Elastic waves

The paper deals with the problem of measuring the moisture of agricultural soils by an accurate, on-site, real-time method. The idea is to estimate the moisture by measuring the speed of sound in the medium: the main issue is therefore to determine a precise relationship between the two quantities. To this purpose, the Brutsaert's model for elastic waves in porous media is applied, taking into consideration different kinds of soil of common interest in agriculture. The authors have derived the speed-moisture curves, the conditions for the actual validity of the curves, and the suitable sound frequency for performing the measurement, for a wide range of agricultural soils in different physical conditions. The paper results are therefore the basis to realize an inexpensive and accurate moisture sensor for farmers.

The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

We considered a muffin-tin periodic potential (-8 inside the spheres and zero outside). Using the augmented-plane-wave method we systematically studied the location of gaps for positive energy and for various values of 8 and the sphere radius a. Our results are applicable to the problem of classical-wave propagation in composite media and relevant to the problem of optical localization. The question of classical-wave localization (CWL), in particular, light localization, ' has received considerable attention recently both experimentally and theoretically. 9 " In spite of this, no proof exists that CWL does indeed take place in systems characterized by a positive definite random dielectric function. In a recent paper Soukoulis et al. 'z demonstrated numerically that CWL does take place in a lattice model. This numerical work, together with approximate calculations based on the coherent-potential approximation (CPA) and the potential-well analogy'

In elastic wave forward modeling, absorbing boundary conditions (ABC) are used to mitigate undesired refl ections from the model truncation boundaries. The perfectly matched layer (PML) has proved to be the best available ABC. However, the traditional splitting PML (SPML) ABC has some serious disadvantages: for example, global SPML ABCs require much more computing memory, although the implementation is easy. The implementation of local SPML ABCs also has some diffi culties, since edges and corners must be considered. The traditional non-splitting perfectly matched layer (NPML) ABC has complex computation because of the convolution. In this paper, based on non-splitting perfectly matched layer (NPML) ABCs combined with the complex frequency-shifted stretching function (CFS), we introduce a novel numerical implementation method for PML absorbing boundary conditions with simple calculation equations, small memory requirement, and easy programming.

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of ''modified bending stiffness'' is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.

Short laser pulses have been used to generate elastic waves in continuous fiber reinforced aluminum or magnesium. With an optical interferometer the run-time of these waves in various directions of the samples can be measured contactless (point-source-pointreceiver technique). From these data, the five independent components of the complete elasticity tensor for the unidirectional fiber reinforced composites can be determined. These results agree with measurements by a resonant beam technique, acoustic resonance and 4-point bending tests. The laser pulse technique has several advantages: it is contactless, non-destructive and it can be used for online quality control in production processes.

Starting with the exact solution for the scattering of a plane P wave by a homogeneous spherical inclusion, various types of approximate solutions are developed and discussed. The standard Rayleigh and Mie approximations are extended to the case of inclusions having arbitrary contrasts in material properties. For the low-contrast case, solutions are developed which are valid over a wide frequency range. Several aspects of these solutions are discussed, including the importance of near-field terms and the relative strength of the scattered P and S fields. The various types of approximate solutions are compared with each other and with the exact solution by calculating and displaying their normalized scattering cross-sections.

A model is developed for the collision between the baseball and bat, taking into account the transverse bending vibrations of the bat. By coupling the flexible bat to the ball via a parametrized force that each mutually exerts on the other, a complete description of the collision process is obtained, including the exit speed of the ball v f . It is shown that vibrations play an important role in determining v f . The model is in excellent agreement with experimental data at low impact velocities. At the higher velocities more appropriate to the game of baseball, v f is shown to coincide with the rigid-body value only over a very small region in the barrel of the bat and to drop off sharply for impacts removed from that region. Some interesting insights into the collision process are obtained, including the observation that for impacts in the barrel of the bat, the momentum transferred to the ball is essentially complete by the time the elastic wave first arrives at the handle and that any clamping action of the hands will affect the bat at the impact point only after the ball and bat have separated. This suggests that v f is independent of the size, shape, and method of support of the bat at distances far from the impact location.

In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements.

