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Spherical Wave Propagation In A Nonlinear Elastic Medium
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Book Synopsis Spherical Wave Propagation in a Nonlinear Elastic Medium by :
Download or read book Spherical Wave Propagation in a Nonlinear Elastic Medium written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear propagation of spherical waves generated by a point-pressure source is considered for the cases of monochromatic and impulse primary waveforms. The nonlinear five-constant elastic theory advanced by Murnaghan is used where general equations of motion are put in the form of vector operators, which are independent of the coordinate system choice. The ratio of the nonlinear field component to the primary wave in the far field is proportional to ln(r) where r is a propagation distance. Near-field components of the primary field do not contribute to the far field of nonlinear component.
Book Synopsis On the Propagation of Waves in a Physically Nonlinear Medium Weakened by a Cylindrical Or Spherical Cavity by : P. F. Sabodash
Download or read book On the Propagation of Waves in a Physically Nonlinear Medium Weakened by a Cylindrical Or Spherical Cavity written by P. F. Sabodash and published by . This book was released on 1974 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations of the propagation of cylindrical waves are obtained taking into account the change of volume and form in a nonlinear elastic medium. The fundamental equations for compressible and incompressible materials are found, taking into account small physical nonlinearity. The fundamental equations of the propagation of spherical waves in a nonlinear elastic medium are determined for small physical nonlinearity, which is characterized by the square of deformation intensity.
Book Synopsis Introduction to Elastic Wave Propagation by : A. Bedford
Download or read book Introduction to Elastic Wave Propagation written by A. Bedford and published by . This book was released on 1994-09-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the basic concepts and methods of the theory of wave propagation in elastic materials. The linear theory of elasticity is covered, culminating in the displacement equations of motion. One-dimensional waves are analyzed through the D'Alembert solution.
Book Synopsis Introduction to Elastic Wave Propagation by : Anthony Bedford
Download or read book Introduction to Elastic Wave Propagation written by Anthony Bedford and published by Springer Nature. This book was released on 2023-11-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated edition expands on its explanations of methods used to analyze waves in solid materials, such as the waves created by earthquakes and the ultrasonic waves used to detect flaws in materials and for medical diagnoses. In addition to the traditional methods used to analyze steady-state and transient waves in elastic materials, the book contains introductions to advanced areas that no other single text covers. These topics include the use of finite elements to solve wave problems, the Cagniard-de Hoop method, the four-pole technique for analyzing waves in layered media, and the growth and decay of shock and acceleration waves. The authors explain the theory of linear elasticity through the displacement equations of motion, methods used to analyze steady-state and transient waves in layered media, and include an appendix on functions of a complex variable. Originally developed for a graduate course for which no suitable text existed, the new edition retains its classroom-tested treatment of the theories of linear elasticity and complex variables for students needing background in those subjects.
Book Synopsis Waves in Nonlinear Elastic Media with Inhomogeneous Pre-stress by : Tom Shearer
Download or read book Waves in Nonlinear Elastic Media with Inhomogeneous Pre-stress written by Tom Shearer and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the effect of inhomogeneous pre-stress on elastic wave propagation and scattering in nonlinear elastic materials is investigated. Four main problems are considered: 1. torsional wave propagation in a pre-stressed annular cylinder, 2. the scattering of horizontally polarised shear waves from a cylindrical cavity in a pre-stressed, infinite, nonlinear elastic material, 3. the use of pre-stress to cloak cylindrical cavities from incoming horizontally polarised shear waves, and 4. the scattering of shear waves from a spherical cavity in a pre-stressed, infinite, nonlinear elastic material. It is observed that waves in a hyperelastic material are significantly affected by pre-stress, and different results are obtained from those which would be obtained if the underlying stress was neglected and only geometrical changes were considered. In Chapter 3 we show that the dispersion curves for torsional waves propagating in an annular cylinder are strongly dependent on the pre-stress applied. A greater pressure on the inner surface than the outer causes the roots of the dispersion curves to be spaced further apart, whereas a greater pressure on the outer surface than the inner causes them to be spaced closer together. We also show that a longitudinal stretch causes the cut-on frequencies to move closer together and decreases the gradient of the dispersion curves, whilst a longitudinal compression causes the cut-on frequencies to move further apart and increases the gradient of the dispersion curves. In Chapter 4 we observe that pre-stress affects the scattering coefficients for shear waves scattered from a cylindrical cavity. It is shown that, for certain parameter values, the scattering coefficients obtained in a pre-stressed medium are closer to those that would be obtained in the undeformed configuration than those that would be obtained in the deformed configuration if the pre-stress were neglected. This result is utilised in Chapter 5 where the cloaking of a cylindrical cavity from horizontally polarised shear waves is examined. It is shown that neo-Hookean materials are optimal for this type of cloaking. A stonger dependence of the strain energy function on the second strain invariant leads to a less efficient cloak. We observe that, for a Mooney-Rivlin material, as S1 tends from 1 towards 0 (in other words, as a material becomes less dependent on the first strain invariant, and more dependent on the second strain invariant), there is more scattering from the cloaking region. For materials which are strongly dependent on the second strain invariant the pre-stress actually increases the scattering cross-section relative to the scattering cross-section for an unstressed material, hence these materials are unsuitable for pre-stress cloaking. Finally, in Chapter 6 we study the effect of pressure applied to the inner surface of a spherical cavity and at infinity on the propagation and scattering of shear waves in an unbounded medium. It is shown that the scattering coefficients and cross-sections for this problem are strongly dependent on the pre-stress considered. We observe that a region of inhomogeneous pre-stress can lead to some counterintuitive relationships between cavity size and scattering cross-sections and coefficients.
