Reflection Of Elastic Waves Research Articles

Effect of fractional interporosity flow on elastic waves propagation through a fluid-saturated double-porosity interlayer

The reflection and transmission behaviors of elastic waves through a fluid-saturated double-porosity interlayer are studied in present work. In order to simulate the interporosity flow, which cannot be appropriately described by the Darcy’s law, a modified transport equation using fractional order derivative is introduced to the double-porosity, dual-permeability model for the wave propagation in fluid-saturated double-porosity solid. The reflection and transmission coefficients are derived by satisfying the interfacial conditions of tractions and displacements. As a main feature of fluid-saturated double-porosity solid, the influences of interporosity flow on the wave propagation behavior are mainly studied. The numerical results are provided and shown graphically. It is observed that the reflection/transmission and the energy dissipation behavior are affected noticeably by the interporosity flow.

Solid-liquid interface reconstruction for sandwich structure metal plate via laser-ultrasonic techniques.

A laser-ultrasonic testing system was built for the purpose of liquid core detection of a moving and inaccessible continuous casting slab. Reflected waves from different solid-liquid interfaces are studied using the simulation model established with the finite element method. The solid-liquid interfaces of a sandwich structure aluminum plate were preliminarily detected and reconstructed using the time of flight data of ultrasound propagated between layers. Multiple equal-interval ultrasonic echoes were detected and analyzed according to the reflection and transmission of elastic waves in the solid-liquid interface. A B-scan map for the sandwich structure sample was obtained to show the difference between echoes reflected from each interface. Interfaces of different samples were used to calculate the interface position with relative error no more than 1.3%.

Calculation of reflection and transmission coefficients for waves in multilayered piezoelectric structures using the mixed variable method.

The reflection and transmission (R/T) behavior of elastic waves in an anisotropic multilayered piezoelectric structure bounded by two homogeneous half-spaces is studied using the mixed variable method. The mixed variable method, which is based on the mixed energy matrix, takes the displacement vector at one end of the structure and the stress vector at other end of the structure as the basic variables. The wave equation for a homogeneous piezoelectric layer is transformed into a first-order state equation in the Hamiltonian system by introducing a dual vector. The general solution of the state equation can be expressed in terms of the eigenvalues and eigenvectors of the complex Hamiltonian matrix. A mixed energy matrix is applied to establish the relationship between the generalized displacement and stress vectors on the upper and lower interfaces of a layer. By an efficient recursive algorithm, the global mixed energy matrix is formed for an arbitrarily anisotropic multilayered piezoelectric structure. The R/T coefficients of the waves in an anisotropic multilayered piezoelectric structure are derived by the global mixed energy matrix. Numerical examples are provided to show the robustness of the mixed variable method. The effects of the incident angles, wavenumbers, and critical angles on the R/T coefficients are discussed.

HORIZONTAL DIKES IN A CRYSTALLINE BASEMENT: SHIELDING EFFECT OF THE BASEMENT-COVER CONTACT

Issues related to the formation of sheetlike, initially horizontally bedded intrusions of basic, utrabasic and alkaline composition in the contact zone of the crystalline basement and the sedimentary cover are considered. The main patterns in the formation of the sheets, as well as their host subhorizontal in situ crushing and/or brecciation zones in basement granitoids and metamorphites were identified for different regions and different geodynamic settings in the Paleoproterozoic-Paleogene interval. A connection was assumed to exist between the appearance of such crushing and/or brecciation zones and the wave process: the reflection of elastic deformation waves from the interface of two media contrasting in physical and mechanical properties (basement-cover) giving rise to standing waves in the basement, which predetermine the localization of in situ crushing zones during stress relief (tectonic caisson effect).

High-Precision Forward Analysis and Field Test of Boulder Detection on Zero-Offset Elastic Wave Method in Shield Tunnel

Efficient and accurate boulder detection technology is essential for shield tunneling safely under complex floodplain geological conditions. The traditional seismic reflection method is not suitable for complex geological conditions and small targets near the surface, the elastic wave reflection method based on zero-offset observation is proposed in this article. Forward is the basis of inversion, a high-order staggered grid finite difference algorithm based on least-squares optimization (LS-SGFD) is established, which has the advantages of higher accuracy and smaller dispersion. Three typical geological models are designed, and the elastic wave reflection characteristics of the method proposed in this paper and the traditional method are systematically analyzed. From the dual perspectives of field experiment and engineering application, the effectiveness of zero-offset observation for the detection of boulders is discussed, and the basic criteria for boulder identification are given. Research shows that this method has good results in detecting boulders on the surface, and it has certain reference significance for similar projects.