A series of experiments were performed to further investigate the phenomenon of shear-banding in surfactant solutions. Many surfactant solutions, through their unique amphiphilic chemistry, form long wormlike micelle structures which behave like living polymers. These wormlike micelles have interesting viscoelastic properties and have been the subject of a number of recent studies. These water-based surfactant systems are widely used in

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incident P waves and incident S waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for both P and S waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of the P~S scattering is generally much stronger than the S-~P scattering. When averaged over all scattering angles, the mean intensity of the P -, S converted waves is 2 Vp 2 / V 4 times the mean intensity of the S ~P converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scattered S waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.

The current study assesses the residual stresses and remnant damage caused by a spherical projectile impacting upon a¯at surface. The immediate application of this information is to the problem of foreign object damage (FOD) associated with the ingestion of debris into an aircraft turbine engine and the subsequent reduction in component lifetime. The work is focused on two primary features: (i) the development of numerical models for the evaluation of the deformation and stresses associated with the impact process and (ii) the use of spatially resolved residual stress measurements to verify experimentally the numerical analysis. As a ®rst approximation, a quasi-static numerical model was developed by ignoring time-dependent eects (i.e., strain-rate sensitivity, wave and inertia eects, etc.), where the eects of velocity were approximated by adjusting the depth and diameter of the resulting impact crater to match that of actual impact craters at the corresponding velocity. The computed residual stresses and associated elastic strain gradients were compared to experimentally measured values, obtained using synchrotron X-ray diraction (XRD) methods. This comparison indicated that the quasi-static numerical analysis was adequate for moderate impact conditions (velocity 200 m/s, energy 2.7 J); however, under more aggressive conditions (velocity 300 m/s, energy 6.1 J), there was signi®cant discrepancy between the numerical predictions and experimental measurements. Such discrepancy may be attributed to several factors that can occur at higher impact velocities, including strain-rate sensitivity, microcrack formation, and shear-band formation. A dynamic simulation, where the time-dependent eects of strain-rate sensitivity and elastic-wave interactions were approximated, provided results in closer agreement with the experimental diraction observations. Ó

The need for high-frequency, wide-band filters has instigated many developments based on combining thin piezoelectric films and high acoustic velocity materials (sapphire, diamond-like carbon, silicon, etc.) to ease the manufacture of devices operating above 2 GHz. In the present work, a technological process has been developed to achieve thin-oriented, single-crystal lithium niobate (LiNbO3) layers deposited on (100) silicon wafers for the fabrication of radio-frequency (RF) surface acoustic wave (SAW) devices. The use of such oriented thin films is expected to favor large coupling coefficients together with a good control of the layer properties, enabling one to chose the best combination of layer orientation to optimize the device. A theoretical analysis of the elastic wave assumed to propagate on such a combination of material is first exposed. Technological aspects then are described briefly. Experimental results are presented and compared to the state of art.

Упругие волны это векторные волны смещений материальных точек. В отличии от элек-тромагнитных волн они могут быть и поперечными и продольными. Обычно для них записывают разные уравнения. Здесь такого разделения не будет. При наличии поверхно-сти раздела между двумя разными средами граничные условия определяются не самими уравнениями, а некоторыми дополнительными условиями. Большой интерес представля-ют поверхностные волны, особенно в связи с землетрясениями, а также волны в анизо-тропных средах. Здесь так же, как в электродинамике, удается построить решения в виде плоских волн, что облегчает исследование процессов отражения от упругих пластин. 6.1 Упругие волны в изотропных средах В теории упругости основным объектом является вектор смещения u(r, t) точки r в мо-мент времени t. Компоненты вектора смещения u j (r, t) определяются с помощью уравне-ния ρ ∂ 2 u j (r, t) ∂t 2 = ∂σ jk (r,

This thesis is devoted to the study of the high frequency Dirichlet and Neumann problems for the elasticity system. We study the reflection phenomenon at the boundary by means of two techniques: Gaussian beams summation and Wigner measures. In chapters 1 and 2, we start by studying the simpler problem of the scalar wave equation with one speed. Under some hypotheses on the initial conditions, we build an approximate solution by a Gaussian beams superposition. Justification of the asymptotics is based on norms estimate of some integral operators with complex phases. For more general initial conditions, we use Wigner measures to compute the microlocal energy density. We compute Wigner transforms of Gaussian beams integrals in an explicit way. The behaviour of the microlocal energy density for the exact solution is deduced from the one for the approximate solution. In chapter 3, we use the established results on infinite sums of Gaussian beams to build an approximate solution for the elasticity equations and to compute its microlocal energy density. We treat new difficulties arising from the existence of two different speeds in the elasticity system.

