Attenuation Zones Research Articles

Numerical analysis of wave propagation and vibration attenuation effects of periodic scattering piles in unsaturated poroviscoelastic ground

ABSTRACT The elastic wave propagation and vibration attenuation zones for periodically scattering piles in unsaturated ground were investigated using Finite-Element Method (FEM) and Bloch periodic theory. The unsaturated ground was modelled by unsaturated poroviscoelastic medium with the weak form governing equations derived from the mass and momentum conservative equations using Galerkin method and Fourier transform. The quadratic polynomial eigenvalue equations for the unsaturated medium were obtained using the Bloch periodic theory, and solved by FEM for the complex eigenvalues to evaluate the band gaps of the pile-soil system. The eigenvalue bands combined with the frequency response function were used to analyse the mitigation effects of piles in unsaturated ground with different soil properties and piles parameters. This research found that the pile-soil system has three propagational waves, in which the shear wave and the slow longitudinal wave carry low-frequency vibrations that undermine the attenuation effects of the piles barrier. The increasing soil saturation degree affects the attenuation effects by reducing the soil modulus and increasing the fluid content. And both of those two mechanisms reduce the frequency of the attenuation zones (AZ), which improves the low-frequency vibration attenuation, and reduces the width of AZ that could reduce the vibration mitigation effects.

Experimental study of passive seismic vibration isolation by trench-type periodic barrier

Seismic isolation systems protect structures and act as decoupling systems with the structure, which aims to uncouple the motion of the structure from incoming waves by reducing the kinetic energy of vibration transferred to structures. This research aims to study a non-invasive vibration isolation system using periodic barriers. A comprehensive field test program is completed to evaluate the wave isolation performance of empty trench and periodic barriers. The precast one-dimensional (1D) periodic barriers are arranged to form one long barrier and one short thick barrier to examine the influence of barrier length and the number of unit cells on the vibration isolation performance. The test program reported in this study is the P0 case (without periodic foundation), which serves as a reference group compared to previous test case P1 (with periodic barrier and reinforced concrete foundation) and test case P2 (with a combination of periodic barrier and periodic foundation). The triaxial (T-Rex) shaker truck generates excitation in three axis and the wave form include sine wave, sweep frequency and seismic waves. Each geophone sensor position records the triaxial soil response. The responses of soil along the direction of wave transfer, the normalized responses, and the frequency response function (FRF) are all provided and discussed. Various excitation inputs are comparable. It is found that the excitation directions influence the periodic barrier's effectiveness because of the dominant waveform. When FRF is compared between benchmark case and test cases, the periodic barriers’ screening effectiveness can be determined in the attenuation zones. These attenuation zones are expected to be the frequency band gaps of the periodic barrier. When the incoming wave frequency falls in this frequency band gap, the periodic barrier can isolate the vibration propagating towards the protected region.

Supratransmission in a vibro-impact chain

The paper addresses the supratransmission (ST), i.e., emergence of the propagating waves in a nonlinear chain forced in the attenuation zone of the linear substructure. In the considered model, the nonlinearity is realized through impacts of particles in a linear chain with on-site constraints. This special form of the nonlinearity allows deriving the exact solutions for edge states of the semi-infinite boundary-driven chain. Stability of these edge states is assessed through semi-analytic procedure for direct evaluation of the monodromy matrix. The ST appears when the instability of the localized edge states leads to solutions with frequency components belonging to the propagation zone of the linear substructure. This mechanism substantially differs from previously observed ST scenarios, related to a generation of the propagating breathers. Various bifurcation sequences eventually leading to the ST are revealed and discussed.

Novel periodic pile barrier with low-frequency wide bandgap for Rayleigh waves

This paper aims to investigate the propagation of low-frequency seismic surface waves in periodic in-filled barriers from the viewpoint of bandgaps. Based on Bloch-Flouquet theory, four configurations of periodic pile barriers with the same filling rate but different cross sections are studied. The periodic boundary conditions are imposed to derive the characteristics equation. Simultaneously, the finite element method is used to calculate the numerical dispersion relation and vibration modes of four types of periodic pile barriers with various inclusions. The sound cone and the energy parameter method are introduced to identify the surface wave modes further. Additionally, the mitigation effectiveness of a finite number of periodic barriers is evaluated using a three-dimensional transmission model. The results show that the initial frequency and bandwidth of the surface bandgaps are sensitive to the shape of the cross-section and mechanical parameters of the inclusions. The surface wave bandgaps within 9.64 ∼ 13.92 Hz are observed for the periodic barrier composed of cross-like polyfoam sections. Moreover, the radiation modes formed by the leakage of some surface waves into the sound cone are expected to widen the attenuation zones of the periodic barriers. The numerical results in frequency and time domains further validate the attenuation effect of finite barrier in the bandgap and the attenuation widening phenomenon caused by the dissipation of the leak modes into the bulk. This study provides new insights into the design of periodic pile barriers. In the future, it is expected to mitigate the low-frequency ground motion by fully designing the section shape and filling materials of pile barriers.

