Seismic Metamaterials Research Articles

A new seismic metamaterial design with ultra-wide low-frequency wave suppression band utilizing negative Poisson's ratio material

In this paper, we present a new seismic metamaterial (SM) for the suppression of Lamb waves and surface waves utilizing the negative Poisson's ratio (NPR) foam. The periodic cell of the metamaterial is composed of a square cylinder made of steel in the center and NPR foam connecters at the corners. Utilizing the unique resonance properties of the NPR material, an ultra-low-frequency broadband wave suppression is achieved. First, the characteristics of bandgaps (BGs) of the proposed structure with different materials were analyzed using the finite element (FE) method. It shows that the application of the NPR foam can significantly broaden the BGs compared with the case using traditional rubber. The vibration modes were analyzed to investigate the mechanism of BG generation, and the results show that the broad BG is achieved via the unique local resonance mechanism of the NPR foam. Subsequently, the frequency-domain analysis was carried out to verify the shielding effect of the designed SM on Lamb waves, using a periodic structure consisting of 10 × 6 unit cells. It shows that the designed SM can effectively attenuate Lamb waves in the range of 3–44 Hz with attenuation up to −590 dB at 32 Hz. A parametric analysis shows that the NPR foam with small thickness, high modulus, low mass density, and low Poisson's ratio can broaden the first complete BG. In addition, the acoustic cone method was combined with the frequency-domain analysis to calculate the BGs of the proposed structure against the surface wave, using a periodic structure consisting of 20 unit cells. It shows that the surface wave can be significantly attenuated within the BG. Finally, real seismic excitations were applied for time-domain analyses, and the simulation results show that the proposed structure can effectively shield the low-frequency seismic surface waves in the range of 0.1–20 Hz. The design scheme proposed in this paper is simple in structure and easy to implement, and is believed to possess bright application potentials in seismic protection.

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

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.

Split-type seismic metamaterials with pseudo-surface wave weakening mechanism

Pseudo surface waves, as a type of propagating wave, are detrimental to the attenuation of seismic Rayleigh waves. A split seismic metamaterial (SSM) that can weaken pseudo surface wave modes and generate ultra wideband gaps of 12.92Hz is proposed. The split configuration of SSM can be obtained by separating the modes of different waves within the energy band curve, which can cause the surface waves inside the sound cone to move outward and weaken the pseudo surface wave modes inside the band gap. Combined with the frequency response curve, it is further demonstrated that the attenuation amplitude of SSM is larger than that of monolithic seismic metamaterials (MSM) within the same bandgap range. Afterwards, by studying the changes in bandgap through structural parameters, the method of a gradient array was used to fuse the characteristic frequency that can generate larger attenuation with the weakened pseudo surface wave mode frequency, resulting in greater attenuation. Finally, it is verified by experiments that SSM can provide ultra-wide low-frequency band gaps while also generating large attenuation accuracy, which provides a practical solution for the application of seismic metamaterials.

Bandgap characteristics of a hybrid multi-resonator elastic metamaterial with negative stiffness mechanism and its application to mitigate seismic response of building structures

Seismic metamaterials have attracted extensive attention due to their unique ability to attenuate the transmission of elastic waves in their frequency bandgaps. However, generating a metamaterial with a low-frequency and wide bandgap remains challenging. Previous studies have shown that negative stiffness mechanisms can lower the frequency range of bandgaps while employing a multi-resonator technique can broaden the width of bandgaps. In this study, by combining these two techniques, a negative stiffness enhanced multi-resonator elastic metamaterial (NMEM) is first proposed. The feasibility of NMEM is validated by comparing the theoretical dispersion relation and the transmission spectra of a finite cell model. The results demonstrate that low-frequency and wide bandgaps can be realized by NMEM. To further widen the bandgap, a hybrid NMEM is proposed by connecting multiple types of cells in series. The proposed hybrid NMEM consists of two types of cells, one with a single resonator and another with two resonators, which merge individual bandgaps into a continuous and wider bandgap. The proposed hybrid NMEM is then adopted as a meta-basement for a case building to demonstrate its effectiveness in mitigating seismic responses. The results show that the seismic responses of the building with the hybrid meta-basement are considerably reduced than those of the building with the conventional basement. However, the hybrid meta-basement may lead to larger structural displacement response when the dominant frequency of ground motion is outside the designed bandgap.