Over the past 20 years, thick-film (screen printed) technology has been shown to possess a variety of desirable characteristics, which are particularly suitable for the realisation of micro-sensors and actuators. In particular, thick-film sensors are noted for their robust, versatile, compact and inexpensive nature. This paper will describe how screen printed thick-films can be used as the basis for a variety of piezoelectric a transducers. It will be shown how the technology can be combined with MicroElectroMechanical Systems (MEMS) to generate new types of microengineered structure. The evolution of the technology to a successful enabling mechanism for modern-day solid state sensors is described. The paper begins with a brief overview of piezoelectric thick-films including a discussion of the main factors relating to paste formulation, characterisation and techniques for fabricating devices. There is also a description of methods for fabricating thick-films on silicon, which opens up the possibility of using thick-film technology in the field of MEMS. A number of specific sensors and actuators are described, including accelerometers, micropumps, ultrasonic motors, slip sensors for prosthetic hands, resonators, elastic wave sensors and ultrasonic separators.

The velocity of compressional waves has been determined by measurement of travel time of pulses in specimens of rock at pressures to 10 kilobars a•d room temperature. Most of the samples, mainly igneous and metamorphic rocks, furnished three specimens oriented at right angles to one another. The present paper gives experimental details, modal analyses, and numerical tables of velocity as function of direction of propagation, initial density, and pressure. Discussion of various aspects of the mea•mrements is reserved for part 2. Introduction. Laboratory measurements of elastic constants or of the velocities of elastic waves in rocks are needed for the interpretation of seismic velocities in terms of materials. The first useful measurements were of compressibility: extended to 10 or 12 kilobars by Adams and his collaborators and by Bridgman, they have guided inferences about crust and substratum and, by extrapolation, still deeper levels. In later investigations [Birch and Bancroit, 1938, 1940], the velocity Vs of shear waves was measured to 4 and then 10 kilobars, with temperatures reaching about 600øC [Birch, 1943, 1955]. This velocity may be found with good precision from the resonant frequency of vibration in the torsional mode of cylindrical bars. Attempts to measure elastic constants entering in the frequency equation of other modes of vibration (extensional, flexural) encountered difficulties x Published under the auspices of the Committee on Experimental Geology and Geophysics and the Division of Geological Sciences at Harvard University. ' Editors' note: Professor Birch is to be the recipient of the Twenty-Second Award of the William Bowie Medal during the 1960 Annual Meeting of the American Geophysical Union. associated with the reaction of the pressure medium upon the motion of the specimen. An effort to determine velocity by observation of the travel times of pulses, made in the late 1930's with the aid of Dr. Dennison Bancroft, was hampered by the inadequacy of the oscilloscopes and other electronic devices of that period; a primitive time-measuring device was constructed, however [Bancro]t, 1940], which showed a degree of promise. This situation was transformed by the wartime development of pulse circuitry, fast-writing oscilloscopes, and many other useful components; it then became relatively easy to accomplish what had previously seemed virtually impossible. Responding to these new possibilities, a number of investigators have published measurements of wave velocities in rocks, as well as in many other materials. Among those especially interesting for geophysical problems are the papers by Hughes and others, showing effects of both pressure and temperature [Hughes approaches (E/p) TM for wavelengths long with respect to the bar diameter. A large number of papers have been devoted to the discussion of wave propagation in cylindrical bars, but there seems to be no complete theoretical solution for the propagation of pulses in short bars. (For a recent review, see, for example, Mason, 1958, p. 40 et seq.) It can be demonstrated experimentally, however, that the first motion does travel with the velocity Vr in materials for which the elastic constants can be determined independently, such as glass, steel, or aluminum, and, by observing with samples of different sizes, that this velocity is independent of length and diameter of sample and of transducer frequency within certain ranges of dimensions and of experimental accuracy. This has been done in the course of the present study, and earlier by students of ultrasonic delay lines and others [for example, Mason and McSkimin, 1947; Roth, 1948; Hughes, Pondtom, and Mims, 1949]. Probably the most comprehensive investigation, though of relatively low precision, is that of $ilaeva and $hamina [1958]. Even for so nearly ideal a medium as silica glass, the first motion arrives gradually, with a 'foot' which recedes toward shorter times as the amplification is increased. This is discussed in more detail below; the principal limitation on accuracy comes from this circumstance. The first motion is followed by a long train of disturbances which have not been much utilized in the present work. Hughes and others (1949 VELOCITY OF COMPRESSIONAL WAVES IN ROCKS 1085 WAVES IN ROCKS

In this paper we evaluate coating-substrate adherence in galvanized steel with the Acoustic Emission (AE) technique applied during scratch tests (ST), analyzing in this way the elastic waves emitted during microfracture processes. Hot-dip galvanized samples were obtained, with different ...