A hybrid nondestructive testing method for detecting cavities behind the retaining wall

This study proposes a combination of nondestructive testing methods for detecting soil cavities behind retaining walls, which adversely affect the stability of the sloping ground or retaining structures. An experimental study is conducted using a soil chamber filled with dry sands retained by a concrete wall plate. A hemispherical soil cavity is simulated just behind the wall plate, and elastic wave reflections of impacts on the wall are measured using accelerometers. The measured elastic waves are analyzed using the signal energy in time domain and predominant frequency and mobility spectrum in frequency domain. In addition, spatiotemporal changes in the surface of the wall during heating and cooling sequences are monitored using infrared thermography. The captured thermal image is then used for identifying the cavity. Experimental results show that the cavity leads to increases in the signal energy, predominant frequency, and flexibility in the mobility spectrum. The contrasts in the thermal images effectively reveal the shapes and locations of the soil cavity. This study demonstrates that the hybrid testing method that conducts a careful inspection by elastic waves on areas suspected in the preliminary scanning by the infrared thermography can be competitive and effective for detecting soil cavities.

Elastic Wave Reflection at the Interface at Preset Stresses

Elastic Wave Reflection at the Interface at Preset Stresses

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

A nonlocal stress expansion Legendre orthogonal polynomial method is proposed to study the reflection and transmission of elastic waves through piezoelectric nanoplates sandwiched in two solid half-spaces. The proposed method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. The reflection and transmission of plane waves and out-plane waves are studied separately with considering the electrical open circuit boundary. The convergence of presented method is discussed. The correctness of presented method is verified by comparing with the published data of piezoelectric nanoplates immersed in water, which can be considered as a simplified situation sandwiched in two solid half spaces. In addition, the nonlocal effect on the wave mode conversion, stress and electric displacement distribution, and piezoelectricity are discussed. Results show that the nonlocal effect reconstructs the wave mode conversion, and enhances the influence of the piezoelectricity on the critical angle.

Modeling elastic wave propagation through a partially saturated poroviscoelastic interlayer by fractional order derivatives

The reflection and transmission problems of elastic waves through a partially saturated porous interlayer sandwiched between two elastic solid half-spaces are investigated. The partially saturated porous interlayer contains solid phase, gas phase and liquid phase. The solid frame is modeled by the fractional Zener model where the fractional order derivatives are used to describe the complex history-dependent viscoelastic behavior. Due to the coupled effects of the multiple fields, there exist three longitudinal waves and one transverse wave in the porous medium. The numerical results of reflection and transmission coefficients and the energy dissipation ratios are provided and shown graphically. The effects of the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame are discussed based upon the numerical results. It is observed that the reflection and transmission coefficients and the energy dissipation ratios are affected noticeably by the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame. In particular, there exists the characteristic gas saturation where the energy dissipation increases drastically.

Elastic waves propagation through a liquid-saturated poroelastic interlayer based on the fractional viscoelastic BISQ model

The reflection and transmission problems of elastic waves, through a liquid-saturated poroelastic interlayer sandwiched between two elastic solid half-spaces, are investigated. The reflection and transmission coefficients are derived based on the Biot/squirt (BISQ) model, which incorporates both the Biot and squirt-flow mechanisms. Moreover, the viscoelasticity of the solid frame and the pore fluid are also considered. The fractional Zener model and the fractional dashpot model (Abel dashpot) are adopted for the solid frame and the pore fluid, respectively. The numerical results are provided and shown graphically. The dependences of the attenuation, the reflection and transmission coefficients upon the characteristic squirt flow length are numerically discussed. Comparing with that predicted by Biot theory without considering the squirt flow effects, it is observed that the reflection and transmission coefficients and the attenuation due to the sandwiched interlayer are affected noticeably by the effect of the squirt flow.

Influence of interface condition on reflection of elastic waves in fluid-saturated porous media

The characteristics of P-wave reflection coefficients can be dependent on the properties of the interface separating the two dissimilar poroelastic media. To evaluate the influence of the interface condition, we have developed a general theoretical formulation of seismic reflection and transmission of waves at arbitrary incidence angles in fluid-saturated porous media. The formulation is derived based on the quasistatic Biot’s theory and incorporates a more general boundary condition for fluid pressure. Simple analytic expressions are obtained for reflection and transmission coefficients at normal incidence. The equations incorporate an interfacial impedance that can be used to effectively characterize the interface condition. Based on the new formulation, we study the coupled effects of dynamic fluid flow and the interface condition on the reflection and transmission coefficients. Two pertinent reflection scenarios in exploration geophysics are considered in the numerical analysis, i.e., a gas-water contact and a free fluid overlying a gas-saturated medium. We examine the corresponding P-wave reflection coefficient resulting from different interface conditions such as imperfect hydraulic contact, capillary pressure, and open- and sealed-pore interfaces. Our results reveal that the interface condition can affect the frequency dependence and amplitude-versus-angle signatures of the reflection coefficient.

