Study Of Elastic Wave Propagation Research Articles

Electromagnetic field generated by acoustic wave scattering at a poroelastic inclusion located in a fluid

The study of elastic wave propagation in poroelastic media is of considerable scientific interest because of some effects that do not appear in monophasic elastic or viscoelastic media. In the case of interconnected pores containing a moving fluid in a poroelastic medium, there exist two types of longitudinal waves. In heterogeneous porous media, the energy of elastic oscillations is redistributed due to mutual transformation of elastic waves of different types at the inclusion boundaries. The filtration flow that appears there results in the case of polar fluids in a displacement of electric double layers at the pore boundaries, and, as a consequence, in generation of an electromagnetic field.We consider the problem of the scattering of an elastic wave by a spherical poroelastic inclusion in a fluid. The solution was obtained for sufficiently low frequencies so that the dispersion of the elastic wave on individual grains of the porous media may be neglected and the averaged equations of the mechanics of continuous media (at the so-named mesoscale) may be used. In order to describe the elastic wave propagation, we have used the Pride system of electrokinetic equations. For the solution of our problem, we have applied the decomposition of the potentials of acoustic and electromagnetic waves into spherical harmonics. We have obtained the dependencies of the generated electromagnetic field on the inclusion porosity and the fluid properties in pores. The results were obtained for fully open pore interface at the inclusion boundary.

Finite-element and semi-analytical study of elastic wave propagation in strongly scattering polycrystals.

This work studies scattering-induced elastic wave attenuation and phase velocity variation in three-dimensional untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite-element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A > 1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 1 < A < 3.2 but it deteriorates as A increases. The wavefields and signals from FE modelling show the emergence of very strong scattering at low frequencies for strongly scattering materials that cannot be fully accounted for by the theoretical models. To account for such strong scattering at A > 1, a semi-analytical model is proposed by iterating the far-field Born approximation and optimizing the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A < 1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed.

Theoretical study of elastic wave propagation through a functionally graded micro-structured plate base on the modified couple-stress theory

In this paper, two different methods, Legendre orthogonal polynomial method (LOPM) and Global matrix method (GMM), are combined with the couple-stress theory to investigate the reflection and transmission of P wave in a functionally graded (FG) couple-stressed plate immersed in liquid. The GMM needs to divide the FG plate into the multilayered model, with each layer containing six partial waves. However, the LOPM only expands the displacement vectors in the FG couple-stressed plate into the Legendre orthogonal polynomial series. The paper shows that both methods are in good agreement. Nevertheless, the proposed LOPM is more efficient for the FG microstructure because it does not require plate delamination and calculation of the displacements of each partial wave. It also shows that the couple-stress effect affects the resonant frequencies of the FG plate, decreasing the number of resonant frequencies. By controlling the gradient field, some resonances can be avoided.

Elastic Weyl Points and Surface Arc States in Three-Dimensional Structures

The study of elastic wave propagation is relevant to many engineering applications, such as crashworthiness, nondestructive testing, and energy harvesting. The authors discuss how elastic energy can be guided along the surface of a three-dimensional mechanical structure, without any penetration to its core. The mechanical design here is inspired by the recent discovery of Weyl semimetals. Using full numerical simulations, they demonstrate robust wave propagation on the surface of a fuselagelike hollow structure, with no backscattering at corners or surface defects.

Elastic-wave transmission through self-similar anisotropic Cantor-like multilayers

Through the study of elastic wave propagation in Cantor-like anisotropic multilayers, this work analyzes the influence of medium geometry on the transmission of elastic waves to yield a better understanding of the connection between topological ordering and physical properties. Cantor-like multilayers, whose homothetic dimension is modified by changing the length of the central segment, are made of one anisotropic material with two orientations. The influence of the combination of self-similarity and anisotropy on the global transmission is investigated by means of iteration order, homothetic dimension and layer orientations. The propagation is described by the stiffness matrix algorithm. The results reveal that the homothetic dimension scales the resonance frequencies and the frequency ranges of the pseudo band gaps, and that layer orientation influences the speed of quasi-transverse waves to enhance the effect of self-similarity. Finally, an extensive study on various frequency ranges is conducted. It is demonstrated that self-similarity may be used to tune the position and the width of the pseudo band gaps to minimize the global acoustic transmission.