Forest trees as a natural metamaterial for surface wave attenuation in stratified soils

Forest trees have been shown to act as a natural metamaterial to attenuate elastic waves. However, the existing studies assumed that forest trees are located on homogeneous soils and did not consider the soil stratification that widely exists in natural strata. This study investigates the forest trees as a natural metamaterial to manipulate the propagation of elastic waves in stratified soils. A semi-analytical method is proposed to calculate the dynamic responses of a layered half-space coupled with arbitrary number of trees. A close-form Green’s function for a harmonic line load on a layered half-space is derived by the thin layer method, and subsequently used to determine the multiple scattered wavefield induced by forest trees as surface oscillators. The attenuation performance of forest trees on stratified soils is systematically investigated. Trees with a graded array of heights can provide a wide attenuation zone at frequencies below 80 Hz. Since the higher surface wave modes in a layered half-space can propagate forward without being affected by trees, the attenuation efficiency of trees on stratified soils is significantly lower than that of trees on corresponding homogeneous soils. The performance uncertainty induced by the randomness of the height, sizes, and spacing of trees is subsequently investigated through a Monte Carlo simulation. The forest trees can still obtain a significant attenuation efficiency at frequencies below 80 Hz even the randomness of tree properties being considered. The randomness in height and radius leads to significant uncertainty in attenuation performance, while the randomness in spacing results in reasonable uncertainty.

Analytical and experimental study of a metamaterial beam with grading piezoelectric transducers for vibration attenuation band widening

This paper analytically and experimentally investigates the potential of a piezoelectric metamaterial beam with a spatial grading pattern for broadband vibration attenuation. Distributed bimorph piezoelectrics with varying lengths form the “graded” manner. A fully coupled analytical model based on the transfer matrix function is developed to exhibit the vibration attenuation capabilities. The band structure of the graded supercell structure and the transmittance response of the finite-length counterpart show that the bandwidth of the vibration attenuation zone can be significantly broadened by the spatial variation of the piezoelectric transducers, while multiple resonant-related passbands/peaks occur. By properly introducing electrical damping (e.g., 200 Ω), the resonant peaks can be significantly attenuated. Subsequently, for the first time, we experimentally confirmed the broadband vibration attenuation performance of the graded piezoelectric metamaterial. The harmonic excitation test demonstrates that the enlarged attenuation region can be achieved: with the spatial variation of 1 mm, the attenuation bandwidth can be increased up to 80 % as compared to conventional metamaterial with identical piezoelectric patches. Furthermore, the white noise excitation test verifies the broadband attenuation capabilities. The results show that the root-mean-square (RMS) acceleration of the graded metamaterial beam is remarkably reduced as compared to that of the conventional one.

Study on the microfiber attenuation in melt-blowing airflow field

Melt blowing (MB) is a process for producing microfiber or nanofiber using high-velocity air to attenuate the polymer jet. Compared to research on the melt-blowing airflow field analysis, the melt blown die optimization, and new materials development, little work has been done on fiber attenuation and whipping in the melt-blowing process. In this study, the airflow field distribution and turbulence fluctuation of the melt-blowing die are investigated using numerical simulation. The fiber motion process is simulated with the bead-viscoelastic element model and obtained using the high-speed camera. The underlying mechanisms leading to melt-blowing fiber attenuation have been discussed. The results show that the airflow field can be separated into three regions. The turbulent fluctuations in Regions I are related to the fiber whipping in the melt-blowing process. The fiber motion in Regions II and III are unsteady, resulting in higher fiber attenuation. Region II is the main zone of fiber attenuation where the fiber whipping increases and the drawing ratio is the largest. The fluctuation of air velocity causes fiber whipping which plays an important role in fiber attenuation. Experimental results of fiber diameter reduction and fiber motion are consistent with the simulation results.