Shear-wave manipulation by embedded soft devices

In accordance with hyperelastic transformation theory, a range of shear-wave manipulation devices can be designed with neo-Hookean materials pre-deformed properly. However, how such devices fit the background medium remains elusive. In this study, a systematic formula is developed in terms of elastic wave transmission and reflection between un-deformed and pre-deformed hyperelastic materials. By both theoretical analyses and numerical simulations, the shear-wave propagation from an un-deformed neo-Hookean material to the pre-deformed one is investigated. Among the three typical deformations, “constrained” uniaxial tension and simple-shear are found to be able to ensure total transmission, whereas ordinary uniaxial tension and hydrostatic compression could cause reflection. Thus, three embedded shear-wave manipulation devices are proposed, namely, a unidirectional cloak, a splicing beam bend and a concave lens; their performance is verified by numerical simulations. This study may underpin the design and realization of soft-matter-based wave control devices. Potential applications can be expected in nondestructive testing, impact protection, biomedical imaging, as well as soft robotics.

Reflection and refraction of elastic waves at the interface of an elastic solid and partially saturated soils

The present problem deals with the reflection and refraction of plane waves at the interface of an elastic solid and partially saturated soils. A mathematical model of partially saturated soils developed by Ghasemzadeh and Abounouri (Soil Dyn Earthq Eng 51:1–8, 2013) is employed. The incidence of two main waves (P and SV) is considered. As a result of the incident wave, two reflected waves (in an elastic solid) and four refracted waves (in partially saturated soils) are generated. The elastic solid behaves non-dissipative, while partially saturated soils behave dissipative due to the presence of viscous pore fluids, as a result of which the incident and reflected waves are homogeneous and all the refracted waves are inhomogeneous. The coefficients of reflection and refraction for a given incident wave result in a non-singular system of linear equations. Further, these reflection and refraction coefficients are used to obtain the energy shares of various reflected and refracted waves. This study has been numerically tested to determine the effects of various properties of partially saturated soils on the various energy shares. The numerical example confirms that during the reflection or refraction process conservation of incident energy is obtained at each angle of incidence.

Converted-wave model building and imaging based on common-focus-point methodology

Seismic images can be viewed as photographs for underground rocks. These images can be generated from different reflections of elastic waves with different rock properties. Although the dominant seismic data processing is still based on the acoustic wave assumption, elastic wave processing and imaging have become increasingly popular in recent years. A major challenge in elastic wave processing is shear-wave (S-wave) velocity model building. For this reason, we have developed a sequence of procedures for estimating seismic S-wave velocities and the subsequent generation of seismic images using converted waves. We have two main essential new supporting techniques. The first technique is the decoupling of the S-wave information by generating common-focus-point gathers via application of the compressional-wave (P-wave) velocity on the converted seismic data. The second technique is to assume one common VP/ VS ratio to approximate two types of ratios, namely, the ratio of the average earth layer velocity and the ratio of the stacking velocity. The benefit is that we reduce two unknown ratios into one, so it can be easily scanned and picked in practice. The PS-wave images produced by this technology could be aligned with the PP-wave images such that both can be produced in the same coordinate system. The registration between the PP and PS images provides cross-validation of the migrated structures and a better estimation of underground rock and fluid properties. The S-wave velocity, computed from the picked optimal ratio, can be used not only for generating the PS-wave images, but also to ensure well registration between the converted-wave and P-wave images.

Reflection of Plane Waves at an Interface of Water/Patchy Saturated Porous Media with Underlying Solid Substrate

The problems with elastic wave reflection at the interface between the water/patchy saturated porous media and the underlying solid matrix are considered. When porous media is saturated by biphasic fluids, the patchy saturation theory can explain the wave dispersion and attenuation better than the classical Biot theory at mesoscopic scales. Based on patchy saturation theory, this paper focuses on the reflection of elastic waves by patchy saturated porous media inclusion in layered media. Using numerical calculation, the reflection coefficients with different excitation frequencies, water saturations, and porous media depths are discussed. The results show that the differences between two kinds of patchy saturated porous media cases in the oil-water model are lower than those between the same two cases in the gas-water model. Low water saturation and high water saturation have significant effects on the reflection coefficient.

Concrete density estimation of linac bunker walls using impact-echo testing.