Accurate finite element simulation and experimental study of elastic wave propagation in a long cylinder under impact loading

For the first time, detailed accurate numerical solutions for elastic wave propagation in a long axisymmetric elastic bar under impact loading are obtained using the new finite element technique proposed in our recent papers. In contrast to known numerical techniques, the new numerical approach quantifies and removes spurious high-frequency oscillations which may invalidate numerical results in impact loading simulations. The comparison of the accurate experimental results for the impact of striker and incident bars with the corresponding accurate numerical results allows us to explain some details of elastic wave propagation in long bars. For example, due to the absence of very high frequencies in the obtained experimental results, the mathematical formulation of the problem should include physical damping for the corresponding range of high frequencies. This range can be defined by the filtering stage of the new approach in terms of the number of finite elements along the radial direction of the bar. By the variation of this number we can fit the experimental curves with the numerical results obtained by the new numerical technique. However, for the accurate numerical solution of the impact problem with zero physical damping, the number of elements in the radial direction should be large. By the comparison of the numerical and experimental data, we can accurately determine the longitudinal wave velocity from experiments. The accurate numerical solutions also allow the analysis of the uniformity of the different strain and velocity components across the radius at different distances from the impact face. The validity of some assumptions used in the 1-D theory for wave propagation in long bars is also checked by the use of the accurate numerical solution. We have also shown that at the elastic impact the known dispersion-correction technique used for the description of the shape of the wave pulse at different locations along the axisymmetric bar is inaccurate for the prediction of pulses close to the impact face.

A New Method of Preparing Artificial Cores with Certain Cracks for Experiment Study of Elastic Wave Propagation

Crack universally existing underground is an important kind of pores. In order to study the elastic wave propagation in fractured medium through experiment, a new method to make artificial core with certain cracks using oil well cement and camphor sheet or thin steel sheet is put forward. Geometric parameters of the crack, such as shape, size and aspect ratio, are approximately equal to that of camphor sheet or thin steel sheet. Using the thin steel sheet to make crack can be more easy and accurate to control the crack angle than using camphor sheet. The crack opening scales at millimeters. The aspect ratio of cracks formed by camphor sheet ranges from 1.4 to 8, and aspect ratio of cracks formed by thin steel sheet ranges from 2.5 to 70. This method is proved simple and feasible by experiment practice, which can provide artificial cores with certain crack for acoustic wave propagation study.

Elastic wave and energy propagation in angled beams

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.

Calculation of vibration transmission over bedrock using a waveguide finite element model

AbstractA finite element method is developed for the study of elastic wave propagation in layered ground environments. The formulation is based on a spectral finite‐element approach using a mixture of high‐order element shape functions and wave solutions. The numerical method provides solutions to vibration transmission on and within layered elastic waveguides. Examples of its use include the theoretical analysis of transmission of vibrations in the vicinity of the surface of the ground. The mathematical model is two dimensional, and the interior of the ground is modelled as an elastic layer overlying a rigid foundation. An analysis of the natural modes of free vibration in a single layer and two layers is presented and compared with known results. In addition the forced response of the layers, for which the surface is assumed to be subjected to a harmonic point force load is shown. These results also include an illustration of the attenuation of surface vibration due to ‘wave impedance blocks’ in the ‘near field’ of the source up to a frequency of 200 Hz for two soil types. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Shear wave splitting in three-dimensional anisotropic media

Splitting intensity, a new seismic observable that characterizes seismic anisotropy, can be expressed as linear combinations of elastic perturbations involving 3-D sensitivity (or Fréchet) kernels. We conduct a numerical study of elastic wave propagation in weakly anisotropic heterogeneous media in order to investigate the validity of the different assumptions made in the derivation of these kernels. For characteristic periods larger than 6 s, the splitting parameters obtained from the analysis of synthetic seismograms calculated using a spectral-element method (SEM) are in excellent agreement with predictions based upon the 3-D kernels. This suggests that the kernels fully capture the complexity of shear wave splitting in heterogeneous anisotropic media and can be used for tomography. In addition, they can be used to calculate synthetic splitting parameters in 3-D anisotropic media, which represents a very small amount of computation compared with finite-difference or finite-element modelling. 3-D kernels distribute sensitivity off of the reference ray given by the laws of geometrical optics. This has important consequences for the interpretation of apparent splitting parameters, which usually relies on ray theory. Apparent splitting parameters estimated at the surface can differ significantly from the anisotropic properties in the underlying medium wherever heterogeneities occur with a characteristic wavelength smaller than approximately 0.75 times the width of the first Fresnel zone , with λ the wavelength and z the depth.