Design and optimization of seismic metamaterials to mitigate ground vibration

Design and optimization of seismic metamaterials to mitigate ground vibration

Feasibility studies in applying cork to pile-type two-layered seismic metamaterials

Seismic metamaterials, a novel seismic engineering technology composed of multiple layers of materials, can form barriers by being periodically arranged to protect properties in a region from earthquake disasters. Parametric analysis of pile-type two-layered seismic metamaterials reveals that the outer layer material with low Poisson's ratio, low Young's modulus, and low density can achieve low and wide frequency band gap, aligning with the design objectives of seismic metamaterials. Since cork, a readily available material, meets the above characteristics, this study aims to investigate its feasibility in being applied to pile-type two-layered seismic metamaterials. Furthermore, the effect of hollows within pile-type seismic metamaterials on lowering the bound frequency of the band gaps is explored. Through laboratory-scale tests at one-fifth scale and numerical simulation, it is demonstrated that cork pile-type seismic metamaterials without hollows can generate a low and wide frequency band gap and effectively attenuate waves at frequencies ranging from 5.6 Hz to 10 Hz. In addition, employing hollows in the cork outer layer can further decrease the lower bound frequency of the band gap by 25 % and result in an effective attenuation range of 4.6 Hz–9.8 Hz while slightly reducing the width of the band gap.

A novel vibration barrier for low-frequency surface waves in the ground

As for certain engineering scenarios, such as open-air quarries and underground pipeline areas, vibration barriers are in urgent need. However, their design and construction face various challenges, especially for attenuating surface waves with low frequencies. Inspired by the topography of hills and periodic phononic crystal structures, a novel vibration barrier consisting of periodic soil strips is proposed. Firstly, utilizing the finite element method and the theory of periodic structures, the dispersion band diagram is calculated for the periodic soil strips. The corresponding band gap mechanisms are discussed by the displacement field of modes in the lower boundary of band gaps. Besides, a simplified model and a theoretical expression are proposed to analyze the minimum frequency of the band gaps. Through frequency domain analysis, the influence of the damping of soil strips on isolation effects is examined, and the dissipated energy is also quantified using a spatial Fast Fourier Transform. Finally, a comparison of the isolation effect between soil strip barriers and typical trench barriers is conducted. The results show that periodic soil strips can exhibit several band gaps, within which surface waves (SWs) can be effectively isolated. Soil strip barriers exhibit similar or even better vibration isolation effects compared to trench barriers, especially for isolating low-frequency vibrations. This study enhances our understanding of surface wave mitigation using periodic barriers and provides fresh insights for designing seismic metamaterials.

Energy attenuation of seismic metamaterials composed of a periodic array of coated elliptical cylinders

Abstract We present a numerical study on energy attenuation of seismic metamaterials consisting of a periodic array of coated elliptical cylinders. The aim is to perceive the effect of aspect ratio for different wave modes so that the metamaterials can interact with the incoming wave causing them to interfere with each other destructively, especially for low-frequency seismic waves with relatively wide bandgap. Previous studies mainly focused on the configuration of coated circular cylinders or spheres, in which the metamaterial is composed of a hard inclusion surrounded by a soft coating layer and dispersed within a hard matrix. Here we utilize numerical simulations based on finite element calculation to analyze the local fields within the unit cell. Effective mass density, mass moment of inertia and shear modulus are analyzed through a homogenization procedure to characterize the macroscopic behavior of the effective medium. The effective behavior will be dependent for different aspect ratios and for different types of wave motions. To verify the effectiveness of energy attenuation, a full-scale model is adopted. Specifically, to identify optimal energy attenuation configurations, we illustrate the attenuation effects of elliptical metamaterials under longitudinal and shear horizontal types of waves. The present study demonstrates that elliptical metamaterials will have more reflexibilities to tune with the aspect ratio of the elliptical geometry as well as the directionality of incidence waves. Based on our simulations, we show the ability of the designed configuration in tuning local resonance frequencies and bandwidths for real implementations and applications of seismic metamaterials.

Complex dispersion analysis of true and pseudo surface waves propagating in two-dimensional viscoelastic seismic metamaterials

In this paper, the wave characteristics of true surface waves (TSWs) and pseudo surface waves (PSWs) in two-dimensional (2D) seismic metamaterials are explored. The 2D seismic metamaterial is formed by placing periodic concrete pillars on the surface of the soil substrate. The complex dispersion curves of the seismic metamaterial are numerically calculated by the ω–kapproach. The Kelvin–Voigt model is adopted to describe the material viscoelasticity. The results show that not only the TSW modes but also the PSW modes should be taken into account to evaluate the mitigation capacity of the seismic metamaterials. Due to the introduction of material viscoelasticity, the TSWs and PSWs convert from the propagative mode to the evanescent mode. When the PSW modes propagate along the substrate surface, their energy gradually leaks into the bulk of the substrate, leading to their transmission coefficient smaller than that of the TSW modes. Compared to the concrete pillars on the substrate surface, the viscoelasticity of the soil substrate plays a more important role in surface wave reduction. Moreover, the wave propagating length in the seismic metamaterials can be predicted by using complex dispersion relations.