Functionally Graded Materials Pile Structure for Seismic Noise Cancellation

This study explores surface-wave propagation through periodic arrangements of multilayered piles in a single-layer soil medium from the viewpoint of bandgaps. The influence of the geometrical parameters of the model on the bandgaps is discussed. The periodic theory of solid-state physics is imposed to derive the dispersion equation. The finite-element method is implemented to calculate the dispersion relation and attenuation zones for surface waves in a periodic pile and soil system. The results show that the bandgaps are sensitive to the size and arrangement of the piles. The practicability of ground vibration-isolation by periodic pile barriers are verified in the time domain. The location and width of bandgaps are further authenticated through finite unit cell–based frequency response analyses. It is found that the frequency range of the Rayleigh wave reduction agrees well with the theoretical attenuation zone. This work provides new insights into the design of periodic piles as wave barriers. This approach has scope for protecting infrastructures, such as nuclear power plants, which pose high environmental risks. It is found that the dispersion analysis gives essential information for Rayleigh wave isolation using piles, including the frequency range and the form of decline.

Research and determination of the acoustic parameters of the movement of a cavitation bubble in a liquid medium according to discrete and continuous models

In the work, the study and determination of the acoustic parameters of the movement of a cavitation bubble in a liquid medium according to discrete and continuous models was carried out. The research is based on the hypothesis that the determination of the effective parameters of the work process of acoustic processing is implemented by applying a transitional physical model from a discrete to a continuous type of processing of the technological environment. The obtained analytical dependences allow to calculate the amplitude of oscillations and the frequency of natural oscillations. With the help of the specified formulas, it is possible to determine the zones of amplification or attenuation of the amplitude of oscillations for different frequencies of oscillations. The proposed formula for determining the frequency of natural oscillations, which takes into account changes in the properties of the medium from homogeneous at the initial stage to the appearance of cavitation bubbles at the specified frequency of natural oscillations. Numerical values of intensity, pressure, amplitude of oscillations, velocity, acceleration, viscosity and maximum bubble radius are given. The obtained numerical values can be used in practical calculations of acoustic processing parameters of different nature and properties of technological environments.

The 21st century water quality challenges for managed aquifer recharge: towards a risk-based regulatory approach

Sustained environmental and human health protection is threatened by ~350,000 chemicals available in global markets, plus new biological entities including coronaviruses. These water-quality hazards challenge the proponents of managed aquifer recharge (MAR) who seek to ensure the integrity of groundwater. A risk-based regulatory framework accounting for groundwater quality changes, adoption in subsurface attenuation zones, and use of advanced monitoring methods is required to support confidence in the sustainability of MAR.

Theoretical and Numerical Study on the Pile Barrier in Attenuating Seismic Surface Waves

The purpose of this study is to investigate the attenuation effect of the pile barrier in blocking seismic surface waves by using theoretical and numerical methods. First, we derive the dispersion characteristics of pile barriers embedded in soil from the perspective of periodicity theory to explain that such periodic barriers can attenuate seismic surface waves when the main frequencies fall into the band gaps of the pile barrier. Second, the dispersion characteristics of periodic barriers composed of different inclusions are discussed, and it is suggested preliminarily that scatters with low stiffness and low density are more conductive to mitigate low-frequency surface waves. Third, a three-dimensional transmission calculation model is also developed to illustrate that the attenuation zone of a finite number of piles is consistent with the surface wave band gap. Finally, transient analysis of the periodic pile barriers is performed to validate the block effects on seismic surface waves. The numerical results show that the frequency band gaps of multi-row pile barriers are in accordance with the frequency band gaps of the surface wave in theory, which can greatly mitigate surface ground vibration. The pile spacing, number of piles, and pile length are the key parameters that can affect the width of attenuation zones of the periodic barriers by an appropriate design.

Breather propagation and arrest in a strongly nonlinear locally resonant lattice

Locally resonant metamaterials have recently drawn the attention of many researchers due to their capability in controlling low-frequency waves by forming a bandgap resulting from mode hybridization. Although linear acoustics of these metamaterials have been extensively explored, only a little is known about their nonlinear acoustics. This work investigates the nonlinear acoustics of a 1D discrete strongly nonlinear locally resonant metamaterial under impulsive force excitation. The metamaterial is modeled as a chain of linearly grounded masses connected by essential strong nonlinearity (purely cubic nonlinearity), and embedded by linear local resonators. Numerical investigations demonstrate the existence of different families of traveling breathers that depend on the coupling coefficient between the local resonator and its holding cell. One of these families is reported for the first time in the current work due to the existence of multiple fast frequencies in its profile. Although the investigated system is undamped, numerical simulations demonstrate that the breather arrest is controlled by certain parameters of the system. In the limit of small energy levels, the complexification averaging method (CX-A) is utilized with the help of numerical observations to demonstrate some aspects of the nonlinear acoustics of the system. Particularly, analytical analysis is used to determine the nonlinear band structure of the system. The outcome indicates the presence of two energy-dependent nonlinear propagation zones (PZs) (i.e., acoustics and optical) and three complementary attenuation zones (AZs) for the infinite lattice case. In addition, the different families of traveling breathers in the semi-infinite lattice are investigated analytically and compared to their corresponding numerical results.