Study of elastic wave propagation induced by piezoelectric actuators for crack identification

The current paper provides a theoretical study of elastic wave propagation in a cracked elastic medium induced by an embedded piezoelectric actuator. The formulation of the problem is based on a newly developed actuator model and the solution of coupled crack and actuator problems. The interaction between an actuator and a crack is studied to develop basic understanding of the effect of the crack upon the wave field generated. The resulting wave field is used to simulate 'sensor signals'. Scattered wave from the crack is then regenerated by solving a reverse elastodynamic problem and used in an imaging technique to identify the crack.

The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials

Finite elements with graded properties are used to simulate elastic wave propagation in functionally graded materials. The graded elements are formulated with continuously nonhomogeneous material property fields and compared to conventionally formulated homogeneous elements. An example problem is solved for the two-dimensional case to show the potential benefits of the graded formulation. It is observed that the conventional elements give a discontinuous stress field in the direction perpendicular to the material property gradient, while the graded elements give a continuous distribution. In the one-dimensional case, the solutions are compared to the analytical solutions by Chiu and Erdogan [J. Sound Vib. 222 (3) (1999) 453]. The results show that for identical levels of mesh refinement, the graded formulation produces similar spatial resolution, and temporal resolution for the range of boundary value problems studied. Observations are explained and their implications for numerical modeling are discussed.

Elastic Wave Propagation in Circumferential Direction in Anisotropic Cylindrical Curved Plates

Ultrasonic nondestructive inspection of large-diameter pipes is important for health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are detected more efficiently by inducing circumferential waves; hence, the study of elastic wave propagation in the circumferential direction in a pipe wall is essential. The current state of knowledge lacks a complete solution of this problem. Only when the pipe material is isotropic a solution of the wave propagation problem in the circumferential direction exists. Ultrasonic inspections of reinforced concrete pipes and pipes retrofitted by fiber composites necessitate the development of a new theoretical solution for elastic wave propagation in anisotropic curved plates in the circumferential direction. Mathematical modeling of the problem to obtain dispersion curves for curved anisotropic plates leads to coupled differential equations. Unlike isotropic materials for which the Stokes-Helmholtz decomposition technique simplifies the problem, in anisotropic case no such general decomposition technique works. These coupled differential equations are solved in this paper. Dispersion curves for anisotropic curved plates of different curvatures have been computed and presented. Some numerical results computed by the new technique have been compared with those available in the literature.

Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method

When there exists anisotropy in underground media, elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media, four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.

Solution of Impact-Induced Flexural Waves in a Circular Ring by the Method of Characteristics

A study of elastic wave propagation in a curved beam (circular ring) is presented. The governing equations of motion are formulated in two forms based on Timoshenko beam theory. Solutions are obtained using the method of characteristics, whereby a numerical scheme employing higher-order interpolation is proposed for the finite difference equations. Results obtained are verified by experiments; it is found that use of the higher-order numerical scheme improves correlation with experimental results. Comparison of the relative accuracy between the two mathematical formulations—one in terms of generalized forces and velocities and the other in terms of generalized displacements—shows the former to be mathematically simpler and to yield more accurate results.

Elastic waves in discontinuous media: Three-dimensional scattering

This report contains an exact study of elastic wave propagation and its scattering in discontinuous media where hard reflectors are onionlike sets of surfaces. In order to reformulate the problem as a finite set of boundary integral equations, the wave motion between reflectors is represented by means of elastic potentials which involve vectorial densities on the surfaces. In the external medium, an outgoing asymptotic condition generalizes the Silver–Müller (and the Sommerfeld) condition to the case of coupled waves (S and P waves) moving with different velocities. The uniqueness of the Green’s function, which guarantees the uniqueness of the direct problem solution, is proven. For any incident wave and arbitrary number of surfaces, the transmission and scattering problems are studied, with and without the simplification obtained by assuming constant Poisson ratios. According to the parameter ranges, the equations which are obtained are well posed, either as second kind Fredholm equations, or because they reduce to the inverse of the sum of the identity operator and a ‘‘small norm’’ bounded operator. The results can be used to describe rigorously the three-dimensional scattering of elastic waves in the frequency domain for any kind of incident wave function (P,S,...) as well as the response to a localized source.