To estimate the concrete density of a newly constructed bunker using impact-echo testing prior to the installation of the linear accelerator. A newly constructed bunker showed visible honeycombing after the removal of the construction formwork. Impact-echo testing, which is based on the propagation and reflection of elastic waves in solids, was applied to confirm the bunker shielding integrity. A mechanical impact on the bunker wall generates a stress pulse, which propagates through the wall and is reflected or refracted by voids or changes in material characteristics such as density. Surface displacements caused by the reflected waves are recorded by a transducer, located near the impact point. The resulting displacement-time curves are analysed in the frequency domain for anomalies. The dominant frequencies are related to the depths from which stress waves are reflected within the structure. If the dynamic elastic modulus and Poisson ratio of the concrete are known, then the measured velocity of the so-called P-wave can be related to the concrete density. Validation measurements on a wall with known concrete density gave an estimate within 3% of the true density. Measured velocities on the honeycombed wall ranged from 3750m/s to 4300m/s, corresponding to densities of 2894kg/m3 and 2201kg/m3 respectively, with the majority of estimated densities ranging from 2307kg/m3 to 2544kg/m3. A radiation survey after the installation of the linear accelerator confirmed adequate shielding. Impact-echo testing presents a viable solution to confirm bunker shielding integrity before the installation of a linac.

Mixed variational one-dimensional dynamic thermo-viscoplasticity for wave propagation

In view of recent developments in advanced manufacturing and nanomaterial technologies, which have enabled realization of novel material architectures at small-scale, a mixed variational temperature-dependent rate-dependent thermo-viscoplastic continuum element is proposed and developed for elastic, plastic, and thermal wave propagation problems. The variational scheme is based on a Hamiltonian approach, while for the temporal and spatial discretization scheme a discrete calculus of variations approach is adopted. Within this framework, an exponential temperature dependence for material properties and second sound effects is included. The developed framework sets the foundations that can lead to new class of temperature dependent models for capturing thermoplastic behavior and wave propagation of different materials. The robustness of the proposed variational approach, and aspects of coupled dynamic temperature-dependent thermoplastic response are demonstrated through several case studies. Applications include elastic, plastic, and thermal wave propagation and reflection in semi-infinite and finite length space at small temporal scales.

Effect of local fluid flow on the reflection and transmission of elastic waves at an interface between an elastic solid and a double-porosity medium

We have studied the reflection and transmission of elastic waves incident on an interface separating an elastic solid and a double-porosity medium described by the Biot-Rayleigh model that considers the effect of local fluid flow (LFF). The P1- and SV-wave incidence generates two reflected elastic waves in the elastic solid and four transmitted inhomogeneous waves in the double-porosity medium, represented by Helmholtz potential functions. The reflection and transmission coefficients are derived in closed form based on the boundary conditions at the interface. Energy ratios are then derived, and energy conservation at the interface is verified. The contribution of fluid flow to the three transmitted longitudinal waves in the double-porosity medium is expressed as a function of frequency, the transmission coefficient, and the corresponding slowness vector. Numerical examples indicate that LFF predicts significant compressional-wave velocity dispersion in the seismic band, and frequency-dependent reflection and transmission coefficients. For the case in which the incidence angle is larger than the critical angle, the transmitted P1-wave shows a nonzero energy flux in the vertical direction, whereas it does not if LFF is absent.

Scattering of qSH-waves from a corrugated interface between two dissimilar nematic elastomers

ABSTRACT This paper aims to investigate the reflection and transmission phenomena of elastic waves due to incident qSH-wave at a corrugated interface between two different nematic elastomer half-spaces. The expression of the phase velocity for shear harmonic wave is derived and observed that this phase velocity depends on the angle of propagation. There exist irregularly reflected and transmitted waves besides the regular waves due to undulated nature of the interface whose nth spectrum is related through Spectrum theorem. The amplitude ratios for various reflected and transmitted waves are derived using boundary conditions. The ratios corresponding to an irregular waves are found to be functions of the incident angle, elastic constants, relaxation times, corrugation and frequency parameters. The energy distribution, and hence the energy ratios due to various reflected and transmitted waves are also obtained. It is observed that the sum of all energy ratios is approximately unity at each value of incident angle which ensures the law of conservation of energy at the interface. A particular case, has been performed to validate the present study for the amplitude and energy ratios. Graphs are plotted for these ratios at different values of corrugation and frequency parameters to discuss their effects.

Scattering and Backscattering Study of Mechanical Plane Wave in Composite Materials Plates (Earth model 1066B and LiNbO3)

Reflection and refraction phenomenon pattern of elastic plane wave at the interface between anisotropic monoclinic elastic half-space and isotropic elastic half-spaces is studied. Closed-form expression for phase velocity is obtained. Reflection and transmission coefficients are obtained using the method of Cramer's rule in determinant form. Also, the energy ratios are calculated in terms of reflection and transmission coefficients. Numerical examples are considered to exhibit all the findings graphically. The energy conservation law is implemented at each angle of incidence to validate the numerical results, and it is found that energy ratios are in good agreement with the energy conservation law.