Mitigation of seismic waves using graded broadband metamaterial

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

Novel periodic pile barriers in saturated soil and applications to propagation attenuation of shear plane waves

The frequency attenuation zones (AZs) of periodic pile barriers have attracted extensive attention in recent years due to their superior performance in ambient vibration reduction. However, the research on vibration isolation of pile barriers in saturated soil is very limited. Also, the configuration of the traditional pile barrier is simple and the AZ width is narrow, which limits its application in engineering practice. In this paper, to develop novel periodic pile barriers with the maximum relative attenuation zone width (RWAZ) in saturated soil, the topology optimization on the periodic pile unit is carried out with the genetic algorithm (GA) and FEM. For different site conditions, the effects of the saturated soil porosity, the drained elastic modulus, the drained density and the tortuosity coefficient of soil on the optimization results are analyzed, and the corresponding optimized pile structures are proposed, respectively. Thus, the effect of material distribution on the RWAZ is disclosed, and novel periodic pile structures for ambient vibration isolation in saturated soil are developed. Furthermore, the superior shear plane wave attenuation performances of the optimized pile structure in saturated soil are both demonstrated by the established 2D and 3D numerical models.

Novel locally resonant and widely scalable seismic metamaterials for broadband mitigation of disturbances in the very low frequency range of 0–33 Hz

Most current shielding mechanisms against seismic disturbances fail in protecting structures from low-frequency vibrations typically in the range of 1–10 Hz. This paper proposes a novel locally resonant Zero-Frequency Stop Band (ZFSB) metamaterial in the form of cylindrical resonators clamped to a 0.5 m thick concrete bed. This concept is convenient for practical implementation, and yields effective broadband wave inhibition in the ultra-low frequency range of 0–33 Hz. Through numerical simulations validated first against published experimental data, the concept is shown to achieve an attenuation zone due to the local resonance occurring between surface waves and the metamaterial features. Dynamic response- and transient time-analyses are used to gain insight into phononic dispersion in the proposed metamaterial, allowing the authors to demonstrate the working of the proposed concept. The effect of the material properties of the clamping bed on the performance of the proposed seismic metamaterial is also studied. The numerical results are then further validated through 1:40 scaled-down laboratory experiments. The proposed metamaterial when combined with soil with layered material properties, is later shown to nucleate wider ZFSB. The concept proposed is widely scalable for practical implementations and thus of much interest for isolation and protection of civil structures from low-frequency seismic disturbances.

MAPPING OF S-WAVES ATTENUATION FIELD AT EAST KAZAKHSTAN AND WEST ALTAY REGIONS BY DATA OF MKAR SEISMIC STATION

We are analyzing recordings of local earthquakes in the regions of Eastern Kazakhstan and Western Altay, obtained by stations MAKZ and MKAR. We consider correlation dependence of maximum amplitudes ratio for Sn and Pn waves (Sn/Pn parameter) on distance. On the base of this dependence mapping of S wave attenuation field in the lithosphere of this region is carried out. A special attention is paid to high attenuation zones, comparison with seismicity is carried out. It is established, that the highest attenuation corresponds to the rupture zone of large Chu earthquake of 2003 (Mw=7.3). Besides, an anomaly of high attenuation is found in the area of Semipalatinsk test site (STS) and to the south of it. We discuss reasons of high shear wave attenuation in rupture zones of large earthquakes, and also within some sections of the STS.