Chronic hepatitis is accompanied by progressive deposit of hepatic fibrosis, which may lead to cirrhosis. Evaluation of liver fibrosis is, thus, of great clinical interest and, up to now, has been assessed with liver biopsy. This work aims to evaluate a new noninvasive device to quantify liver fibrosis: the shear elasticity probe or fibroscan. This device is based on one-dimensional (1-D) transient elastography, a technique that uses both ultrasound (US) (5 MHz) and low-frequency (50 Hz) elastic waves, whose propagation velocity is directly related to elasticity. The intra-and interoperator reproducibility of the technique, as well as its ability to quantify liver fibrosis, were evaluated in 106 patients with chronic hepatitis C. Liver elasticity measurements were reproducible (standardized coefficient of variation: 3%), operator-independent and well correlated (partial correlation coefficient ‫؍‬ 0.71, p < < 0.0001) to fibrosis grade (METAVIR). The areas under the receiver operating characteristic (ROC) curves were 0.88 and 0.99 for the diagnosis of patients with significant fibrosis (> F2) and with cirrhosis ( ‫؍‬ F4), respectively. The Fibroscan is a noninvasive, painless, rapid and objective method to quantify liver

Both time-and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.

This paper is concerned with the experimental identification of the whole dynamic elastic stiffness tensor of a transversely isotropic clayrock from a single cylindrical sample under loading. Measurement of elastic wave velocities (pulse at 1 MHz), obtained under macroscopically undrained triaxial loading conditions are provided. Further macroscopic (laboratory scale) interpretation of the velocity measurements is performed in terms of (i) dynamic elastic parameters; and (ii) elastic anisotropy. Experiments were performed on a Callovo-Oxfordian shale, Jurassic in age, recovered from a depth of 613 m in the eastern part of Paris basin in France. Moreover, a physically-based micromechanical model is developed in order to quantify the damaged state of the shale under loading through macroscopic measurements. This model allows for the identification of the pertinent parameters for a general transversely isotropic orientational distribution of microcracks, superimposed on the intrinsic transverse isotropy of the rock. It is directly inspired from experimental observations and measurements. At this stage, second-and fourth-rank tensors a ij and b ijkl are identified as proper damage parameters. However, they still need to be explicited in terms of micromechanical parameters for the complex case of anisotropy. An illustration of the protocole of this microstructural data recovery is provided in the simpler case of isotropy. This microstructural insight includes cavities geometry, orientation and fluid-content.

In the present letter, the authors consider the diffraction of plane harmonic compressional wave ͑P wave͒ by a nanosized circular hole. The surface elasticity theory is employed to incorporate the surface effects. The results show that once the radius of hole reduces to nanometers, surface energy significantly affects the diffraction of elastic waves. For incident waves with different frequencies, the influences of surface elasticity on dynamic stress concentration are discussed in details.

As a non-destructive, non-invasive and non-ionizing evaluation technique for heterogeneous media, the ultrasonic method is of major interest in industrial applications but especially in biomedical fields. Among the unidirectionally heterogeneous media, the continuously varying media are a particular but widespread case in natural materials. The first studies on laterally varying media were carried out by geophysicists on the Ocean, the atmosphere or the Earth, but the teeth, the bone, the shells and the insects wings are also functionally graded media. Some of them can be modeled as planar structures but a lot of them are curved media and need to be modeled as cylinders instead of plates. The present paper investigates the influence of the tubular geometry of a waveguide on the propagation of elastic waves. In this paper, the studied structure is an anisotropic hollow cylinder with elastic properties (stiffness coefficients c ij and mass density q) functionally varying in the radial direction. An original method is proposed to find the eigenmodes of this waveguide without using a multilayered model for the cylinder. This method is based on the sextic Stroh's formalism and an analytical solution, the matricant, explicitly expressed under the Peano series expansion form. This approach has already been validated for the study of an anisotropic laterally-graded plate Baron and Naili, 2010) [6,5]. The dispersion curves obtained for the radially-graded cylinder are compared to the dispersion curves of a corresponding laterally-graded plate to evaluate the influence of the curvature.

