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Author: R.C. Payton
Publisher: Springer Science & Business Media
ISBN: 9400968663
Category : Science
Languages : en
Pages : 203
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Book Description
In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.
Author: R.C. Payton
Publisher: Springer Science & Business Media
ISBN: 9400968663
Category : Science
Languages : en
Pages : 203
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Book Description
In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.
Author: E. R. C. Marques
Publisher:
ISBN:
Category : Ultrasonic waves
Languages : en
Pages : 52
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Book Description
The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.
Author: F. McCarthy
Publisher: Elsevier
ISBN: 1483290662
Category : Science
Languages : en
Pages : 663
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Book Description
This volume contains a timely collection of research papers on the latest developments in the ever-increasing use of elastic waves in a variety of contexts. There are reports on wave-propagation in various types of media: in both isotropic and anisotropic bodies; in homogeneous and inhomogeneous media; in media with cracks or inclusions in random media; and in layered composites. The bulk of the papers are concerned with propagation in elastic media, but also included are viscoelastic, thermoelastic and magneto-electroelastic wave propagation, as well as waves in porous and piezo-electric bodies. Consideration is given to propagation in bodies as diverse as stretched elastic strings to surfaces such as thin walled cylinders, and thin films under stress. Applications considered include the determination of the depth of cracks; analysis of ground motions generated by a finite fault in seismology; surface wave spreading on piezo-electric solids; and dynamical stress intensity factors. Most of the papers are theoretical in nature, and many are complemented by numerical studies. Also included are a general survey on experimental techniques, and reports on experimental work. The volume will be of interest to those who do theoretical studies of elastic wave propagation and to those who apply elastic waves whether in seismology, non-destructive testing, the fabrication of devices or underwater acoustics, etc.
Author: DANIEL ROYER
Publisher: Springer Science & Business Media
ISBN: 9783540659327
Category : Science
Languages : en
Pages : 394
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Book Description
Elastic waves possess some remarkable properties and have become ever more important to applications in fields such as telecommunications (signal processing), medicine (echography), and metallurgy (non-destructive testing). These volumes serve as a bridge between basic books on wave phenomena and more technically oriented books on specific applications of wave phenomena. The first volume studies the different mechanisms of propagation in isotropic and anisotropic media. The second volume describes the generation and applications of free and guided waves.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 66
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Book Description
The far-field displacements in an infinite transversely isotropic elastic medium subjected to an oscillatory concentrated force are derived. The concepts of velocity surface, slowness surface and wave surface are used to describe the geometry of the wave propagation process. It is shown that the decay of the wave amplitudes depends not only on the distance from the source (as in isotropic media) but also depends on the direction of the point of interest from the source. As an example, the displacement field is computed for a laboratory fabricated unidirectional fiberglass epoxy composite. The solution for the displacements is expressed as an amplitude distribution and is presented in polar diagrams. This analysis has potential usefulness in the acoustic emission (AE) and ultrasonic nondestructive evaluation of composite materials. For example, the transient localized disturbances which are generally associated with AE sources can be modeled via this analysis. In which case, knowledge of the displacement field which arrives at a receiving transducer allows inferences regarding the strength and orientation of the source, and consequently perhaps the degree of damage within the composite.
Author: J.H.M.T. van der Hijden
Publisher: Elsevier
ISBN: 1483295907
Category : Science
Languages : en
Pages : 298
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Book Description
Seismic waves are one of the standard diagnostic tools used to determine the mechanical parameters (volume density of mass, compressibility, elastic stiffness) in the interior of the earth and the geometry of subsurface structures. There is increasing evidence that in the interpretation of seismic data - especially shear-wave data - the influence of anisotropy must be taken into account. This volume presents a method to compute the seismic waves that are generated by an impulsive source in a stratified anisotropic medium. Although written with the seismic applications in mind, the method that is developed is not limited to solid-earth geophysics. In fact, the methods discussed in this monograph are applicable wherever waves propagate in stratified, anisotropic media. The standard approach to this problem is to employ Fourier transformations with respect to time and with respect to the horizontal spatial coordinates. To obtain numerical results, the relevant inverse transformations then have to be evaluated numerically. In this monograph the problem is, in contrast to the standard approach, solved by applying the Cagniard-de Hoop method and by representing the wave field as a sum of generalized rays. With this method, the computational results can be obtained relatively easily with any degree of accuracy, and with considerably less computation time. For completeness, analysis of acoustic waves in stratified isotropic media is included. Furthermore, for large horizontal or vertical source-receiver separations very efficient approximations are derived. Several examples and applications are given.
Author: L Brekhovskikh
Publisher: Elsevier
ISBN: 0323161626
Category : Science
Languages : en
Pages : 520
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Book Description
Waves in Layered Media discusses different theories about the relationship between waves and media. The book specifically covers several factors that can affect the behavior and formation of various kinds of waves in different types of media. Comprised of nine chapters, the book establishes the fundamentals by first tackling simplest concepts, such as the behavior plane wave and discretely layered media. The succeeding chapters cover much more complex ideas, such as the refraction and reflection of waves, spherical wave, and wave in inhomogeneous media. The book will be a great asset to researchers whose work involves acoustics, or to professionals whose line of work involves sound waves.
Author: J. D. Achenbach
Publisher: Elsevier
ISBN: 1483163733
Category : Science
Languages : en
Pages : 440
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Book Description
Wave Propagation in Elastic Solids focuses on linearized theory and perfectly elastic media. This book discusses the one-dimensional motion of an elastic continuum; linearized theory of elasticity; elastodynamic theory; and elastic waves in an unbounded medium. The plane harmonic waves in elastic half-spaces; harmonic waves in waveguides; and forced motions of a half-space are also elaborated. This text likewise covers the transient waves in layers and rods; diffraction of waves by a slit; and thermal and viscoelastic effects, and effects of anisotropy and nonlinearity. Other topics include the summary of equations in rectangular coordinates, time-harmonic plane waves, approximate theories for rods, and transient in-plane motion of a layer. This publication is a good source for students and researchers conducting work on the wave propagation in elastic solids.
Author: Alfredo Berm?dez
Publisher: SIAM
ISBN: 9780898714708
Category : Science
Languages : en
Pages : 1062
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Book Description
This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.
Author: Fedor I. Fedorov
Publisher: Springer Science & Business Media
ISBN: 1475712758
Category : Science
Languages : en
Pages : 377
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Book Description
The translation into English of Academician Fedorov's ex cellent treatise on elastic wave propagation in solids has come at an opportune time. His systematic exposition of all aspects of this field is most lucid and straightforward. The author has gone to considerable pains to develop in his mathematical background a consistent tensor framework which acts as a unifying motif through out the various aspects of the subject. In many respects his approach will appear quite novel as his treatment introduces several concepts and parameters previously unfamiliar to the literature of the West. Extensive tables in the final chapters illustrate the application of these ideas to the exist ing body of experimental data. The book is both extensive and comprehensive in al1 phases of the subject. Workers in the fields of ultrasonic propagation and elastic properties will find this treatise of great interest and direct concern. H. B. Huntington Rensselaer Polytechnic Institute Troy, New York November 1967 v Preface to the American Edition In preparing this edition I have corrected various misprints and errors appearing in the Russian edition, but I have also incorpo rated some substantial changes and additions, the latter representing some results I and my colleagues have recently obtained and pub_ lished in Russian journals. For example, in section 32 I have added a general derivation of the equation for the seetion of the wave surface by a symmetry plane for cubic, hexagonal, tetragonal, and orthorhombic crystals.
