Propagation Characteristics Of Elastic Waves Research Articles

Elastic wave propagation characteristics of periodic track structure in high-speed railway

Wave propagation in the ordered and randomly disordered periodic track structure in high-speed railways are investigated theoretically and experimentally. Taking the CRTS-I double-block ballastless track structure in China as the research object, a theoretical model of periodic track structure is established. The rail is modelled as a Timoshenko beam considering the bending–torsional coupling. The dispersion curves of the periodic track structure are obtained according to the transfer matrix method and Bloch theory. Based on the Lyapunov exponent algorithm, the elastic wave propagation characteristics of the randomly disordered periodic track structure are further calculated and analyzed considering the random disorder of structure parameters. The obtained results show that the periodic track structure is characterized by band gaps, elastic wave propagation attenuates significantly within the band gap, and random disorder in the track structure can expand the attenuation regions. Finally, the band gap characteristics of the vertical/lateral flexural wave and torsional wave are verified respectively through an in situ experiment.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

ELASTIC REVERSE TIME MIGRATION BASED ON WAVEFIELD SEPARATION

AbstractCompared with other imaging algorithms (e.g., ray‐based, one‐way wave equation), reverse time migration (RTM) based on the two‐way wave equation exhibits greater superiority, especially in handling steeply dipping structures. However, imaging with conventional single‐component seismic data is unsuited for some complicated structures (e.g., gas clouds). Elastic RTM, which is based on the elastodynamic equation and uses multi‐component seismic data to extract PP and PS reflectivity and subsurface information, can more consistently reproduce the characteristics of elastic wave propagation in real Earth media, resulting in seismic images that more accurately characterize the subsurface. To begin with, we exploit the first order stress‐velocity equations to extrapolate the elastic vector wavefield, then the P‐ and S‐wavefields are separated by computing the divergence and curl operator of the extrapolated particle‐velocity wavefield. Then, imaging profiles with pure wave modes are computed by applying the source normalized cross‐correlation imaging condition, thus avoiding crosstalk between unseparated wave modes. To address the polarity reversal problem of the converted image, we propose an alternative method in the common‐shot domain. We also develop an efficient method that reconstructs the source wavefield in the reverse time direction to save storage in the GPU and to avoid large input/output in the elastic reverse time migration. During the forward modeling, the method only saves the particle‐velocity wavefield of all time intervals within an efficient absorbing boundary and the total wavefields in the final time interval. When we extrapolate the receiver wavefield in the reverse time direction, we simultaneously reconstruct the total source wavefields via the saved wavefields. Numerical examples performed with the graben and Marmousi2 models have shown that the polarity reversal correction method works, and elastic reverse time migration can accurately characterize complicated structures.

Blasting Source Equivalent Load on Elastic–Plastic Boundary for Rock Blasting

AbstractElastic and plastic zone development law is discussed according to the propagation characteristics of elastic and plastic waves induced by rock blasting. The calculation method of the elast...

各向异性压电介质摩擦接触界面波动特性分析

The Fourier analysis and the singular integral equation technique were used to investigate the propagation characteristics of elastic wave through frictional contact interface between 2 generally anisotropic piezoelectric materials. The method and procedure were developed to solve the question in the case of slipping but not separating in local interface areas, and the extents and locations of slipping and sticking regions varying with the external mechanical-electrical loads were given. Furthermore, with a polarized ceramic material and quartz, which belong to the hexagonal crystal system and the trigonal crystal system respectively, as the examples, different responses of the friction contact interface between different materials to incident elastic wave were analyzed, and the interface behaviors influenced by different incident angles and external mechanical-electrical loads were studied. High-frequency harmonics will occur because of non-linearity (boundary non-linearity) brought by separation or slip in local interface areas if the incident wave is strong enough. Finally, with quartz as an example, the amplitudes of the reflected and refracted high-frequency harmonics varying with mechanical-electrical loads were comparatively discussed.

Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.

Periodic structure with interconnected nonlinear electrical networks

This article aims at investigating the filtering abilities of periodic structures with nonlinear interconnected synchronized switch damping on inductor electrical networks. Periodic structures without electrical networks themselves naturally have the function of filtering since the structure response breaks into pass bands and stop bands when the structure is excited by an external force with multiple or varying frequencies. Introduction of linear electrical networks in the periodic structure makes stop bands of the structure wider than that of the structure without electrical networks. However, nonlinear piezoelectric electrical networks may have better effect on the mechanical wave attenuation than linear piezoelectric electrical networks in terms of frequency band. Therefore, this article proposes a piezoelectric periodic structure with nonlinear interconnected synchronized switch damping on short-circuit/synchronized switch damping on inductor electrical network. A transfer matrix formulation including the interconnected electrical network is also proposed for deriving the characteristics of elastic wave propagation. The results show that the proposed technique permits enhancing the damping abilities in particular frequency bands compared to electrically independent periodic cells, which, combined with structural tailoring, would allow achieving high damping performance.

Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials

Longitudinal elastic wave propagation characteristics of acoustic metamaterials with various inerter configurations are investigated using their representative one-dimensional discrete element lattice models. Inerters are dynamic mass-amplifying mechanical elements that are activated by a difference in acceleration across them. They have a small device mass but can provide a relatively large dynamic mass presence depending on accelerations in systems that employ them. The effect of introducing inerters both in local attachments and in the lattice was examined vis-à-vis the propagation characteristics of locally resonant acoustic metamaterials. A simple effective model based on mass, stiffness, or their combined equivalent was used to establish dispersion behavior and quantify attenuation within bandgaps. Depending on inerter configurations in local attachments or in the lattice, both up-shift and down-shift in the bandgap frequency range and their extent are shown to be possible while retaining static mass addition to the host structure to a minimum. Further, frequency-dependent negative and even extreme effective-stiffness regimes are encountered. The feasibility of employing tuned combinations of such mass-delimited inertant configurations to engineer acoustic metamaterials that act as high-pass filters without the use of grounded elements or even as complete longitudinal wave inhibitors is shown. Potential device implications and strategies for practical applications are also discussed.

해저터널 주변 그라우팅 보강암반의 탄성파 전달특성 평가

해저터널 시공 중 단층, 파쇄대 및 미고결층 등의 취약한 지반조건에서 일어나는 문제점을 극복하기 위해 시공 중 그라우팅을 진행한다. 암반에서 그라우팅은 주로 불연속면을 따라 주입되므로 절리의 분포, 거칠기 또는 폭과 같은 절리 인자들이 그라우팅 보강암반의 물성에 지대한 영향을 미친다. 해저터널 주변의 그라우팅 보강암반은 해저환경에서 정수압을 다 부담하여 장기적인 열화와 미세구조변화 및 균열 등이 발생하며 암반물성이 시간에 따라 변하므로 그라우팅으로 인한 해저터널 주변암반의 장기적인 거동평가가 요구된다. 본 연구에서는 실내실험을 통해 다양한 축 응력, 양생기간 및 절리조건에서 그라우팅 보강암반의 탄성파 전달특성을 분석하였고 국내에서 사용되는 다양한 암반분류법들의 탄성파 기준을 고려하여 그라우팅 보강암반의 보강정도를 탄성파 속도로 추론하였다. Grouting is frequently used before the construction of subsea tunnels to mitigate problems that can occur in weak ground zones such as joints, faults or unconsolidated settlements during construction. The grout material injected into rock mass often flows through the discontinuities present in the host rock and hence, joint properties such as its distribution, roughness and thickness greatly affect the properties of grouting-improved rocks. The grouting-improved zones near subsea tunnels are also subjected to high water pressures that can cause long-term weathering in the form of changes in grout microstructure and crack formation and lead to subsequent changes in ground properties. Therefore, an assessment method is needed to accurately measure changes in the grouting-improved zones near subsea tunnels. In this study, the elastic wave propagation characteristics in grouting-improved rocks were tested for various axial stress levels, curing time, joint roughness and thickness conditions under laboratory conditions and the results were compared with wave velocity standards in different Korean rock mass classification systems to provide a basis for inferring improvement in grouted rock-mass.

Speed and attenuation of acoustic waves in snow: Laboratory experiments and modeling with Biot's theory

Monitoring acoustic emissions (AE) prior to imminent failure is considered a promising technique for assessing snow slope instability. Gaps in elastic wave propagation characteristics in snow hinder quantitative interpretation of AE signals. Our study focuses on characterizing the propagation of acoustic reference signals in the ultrasonic range across cylindrical snow samples with varying density (240–450kgm−3). We deduced the acoustic attenuation coefficient within snow by performing experiments with different column lengths to eliminate possible influences of the snow-sensor coupling. The attenuation coefficient was measured for the entire burst signal and for single frequency components in the range of 8 to 35kHz. The acoustic wave propagation speed, calculated from the travel time of the acoustic signal, varied between 300ms−1 and 950ms−1, depending on the density and hardness of snow. From the sound speed we also estimated the Young's modulus of our snow samples; the values of the modulus ranged from 30 to 340MPa for densities between 240 and 450kgm−3. In addition, we modeled the sound propagation for our experimental setup using Biot's model for wave propagation in a porous medium. The model results were in good agreement with our experimental results and suggest that our acoustic signals consisted of Biot's slow and fast waves. Our results can be used to improve the identification and localization of acoustic emission sources within snow in view of assessing snow slope instability.