We derive the nondiffracting X waves, first discussed within acoustics by Lu and Greenleaf ͓IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19 ͑1992͔͒, using the general mathematical formalism based on an angular spectrum of plane waves. This serves to provide a unified treatment of not only the fundamental zeroth-order X waves of Lu and Greenleaf, but also of the lesser-known higher-order derivative X waves, first discussed here in terms of a single, universal, angular spectrum. The characteristic crossed ͑letter-X-like͒ shape and the special properties of the X waves, as well as of their angular-spectrum representation, are discussed and illustrated in detail. Asymptotically, for increasing order, the appearance of the X waves is found to transform into a triangular wedgelike waveform. ͓S1063-651X͑96͒04910-0͔

A simple method for preparing artificial kidney stones with varying physical properties is described. BegoStone was prepared with a powder-to-water ratio ranging from 15:3 to 15:6. The acoustic properties of the phantoms were characterized using an ultrasound transmission technique, from which the corresponding mechanical properties were calculated based on elastic wave theory. The measured parameters for BegoStone phantoms of different water contents are: longitudinal wave speed (3,148–4,159 m/s), transverse wave speed (1,813–2,319 m/s), density (1,563–1,995 kg/m3), longitudinal acoustic impedance (4.92–8.30 kg/m2 s), transverse acoustic impedance (2.83–4.63 kg/m2 s), Young’s modulus (12.9–27.4 GPa), bulk modulus (8.6–20.2 GPa), and shear modulus (5.1–10.7 GPa), which cover the range of corresponding properties reported in natural kidney stones. In addition, diametral compression tests were carried out to determine tensile failure strength of the stone phantoms. BegoStone phantoms with varying water content at preparation have tensile failure strength from 6.9 to 16.3 MPa when tested dry and 3.2 to 7.1 MPa when tested in water-soaked condition. Overall, it is demonstrated that this new BegoStone preparation method can be used to fabricate artificial stones with physical properties matched with those of natural kidney stones of various chemical compositions.

It is known that rock anisotropy can significantly influence the phase and energy velocities of an elastic wave, as well as its reflection/transmission (R/T) coefficients. As a result, it can distort the velocity analysis of seismic-reflection data. In this work we present a velocity analysis for seismic-reflection data based on the available anisotropic rock parameters. We analyzed the created errors on time-depth relation of the seismic-reflection data in neglecting rock anisotropy and/or neglecting the difference between energy velocity and phase velocity, including the case of wide-angle reflection. The calculated results show that the effect of rock anisotropy on time-depth relation of seismic-reflection data is dependent not only on the values of anisotropic parameters, but also on the space arrangement of both source and receiver-array. For all studied cases (weak, moderate or strong anisotropy), we found that the effect of rock anisotropy on time-depth relation could not be neglected. Nevertheless, for the case of weak anisotropy, the energy velocity may be replaceable by the phase velocity to obtain a very good approximation on time-depth relation. Consequently, the seismic-reflection data processing algorithm for numerical computations can be simplified. rock anisotropy, phase velocity, energy velocity, time-depth relation Citation: Fa L, Castagna J P, Zeng Z W, et al. Effects of anisotropy on time-depth relation in transversely isotropic medium with a vertical axis of symmetry.

Guided elastic waves in the frequency range of a few hundred kHz, generated and detected by appro- priate transducer arrays, are used to monitor the structural integrity of pipes by comparing their actual state with a predefined reference state. For these purposes, theoretical, numerical, and experimental results are combined to study guided wave propagation and wave interaction with relevant defects in detail. Based on these findings, a guided wave based multi-channel structural health monitoring (SHM) system is designed and applied to identify and monitor structural defects in various piping components. The potential use of synthetic aperture techniques is discussed yielding spatial distributions of damage parameters along the pipe. The results reveal that guided wave based SHM in the kHz frequency regime has great potential for online monitoring of piping systems. It combines imaging techniques with long range detection capabilities and therefore closes the gap between local high...

