant phononic crystal