Computation of dispersion relations of functionally graded rectangular bars

The propagation characteristics of elastic wave in the functional graded rectangular bars are studied by the two dimensional Rayleigh–Ritz method. Legendre orthogonal polynomials are used as trial functions. The material properties are assumed to be graded along the width direction. This dispersion equation is obtained from the 3D variational formulation governing elastodynamics. The convergence and accuracy are demonstrated by comparisons with the available solution of the scaled boundary finite element method. Finally, we give some phase and group curves of various rectangle waveguides and analyze influences of the width to length ratio and volume fraction indexes on dispersive behavior for wave propagation.

Low frequency acoustic characteristics of periodic honeycomb cellular cores: The effect of relative density and strain fields

Aluminum honeycomb cores, widely used in lightweight composite sandwich structures, are inherently weak and highly susceptible to buckling, permanent deformation and damage. This damage can detrimentally affect the structural integrity of sandwich structures and should be detected and repaired. Detecting damage to honeycomb cores is difficult as cores are sandwiched between composite sheets and not accessible. Typically, for such scenario a non-destructive testing method such as ultrasound is appealing. However, with the periodic and porous structure of honeycomb cores, at ultrasound frequencies they are dispersive and exhibit high transmission loss; thus they are incompatible with standard ultrasound techniques. Conversely, at sub-ultrasound frequencies honeycomb cores are less dispersive. Therefore low frequency elastic waves can potentially be used to non-destructively inspect honeycomb cores. To enable low frequency non-destructive testing of honeycombs, it is instrumental first to characterize their sub-ultrasound wave propagation and dispersion characteristics. Accordingly, this work, using finite element analysis, provides insights into the propagation characteristics of low frequency acoustic elastic waves in aluminum honeycomb cores in terms of phase velocity; dispersion and directionality characteristics; and frequency band gaps. Also, the effect of relative density and defects in the form of deformation on sub-ultrasound wave characteristics are explored.

DYNAMIC AND EQUILIBRIUM PROPERTIES OF THE INHOMOGENEOUS GEOLOGICAL ENVIRONMENT

Purpose. The goal of this work is to study the properties of structurally heterogeneous geological mediums by the example of Meotian sediments which form landslide areas of the Odessa coast. Methodology. Acoustic properties of Meotian sediments were investigated in laboratory conditions by sounding of selected samples by ultrasonic pulses at different frequencies. Finding. The results of researches of physical-mechanical and acoustic properties of the samples of Meotian sediments at various depths of occurrence are given. A good co-ordination between the results of sounding rocks and their physical and mechanical properties with the results of theoretical studies of the frequency dependence of the sound velocity and absorption coefficient in heterogeneous media was obtained. The revealed anomalies have indicated that structural nonlinearities determine a character of propagation of the acoustic field in such media. Results. On the basis of analysis of changes in kinematic and dynamic characteristics of elastic wave propagation in rocks, acoustic methods are considered as the most informative ones in engineering-geological practice and in geological survey too.

Metamaterial based on elastic mechanics

In recent years, artificial metamaterials base on micro structures are showing huge development potential in fields of materials science, acoustics, seismology and information technologies, due to their devisable physical singularities which do not exist in natural materials. The study of metamaterial was born out of electromagnetic metamaterial. Nowadays, metamaterials have achieved a big leap forward with developments in the fields of acoustic, thermal, static, static magnetic and elastic mechanics, which greatly expand their study fields. With the help of a Milton graph, we focus on the extraordinary characteristics of novel elastic mechanics-based metamaterials and their species, such as acoustic metamaterials with negative mass density and elastic modulus, auxetic metamaterials with negative Poissons ratio, inverse bulging metamaterials with shear modulus G =0 and ultra-light materials with high strength. In addition, combining with the transform mechanical, this paper focuses on the propagation characteristics of acoustic and elastic waves in this elastic mechanics metamaterial and then elaborated the characteristics and physical effects of surface acoustic waves in the interface of metamaterials with negative elasticity parameters. Finally, we make a summary and prospect of the development of metamaterials combining with the elastic mechanics metamaterial research condition in China, such as metamaterial and acoustic metamaterial operating acoustic and elastic wave propagation using the elastic mechanics, design and development of a new type of elastic mechanics metamaterial. We hope this will help to accelerate the application of this metamaterial in many research fields.