Plane-wave reflection coefficients ͑PWRCs͒ are routinely used in amplitude-variation-with-offset analysis and for generating boundary data in Kirchhoff modeling. However, the geometrical-seismics approximation based on PWRCs becomes inadequate in describing reflected wavefields at near-and postcritical incidence angles. Also, PWRCs are derived for plane interfaces and break down in the presence of significant reflector curvature. Here, we discuss effective reflection coefficients ͑ERCs͒ designed to overcome the limitations of PWRCs for multicomponent data from heterogeneous anisotropic media. We represent the reflected wavefield in the immediate vicinity of a curved interface by a generalized plane-wave decomposition, which approximately reduces to the conventional Weyl-type integral computed for an apparent source location. The ERC then is obtained as the ratio of the reflected and incident wavefields at each point of the interface. To conduct diffraction modeling, we combine ERCs with the tip-wave superposition method ͑TWSM͒, extended to elastic media. This methodology is implemented for curved interfaces that separate an isotropic incidence half-space and a transversely isotropic ͑TI͒ medium with the symmetry axis orthogonal to the reflector. If the interface is plane, ERCs generally are close to the exact solution, sensitive to the anisotropy parameters and source-receiver geometry. Numerical tests demonstrate that the difference between ERCs and PWRCs for typical TI models can be significant, especially at low frequencies and in the postcritical domain. For curved interfaces, ERCs provide a practical approximate tool to compute the reflected wavefield. We analyze the dependence of ERCs on reflector shape and demonstrate their advantages over PWRCs in 3D diffraction modeling of PP and PS reflection data.

The detection and characterization of defects in structures is an important issue in non-destructive testing. To avoid the scanning of large samples, guided elastic waves, which propagate along the structure, are excited. These waves interact with a defect, which results in a scattered wave field. In an experiment, the displacements of these scattered waves are recorded over time for a fixed axial coordinate at a number of circumferential positions of a circular cylindrical tube. Since in complex structures it is difficult to determine the axial and particularly circumferential position of the defect directly from the time signals, a time reversed numerical simulation is performed. There the measured displacement histories are reversed in time and used as displacement excitations in a simulation of the tested structure. A three-dimensional code in cylindrical coordinates, based on a velocity-stress finite-difference method, is used to simulate the wave propagation. As long as the ge...

We present a new method for wave propagation in global earth models based upon the coupling between the spectral element method and a modal solution method. The Earth is decomposed into two parts, an outer shell with 3-D lateral heterogeneities and an inner sphere with only spherically symmetric heterogeneities. Depending on the problem, the outer heterogeneous shell can be mapped as the whole mantle or restricted only to the upper mantle or the crust. In the outer shell, the solution is sought in terms of the spectral element method, which stem from a high order variational formulation in space and a second-order explicit scheme in time. In the inner sphere, the solution is sought in terms of a modal solution in frequency after expansion on the spherical harmonics basis. The spectral element method combines the geometrical flexibility of finite element methods with the exponential convergence rate of spectral methods. It avoids the pole problems and allows for local mesh refinement, using a non-conforming discretization, for the resolution of sharp variations and topography along interfaces. The modal solution allows for an accurate isotropic representation in the inner sphere. The coupling is introduced within the spectral element method via a Dirichlet-to-Neumann (DtN) operator. The operator is explicitly constructed in frequency and in generalized spherical harmonics. The inverse transform in space and time requires special attention and an asymptotic regularization. The coupled method allows a significant speed-up in the simulation of the wave propagation in earth models. For spherically symmetric earth model, the method is shown to have the accuracy of spectral transform methods and allow the resolution of wavefield propagation, in 3-D laterally heterogeneous models, without any perturbation hypothesis.

In order to reduce the costs related to corrosion damage in aircraft structures, it is vital to develop new robust, accurate and reliable damage detection methods. A possible answer to this problem is offered by newly developed nonlinear ultrasonic techniques, which monitors the nonlinear elastic wave propagation behaviour introduced by damage, to detect its presence and location.In this paper, a new nonlinear time reversal technique is presented for the detection and localization of a scattered zone (damage) in a multi-material medium. In particular, numerical findings on a friction stir-welded aluminium plate-like structure are reported. Damage was introduced in the heat affected zone and modelled using a multi-scale material constitutive model (Preisach–Mayergoyz space).Studies were conducted for two different transducer configurations. Particular attention was devoted to find the optimum time-reversed window to be re-emitted in the structures. The methodology was compared with traditional time-reversal acoustics (TRA), showing significant improvements. While the traditional TRA was not able to clearly localise the damage, the developed technique identified in a clear manner the faulted zone, showing its robustness to locate and characterize nonlinear sources, in presence of a multi-material medium.