On the use of localization theory to characterize elastic wave propagation in randomly stratified 1-D media

In a series of papers Benjamin White, Ping Sheng, George Papanicolaou and others have described the application of localization theory to the study of elastic wave propagation in randomly stratified one‐dimensional (1-D) media. They describe methods for computing the localization parameters and apply the results to sonic well‐log data. In this note, I will show that, at least in the seismic band, the results of their calculations disagree with effective medium theory. This disagreement may to be due to the lack of low‐frequency information in exploration seismic data.

RECENT ADVANCES IN WAVES IN LAYERED MEDIA

The topic of wave propagation in layered media has for a long time been of major interest in underwater and geophysical acoustics. Later on interest in this field arose due to needs in acousto-microelectronics, mainly surface acoustic wave devices, nondestructive evaluation of composite and layered materials and oil exploration. New applications have presented new challenging theoretical and experimental problems. One trend is to describe more complicated media including anisotropy, nonhomogeneity, imperfect interfaces, and wave diffraction on inhomogeneities ; a second trend is related to solutions of the inverse problem, in which properties of the media should be determined from the wave signature. In this paper we review recent developments in theoretical and experimental studies of elastic wave propagation in layered media with applications to ultrasonic evaluation of materials. We will focus mainly on anisotropy and media property reconstruction. We will also discuss the boundary conditioned for the imperfect interface, which may involve partial contact or other interface inhomogeneities. Such generalized boundary conditions can be systematically incorporated in the transfer matrix approach.

Numerical simulation of ultrasonic wave propagation in anisotropic and attenuative solid materials

The axisymmetric elastodynamic finite element code developed is capable of predicting quantitatively accurate displacement fields for elastic wave propagation in isotropic and transversely isotropic materials. The numerical algorithm incorporates viscous damping by adding a time-dependent tensor to Hooke's law. Amplitude comparisons are made between the geometric attenuation in the far field and the corresponding finite element predictions to investigate the quality and validity of the code. Through-transmission experimental measurements made with a 1 MHz L-wave transducer attached to an aluminum sample support the code predictions. The algorithm successfully models geometric beam spreading dispersion and energy absorption due to viscous damping. This numerical model is a viable tool for the study of elastic wave propagation in nondestructive testing applications.

Some experimental studies in elastic wave propagation

A number of experimental studies of elastic wave propagation in solids, with which the author has been associated, are reviewed. These concern the propagation and reflection of mechanical pulses in elastic solids. In most of these studies, unexpected mechanical response has been observed. The problems discussed include that of a glass beam subjected to flexural loading [H. Kolsky, Dynamic Crack Propagation, edited by G. C. Shih (Noordhoff, Groningen, 1973), pp. 399–414; V. Kinra and H. Kolsky, Eng. Fracture Mech. 9, 423–432 (1977); H. J. Schindler and H. Kolsky, J. Mech. Phys. Sol. 31, 427–437 (1983)] and it has been shown that the time for the fracture to be completed is equal to the time it takes the extensional compressive wave generated by the growing crack to travel to the free ends of the beam and be reflected back as a tensile pulse. Another problem discussed is that of the elastic impact of a sphere on a plate. When the plate is sufficiently thick, i.e., its thickness is such that the sphere separates from the plate before reflected waves reach the region of contact. The problem, which was first treated by Hertz, has more recently been treated by S.C. Hunter [J. Mech. Phys. Solids 5, 162 (1957)], who showed that about 1% of the energy is converted into elastic vibrations of the block. C. Zener [Phys. Rev. 59, 669 (1941)] has shown that the low coefficients of restitution observed for thin plates can be explained in terms of flexural plate waves. More recently, M. G. Koller and H. Kolsky [Int. J. Solids Structures 23, 1387–1400 (1987)] have studied the problem in detail in terms of the propagation and reflection of the waves generated by the impact and shown two unexpected phenomena, namely the propagation of a longitudinal disturbance at the S-wave velocity, and an enhancement of amplitude on reflection of an outgoing P wave. Other studies which will be discussed are the change in pulse shape which occurs when a unidirectional pulse is reflected at the boundary between two noncollinear rods [J. P. Lee and H. Kolsky, J. Appl. Mech. 39, 809–813 (1972)], and between a rod and a half-space [S. Boucher and H. Kolsky, J. Acoust. Soc. Am. 52, 884–898 (1972)].