СЕЙСМИЧЕСКАЯ ЗАЩИТА ЗДАНИЙ И СООРУЖЕНИЙ С ПРИМЕНЕНИЕМ МЕТАМАТЕРИАЛОВ: ТЕКУЩЕЕ СОСТОЯНИЕ И ПЕРСПЕКТИВЫ РАЗВИТИЯ

Due to the compaction of urban development and increase in its number of floors, the number of studies in the field of protection of buildings and structures from seismic waves is growing in the world, as the wave seismic front in the soil mass can lead to enormous destruction and mass casualties. The most common methods of seismic protection of buildings and structures in civil engineering today are constructive and territorial methods. The first method includes a set of structural measures, among of them an important place is occupied by the use of seismic isolators – special devices inserted into the foundation and reducing inertial seismic effects on building structures. The second way is the use of various barriers in the path of seismic wave propagation. In recent years, there has been a clear trend towards finding new approaches to territorial seismic protection. The analysis of academic databases revealed a large number of studies (mostly foreign) devoted to the development of ways to protect buildings and structures from wave action using various kinds of composite structures – metamaterials. Some researchers conditionally divide these methods into two groups: the first performs the tasks of masking, when the wave front deviates and wraps around the protected object, and the second creates an artificial shadow zone where seismic waves are damped without significantly affecting buildings and structures. Since the development of seismic metamaterials is still a new but certainly promising area of research for Russian science, the purpose of this review was to systematise the available data on the methods of effective protection of buildings and structures from wave impacts.

Train Mitigation Measures in the Transmission Path: Seismic Metamaterial and Granular Barriers

The development of new mitigation measures is an effective solution to the annoyance generated by the induced vibration coming from the railway traffic to the residents of urban areas. This paper aims to give a brief comparison of two novel concepts of mitigation measures applied within the transmission path presented recently in the literature. In particular, the use of seismic metamaterial will be compared to the use of heterogeneous barriers, to evaluate to which extent these two mitigation measures can help to tackle the problem of ground-borne vibration and noise. These two cases will be related by considering the same railway environment based on a two-step approach, already validated in the past; in this study, the soil simulated in the second step is reproduced using the finite element method and spectral element method for the seismic metamaterial and heterogeneous barriers respectively. Finally, a parametric investigation is conducted to understand how the material and geometrical proprieties affect the attenuation levels of the two measures.

Attenuation of Rayleigh and pseudo surface waves in saturated soil by seismic metamaterials

Seismic metamaterials have received extensive research interest due to their bandgap properties, simplicity in design principles, and stability in response. They have been developed to protect buildings or architectures susceptible to damage from surface elastic waves. In practice, the ground soil is generally a multiphase medium, and the influence of its permeability and viscosity on seismic metamaterials is not yet clear. In this work, we developed a formulation that combines Biot’s theory and Bloch-Floquet theorem to investigate the complex band structures and transmission properties of Rayleigh and pseudo surface waves (PSWs) for pillared and inclusion-embedded seismic metamaterials in saturated soil. It is shown that the ratio of fluid viscosity and permeability η/κ have an impact on the surface wave attenuation and the performances of seismic metamaterials, where the smaller ratio benefits the surface wave broadband attenuation and metamaterials attenuating effects. The complex band structures reveal that inclusion-embedded metamaterials can support the propagation of PSWs having a phase velocity higher than that of the transverse bulk waves. The PSWs are significantly affected by the rubber viscosity due to the mode displacements concentrated in the rubber coatings. The higher viscosity of metamaterials also allows for broadband attenuation of Rayleigh surface waves. The results of this study will present an appropriate way to design viscoelastic seismic metamaterials in saturated soil for low-frequency surface wave attenuation.

Low-frequency and wide bandgap seismic metamaterials for Rayleigh wave attenuation

This study introducesa seismic metamaterial (SM) for mitigating low-frequency seismic Rayleigh waves when embedded in the ground.. Dispersion curves and vibration modes of a unit cell incorporatingthe SM were calculated using the Bloch theorem and sound cone method in a numerical model. The lowest frequency of the bandgaps (BGs) is 1.6 Hz, with the maximum absolute bandwidth reaching 18 Hz, matching the seismic wave considered in this study. Furthermore, a comprehensive analysis of vibrational modes revealed the mechanism responsible for BG formation. Numerical simulations in both the time and frequency domains confirmed the attenuation of Rayleigh waves by finite models containing SMs, along with theconversion of Rayleigh waves into body waves. Additionally, the effects of material and geometric parameters on BG frequency range is discussed. Complex SM structures were devised by combining two distinct SMs with varying geometric parameters, achieving a complete broadband attenuation range. Finally, realistic seismic Rayleigh wave propagation through complex SMs was simulated, conclusively validating their effectiveness in providing broadband attenuation.