The paper gives effective use of the elastic and plastic properties of the material pre-stressed in steel beams with a significant increase in dry capacity with a change in the cross section of the upper and lower shelves, reducing material consumption and cost of construction.

The Micro-and Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives, trends, and directions in mechanics of heterogeneous materials in January 2010. The international journal, Acta Mechanica Solida Sinica, is devoted to all fields of solid mechanics and relevant disciplines in science, technology, and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. On the occasion of the 30 th anniversary of Acta Mechanica Solida Sinica, its editor-in-chief, Professor Q.S. Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids, with a particular emphasis on the recent research development results of Chinese scientists. Their reviews are organized into five research areas as reported in different sections of this paper. §I firstly brings in focus on micro-and nano-mechanics, with regards to several selective topics, including multiscale coupled models and computational methods, nanocrystal superlattices, surface effects, micromechanical damage mechanics, and microstructural evolution of metals and shape memory alloys. §II shows discussions on multifield coupled mechanical phenomena, e.g., multi-fields actuations of liquid crystal polymer networks, mechanical behavior of materials under radiations, and micromechanics of heterogeneous materials. In §III, we mainly address the multiscale mechanics of biological nanocomposites, biological adhesive surface mechanics, wetting and dewetting phenomena on microstructured solid surfaces. The phononic crystals and manipulation of elastic waves were elaborated in §IV. Finally, we conclude with a series of perspectives on solid mechanics. This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development. Supports from NSFC and MOST are acknowledged. · 2 · ACTA MECHANICA SOLIDA SINICA 2011 I. MICRO-AND NANO-MECHANICS 1.1

To accurately predict production in compactible reservoirs, we must use coupled models of fluid flow and mechanical deformation. Staggered-in-time loose coupling of flow and deformation via a high-level numerical interface that repeatedly calls first flow and then mechanics allows us to leverage the decades of work put into individual flow and mechanics simulators while still capturing realistic coupled physics. These two processes are often naturally modeled using different time stepping schemes and different spatial grids-flow should only model the reservoir, whereas mechanics requires a grid that extends to the earth's surface for overburden loading and may extend further than the reservoir in the lateral directions. Although spatial and temporal variability between flow and mechanics can be difficult to accommodate with full coupling, it is easily handled via loose coupling. We cal-culate the total stress by adding pore pressures to the effective rock stress. In turn, changes in volume strain induce updates to porosity and permeability and, hence, dynamically alter the flow solution during simulation. Incorporating the resulting time-dependent pressures, saturations, and porosities (from coupled flow and mechanics) into Gassmann's equations results in seismic wave velocities and densities that can differ markedly from those calculated from flow alone. In a synthetic numerical experiment based on Belridge field, California, incorporation of coupled flow and mechanical deformation into time-lapse calculations produces compressional wave velocities that differ markedly from those produced by flow alone. In fact, it is the closing of the pores themselves (reduction in permeability) in this example which has the greatest impact on fluid pressures and saturations and, hence, elastic wave parameters such as velocity.

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is to evaluate the dynamic behavior of two-dimensional cellular structures, with the focus on the effect of the geometry of unit cells on the dynamics of the propagation of elastic waves within the structure.

Thin NiAl bicrystals 5 mm in diameter and 150-350 m thick were tested under laser-induced shock compression to evaluate the material behavior and the effect of localized strain at the grain boundary on the failure of these specimens. Circular NiAl bicrystal samples with random misorientation were grown using a modified Czochralski technique and samples were prepared for shock compression at moderate pressures (<10 GPa). The observed crack patterns on the drive surface as well as the free surface were examined using optical microscopy. Transmission electron microscopy (TEM) of the drive surface as well as in the bulk of one grain was performed on recovered specimens following shock compression. This revealed that a nanocrystalline region with a grain size of 15-20 nm formed on a thin layer at the drive surface following the plasma expansion phase of the laser-induced shock. TEM in the bulk of one grain showed that plastic deformation occurred in a periodic fashion through propagation of dislocation clusters. Cracking on the free surface of the samples revealed a clear grain boundary affected zone (GBAZ) due to scattering of the shock wave and variations in wave speed across the inclined boundary. Damage tended to accumulate in the grain into which the elastic wave refracted. This damage accumulation corresponds well to the regions in which the transmitted waves impinged on the free surface as predicted by elastic scattering models.