Adaptive genetic algorithm enabled tailoring of piezoelectric metamaterials for optimal vibration attenuation

Piezoelectric metamaterials with shunt resonant circuits have been extensively investigated for their tunability in bandgaps. However, the vibration attenuation ability induced by the electromechanical coupling is generally weaker than that of mechanical metamaterials, limiting their applications in engineering practice. This research presents a non-uniform piezoelectric metamaterial beam with shunt circuit parameters optimized by an adaptive genetic algorithm (AGA) for tailoring the vibration attenuation zone. First, the non-uniform piezoelectric metamaterial beam is modeled for transmittance analysis and verified by the finite element method. By simultaneously tuning the resonance frequencies and the resistance of the shunt circuits, it is conceptually demonstrated that the attenuation zone can be broadened, and the undesired localized vibration modes can be mitigated. Subsequently, two optimization strategies are proposed respectively for two typical vibration scenarios. The inductances and the load resistance in the shunt circuits constitute the set of design variables and are optimized by the AGA. Dedicated case studies are carried out, and the results show that the objective-oriented circuitry parameters can greatly enrich the design freedom, and tailor the transmittance profile according to a given vibration spectra. As compared to the conventional uniform and the graded piezoelectric metamaterial beams, the proposed design provides superior vibration attenuation performance and demonstrates a promising approach for tailoring piezoelectric metamaterials systems.

Broadband wave attenuation and topological transport in novel periodic pile barriers

Topological insulator (TI) has received enormous attention in recent years due to its intriguing dynamic characterizes of topologically protected wave transport and defect immunity. Besides, the elastic waves can propagate along the pre-designed interface but body, which may dramatically promote practical applications of novel devices. This work introduces the concept of TI into the design of periodic pile barriers, which is expected to realize vibration mitigation and waveguiding simultaneously. By tuning the difference of pile radius, the inversion symmetry is broken and the attenuation zone (AZ) emerges. Then, the topological phase transitions happen when pile positions are interchanged in a unit cell and the opposite valley Chern numbers (Cv) are obtained meanwhile. Based on the complex dispersion (k(ω) method) analysis of supercell, the existence of topological edge states between two types of unit cells with distinct topological phases is confirmed at first. Second, some key parameters affecting the design of periodic pile barriers is discussed comprehensively, especially the influence of soil damping on attenuation zones and edge states. Compared to the traditional real dispersion (ω(k) method), the complex dispersion can describe the propagation property and attenuation property synchronously, providing useful guidances for this novel multifunctional periodic pile barriers. Subsequently, broadband wave attenuation and topological wave transport of novel periodic pile barriers are further validated by the analysis in both frequency domain and time domain, showing high vibration reduction and transmission efficiency. This new kind of wave barriers may have great potential for both vibration mitigation and elastic wave energy harvesting.

The effect of viscosity of saturated soil on the surface wave attenuation by periodic in-filled trench

Investigations on the ambient vibration reduction by periodic wave barriers have been received more and more attention in recent years. However, the role of energy dissipation caused by the viscosity of soil is usually ignored in most of the previous studies. The surface wave attenuation in saturated viscoelastic soil by periodic in-filled trench is investigated in this study. Firstly, the constitutive model of saturated viscoelastic soil is constructed by introducing Kelvin viscoelastic model into the Biot's theory. Secondly, the complex band structure of surface waves propagating in periodic in-filled trench is calculated. A finite model for analyzing ambient vibration isolation is built, and the responses of the site under external excitation are numerically solved both in frequency domain and time domain. The roles of the viscosity of soil and the periodic barrier in the surface wave attenuation are comprehensively discussed, and some findings are obtained. Soil's viscosity reinforces the attenuation when the frequencies of surface waves fall in the attenuation zone. However, the contribution of the viscosity is not obvious. Contrary to the attenuation zone, soil's viscosity plays a key role in the attenuation when the frequencies of surface waves are out of the attenuation zone.

Experimental study of effect of equivalence ratio and initial turbulence on the explosion characteristics of LPG/DME clean blended fuel

The effects of initial turbulence and equivalence ratio on the explosion characteristics of LPG/DME clean blended fuel were investigated experimentally. The results showed that as equivalence ratio increase, the explosion overpressure, rate of pressure rise, and propagation velocity of shock wave assume a "three-zone" structure, that is, first acceleration zone, then attenuation zone, finally stabilization zone. With the increase of initial turbulence, the explosion characteristic parameters such as the maximum explosion overpressure, the maximum pressure rise rate, and the maximum shock wave propagation velocity all showed different degrees of increase, and the reasons for these growths are not the same, which leads to the inconsistent levels of growth. However, the chain-based growth rate of these explosion characteristics parameters decreases with the increase of initial turbulence, which meant that the influence of initial turbulence on explosion intensity was weakened gradually. The maximum explosion overpressure and the maximum rate of pressure rise basically conformed to a linear relationship with the initial turbulence. The results of the paper can provide more basic but important information for the practical use of LPG/DME clean blended fuel, especially in safety protection strategies.