Double-gradient seismic metamaterials with zero-frequency bandgap characteristic in a layered soil medium

Seismic metamaterials (SMs) are an artificially composite material designed within the sub-wavelength range. To attenuate low-frequency seismic surface waves, a metamaterial structural unit composed of a lead core and an auxetic foam coating layer was proposed; the higher impedance ratio results in the creation of a zero-frequency bandgap under layered soil conditions. To broaden the attenuation zone (AZ), double-gradient seismic metamaterials (DGSMs) were designed. The frequency domain analysis indicates that the attenuation area covering the range of 0–10 Hz is 89.8%. Through displacement-field analysis, the attenuation mechanism of DGSM on specific frequency surface waves can be fully explained. Finally, Taft seismic wave excitation is input for time history analysis, and the acceleration amplitude within 0–2 Hz decreases by 58.6%, which verifies the effectiveness of DGSMs in attenuation of low-frequency seismic waves.

Burr Puzzle-Inspired Seismic Metamaterials

Two novel seismic metamaterials models, trophy and apple core, inspired by an ancient Chinese puzzle are proposed in this study. Bandgaps below 15[Formula: see text]Hz are achieved by exclusively using concrete as the base material in the designs. Vibration modes are investigated to clarify the bandgap formation. Through comparison, we found that under the same volume, the apple core model can provide a lower frequency bandgap than the trophy model. Results from transient simulations and band structures are in good agreement, validating the accuracy of the simulation results. To broaden the bandwidth, the radii of the apple core models are varied and arranged in a gradient pattern. Transient analyses using a Gaussian wave packet and Taiwan’s Chi-Chi earthquake dataset are conducted to verify the effectiveness of the gradient apple core seismic metamaterial.

Tuning Fork Seismic Metamaterial for Low-Frequency Surface Wave Attenuation with Locally Resonant Band Gaps

Tuning Fork Seismic Metamaterial for Low-Frequency Surface Wave Attenuation with Locally Resonant Band Gaps

Orthotropic metamaterials with freely tailorable elastic constants

To control mechanical waves and structural vibrations, an important method is to design metamaterials with tailored elastic constants, but it is very difficult. In this paper, a simple and universal metamaterial design method is proposed. This orthotropic metamaterial is composed of elements arrayed periodically in space. The element includes two cuboid structures. The first structure is the basic structure of the element, and the second structure is the transformation of the first structure of the element. The first structure of the element is a cuboid structure composed of 24 bars connected by 8 nodes, and the second structure of the element is a cuboid structure composed of 36 bars connected by 14 nodes. This metamaterial has six independent elastic constants, so there is a large degree of freedom in the material design. Therefore, it has great application value in the fields of mechanical metamaterials, elastic wave metamaterials, acoustic metamaterials, and seismic metamaterials, and has also laid the foundation for realizing the dream of controlling mechanical waves and structural vibrations.

A surface-wave seismic metamaterial filled with auxetic foam

Auxetic materials with negative Poisson's ratio (PR) exhibit superior mechanical properties with regard to energy absorption, while their potential for surface wave shielding is only in its beginnings. To attenuate surface waves in ultra-low frequencies (the starting frequency close to 0 Hz), which is the main scope of concern in seismic protection, this paper presents a novel type of seismic metamaterial (SM) with square pillars embedded as vibrators that is filled by auxetic foam. The designed SM is comprised of three commonly used construction materials, i.e., soil, concrete and auxetic foam. Combining the dispersive analysis and sound cone method, an ultra-low-frequency bandgap from 0 to 16.42 Hz is opened via the tensile resonance of the auxetic foam and the inverse dispersion effect. Furthermore, the parametric analysis further shows that filling material with a low Poisson ratio and low mass density is more favorable to widening the first complete bandgap (FCB), which means that foam is the ideal filling material for SM. The transmission spectra of the corresponding finite samples coincide well with the bandgap calculations. And the dynamic response of a scaled-down setup with a characteristic size of 1/10 of the original metamaterial is experimentally tested to validate the effectiveness of our study. We expect that this study prompts the engineering application of auxetic materials and ordinary building materials in seismic wave shielding at deep sub-wavelength frequencies.

A new periodic seismic metamaterial with ultra-low bandgap for lamb waves

In this paper, we propose a new seismic metamaterial (SM) that can cover the main frequency range of earthquakes by introducing curved boundaries on a square cross-section and reducing the contact area between adjacent cells, which results in a wide bandgap at very low frequencies. The vibration modes at the edge of the first bandgap are analyzed, and the effects of the geometric and material parameters of the rubber on the first bandgap are studied. Meanwhile, vibration experiments are performed. Finally, finite structural dynamics response analysis is performed. The results show that the structure has excellent damping performance in low frequency band. At the same time, it can achieve effective attenuation for Oroville, Gilroy, and Corralitos earthquakes, which has potential applications in the field of seismic isolation and attenuation of buildings.