In this paper, we generalize the high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, designed earlier by us in Xing and Shu (2005, J. Comput. phys. 208, 206-227) for the shallow water equations, to solve a wider class of hyperbolic systems with separable source terms including the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. Properties of the scheme for the shallow water equations (Xing and Shu 2005, J. Comput. phys. 208, 206-227), such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions, are maintained for the scheme when applied to this general class of hyperbolic systems.

We consider a three-dimensional composite material made of small inclusions periodically embedded in an elastic matrix, the whole structure presents strong heterogeneities between its different components. In the general framework of linearized elasticity we show that, when the size of the microstructures tends to zero, the limit homogeneous structure presents, for some wavelengths, a negative mass density tensor. Hence we are able to rigorously justify the existence of forbidden bands, i.e., intervals of frequencies in which there is no propagation of elastic waves. In particular, we show how to compute these band gaps and we illustrate the theoretical results with some numerical simulations.

We report an actively Q-switched all-fibre laser using a fibre-optic resonant acousto-optic modulator as Q-switching element. The modulator consists of a short-length fibre Bragg grating modulated by a standing longitudinal elastic wave, being the grating length much shorter than the acoustic wavelength. Q-switch pulses were successfully obtained from an Er3+-doped fibre laser at repetition rates of 18 and 37 kHz.

Dynamic crack growth along the interface of a ÿber-reinforced polymer composite-Homalite bimaterial subjected to impact shear loading is investigated experimentally and numerically. In the experiments, the polymer composite-Homalite specimens are impacted with a projectile causing shear dominated interfacial cracks to initiate and subsequently grow along the interface at speeds faster than the shear wave speed of Homalite. Crack growth is observed using dynamic photoelasticity in conjunction with high-speed photography. The calculations are carried out for a plane stress model of the experimental conÿguration and are based on a cohesive surface formulation that allows crack growth, when it occurs, to emerge as a natural outcome of the deformation history. The e ect of impact velocity and loading rate is explored numerically. The experiments and calculations are consistent in identifying discrete crack speed regimes within which crack growth at sustained crack speeds is possible. We present the ÿrst conclusive experimental evidence of interfacial crack speeds faster than any characteristic elastic wave speed of the more compliant material. The occurrence of this crack speed was predicted numerically and the calculations were used to design the experiments. In addition, the ÿrst experimental observation of a mother-daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack is documented. The calculations exhibit all the crack growth regimes seen in the experiments and, in addition, predict a regime with a pulse-like traction distribution along the bond line. ?

In this paper we present the results of a systematic theoretical and experimental investigation of the fundamental aspects of using piezoelectric wafer active sensors (PWASs) to achieve embedded ultrasonics in thin-gage beam and plate structures. This investigation opens the path for systematic application of PWASs for in situ health monitoring. After a comprehensive review of the literature, we present the principles of embedded PWASs and their interaction with the host structure. We give a brief review of the Lamb wave principles with emphasis on the understanding the particle motion wave speed/group velocity dispersion. Finite element modeling and experiments on thin-gage beam and plate specimens are presented and analyzed. The axial (S 0 ) and flexural (A 0 ) wave propagation patterns are simulated and experimentally measured. The group-velocity dispersion curves are validated. The use of the pulse-echo ultrasonic technique with embedded PWASs is illustrated using both finite element simulation and experiments. The importance of using highfrequency waves optimally tuned to the sensor-structure interaction is demonstrated. In conclusion, we discuss the extension of these results to in situ structural health monitoring using embedded ultrasonics.

Active sensor wave propagation technique is a relatively new method for in-situ nondestructive evaluation (NDE). Elastic waves propagating in material carry the information of defects. These information can be extracted by analyzing the signals picked up by active sensors. Due to the physical property of wave propagation, large area can be interrogated by a few transducers. This simplifies the process