Analysis of the Attenuation Characteristics of an Elastic Wave Due to the Wave-Induced Fluid Flow in Fractured Porous Media

A theoretical model is presented to describe the elastic wave propagation characteristics in porous media of periodically arranged fractures. The effects of fracture geometric parameters on a compressional wave (p-wave) are considered through analysis of the wave induced fluid flow (WIFF) process between the fractures and the background media. The diffusion equation in porous media is used to reveal how the entire diffusion process affects the wave propagation. When the thickness proportion of fractures tends to 0 and 1, the WIFF does not take place almost between fractures and background matrix porosity, and therefore the media elasticity modulus is perfectly elastic. When the fracture thickness fraction achieves a certain value, the peak of the attenuation curve reaches the maximum value at a particular frequency, which is controlled by the fluid mass conservation and stress continuity conditions on each fracture boundary. That is, the inter-coupling of fluid diffusion between the adjacent layers is important for waves attenuation. Physically speaking, the dissipation of a wave is associated with the fluid flux essentially.

Elastic wave propagation characteristics under anisotropic squirt-flow condition

A theoretical model of elastic wave propagation in a cracked porous medium is developed in this paper. When elastic wave propagates through the cracked porous medium, the different physical properties and geometries in different pores structures lead to the fluid pressure gradient in cracks and between cracks and pores. The squirt-flow will take place in two mutually-perpendicular directions, thus, it has anisotropic characteristic. The wave respond contains the crack and background medium permeability information simultaneously. Owing to the fluid dynamic flow process, the effective elastic modulus is complex and frequency-dependent. When the wave frequencies are in high and low limit, the porous medium is elastic. The wave attenuation is obvious and the attenuation is frequency-dependent in the middle frequency region. The anisotropic permeability corresponding to anisotropic characteristic times in the cracked porous medium causes the wave propagation to be affected by the crack connectivity. There appears a second attenuation peak for larger thickness value of crack, meanwhile, and the peak of attenuation is influenced by the thickness value and radius of crack.

Numerical Study of Elastic Wave Propagation Characteristics in Cracked Rock

Numerical methods can provide extremely powerful tools for analysis and design of engineering systems with complex factors that are not possible or very difficult with the use of the conventional methods. In this paper, we use the 2-D boundary element method (BEM) program to model elastic wave excited by a point explosive source propagating in cracked rocks. As an example, we consider the typical crack distributions in rocks, both models for the real crack structure are also talked about. The elastic wave propagating in rocks with aligned cracks and parallel fractures is assumed. Effects of different crack parameters, such as crack scale length and crack density are analyzed. Numerical results show that the BEM is a powerful interpretive tool for understanding the complicated wave propagation and interaction in cracked solids.

Band Gaps of 2D Phononic Crystal with Imperfect Interface

Propagation characteristics of elastic waves in 2D phononic crystal consisting of parallel cylinders embedded periodically in a homogeneous host medium are investigated. The multiple scattering method and the Bloch wave theory in a periodic system are used to derive the dispersive equation. Dispersive curves are evaluated numerically in the reduced Brillouin zone and the wave band gaps are obtained. The imperfect interface between the scatterer and the host, namely, the displacement or traction vector are not continuous, are considered. These imperfect interfaces considered include the spring interface, the mass interface, spring-mass interface, and the slide interface. The influence of the imperfect interface upon the wave band gaps is discussed based on the numerical results. Some interesting phenomena are observed and physical explanations are given.

Elastic wave propagation in nano-composites with random distribution of spherical inclusions

In the present study, efforts have been made to theoretically study the diffraction of plane harmonic compressional waves by a spherical nano-inclusion based on the Gurtin-Murdoch surface/interface elasticity theory in which the interface between the nano-inclusion and the matrix is considered as the material surface which has their own mechanical properties. Furthermore, a nano-composite has been considered in order to assess the size effect on the wave propagation characteristics of a plane compressional elastic wave containing the randomly distributed spherical nano-inclusions. Also, the phase velocities and attenuations of P and SV elastic waves along with the related dynamic effective elastic properties have been investigated for a wide variety of frequencies and volume fractions.

Propagation characteristics of elastic wave in layered medium and applications of impact imaging method

It is an important subject to probe the structure in the medium by various kinds of detection methods in the geotechnical engineering. Based on the propagation theory of elastic wave in half-space layered medium, the propagation characteristics of elastic wave in layered medium with different elastic parameters are discussed using dynamic analysis of finite element method. It is known that the S-wave velocity, density and thickness of layer are related to the properties of the elastic wave including waveform characteristics, spectral characteristics and time-frequency characteristics. We pay special attention to the structure with low velocity interlayer. The impact imaging method is applied to the grouting construction of the immersed tube tunnel. Data acquisition and analytical method are introduced in detail. The grouting effects can be qualitatively evaluated by comparing the characteristics of elastic wave before grouting with those after grouting. Finally, a quantitative evaluation is obtained according to the relationship between energy response of elastic wave and impedance ratio.