Book Synopsis Nonlinear Waves in Elastic Media by : A.G. Kulikovskii
Download or read book Nonlinear Waves in Elastic Media written by A.G. Kulikovskii and published by CRC Press. This book was released on 2021-06-30 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
Book Synopsis Spherical Wave Propagation in Elastic Media and Its Application to Energy Coupling for Tamped and Decoupled Explosions by :
Download or read book Spherical Wave Propagation in Elastic Media and Its Application to Energy Coupling for Tamped and Decoupled Explosions written by and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The effects of variation in source and medium properties upon near- and far-field spectra for elastic waves are examined theoretically by considering spherical wave propagation in unbounded elastic media. This type of analysis, although idealized, provides insight into the relative effects of the various source and medium parameters on both tamped and decoupled explosions. It also provides a basis for interpreting both field and laboratory experimental data obtained during spherical wave propagation in real media. In this paper I attempt to unify the work that has been done on spherical wave propagation in elastic media. I present the results in nondimensional forms, in hopes that others may find these forms of the solutions useful and some of the conclusions, based upon my parameter studies, enlightening. Also included is a discussion of some of the limitations of the theory and examples of applications of the spherical wave propagation theory in real media.
Book Synopsis Wave Propagation in Elastic Solids by : J. D. Achenbach
Download or read book Wave Propagation in Elastic Solids written by J. D. Achenbach and published by Elsevier. This book was released on 2016-01-21 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-linear Spherical Wave Propagation with Attenuation by : N. H. Johannesen
Download or read book Non-linear Spherical Wave Propagation with Attenuation written by N. H. Johannesen and published by . This book was released on 1980 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dispersion Due to Small Non-geometric Effects in Linear Elastic Wave Propagation by : Adnan H. Nayfeh
Download or read book Dispersion Due to Small Non-geometric Effects in Linear Elastic Wave Propagation written by Adnan H. Nayfeh and published by . This book was released on 1971 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Wave Propagation in an Elastic Medium: Generalized Davey-Stewartson Equations by : Ceni Babaoğlu
Download or read book Wave Propagation in an Elastic Medium: Generalized Davey-Stewartson Equations written by Ceni Babaoğlu and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present study, the problem of (2 + 1) (two spatial and one temporal) dimensional nonlinear wave propagation in a generalized elastic medium is considered. The modulation of (2 + 1) dimensional waves is examined in an infinite; homogenous, weakly nonlinear and weakly dispersive elastic medium. The study corıtaİns five ınaİrı sections. In the first section, a general introduction is given including some information about the nonlinear systems characterizing the modulation problems and the special solutions of these systems. In the second section, nonlinear evolution equations are derived describing the asymptotic behavior of waves for (2 + 1 ) dimensional wave modulation problem. While deriving the equations an asymptotic technique called reductive perturbation method is used and it is shown that the problem of wave modulation is characterİzed by a system of three nonlinear partial differential equations. These equations involve interactions of a free short transverse, a free long longitudinal and a free long transverse wave modes, and is called the ''generalized Davey-Stewartson equations''. Under some restrictions on parameter values, it is .. shown that the generalized Davey-Stewartson equations reduce to the well-known Davey-Stewartson and to the nonlinear Schrödinger equations. Besides, some special solutions of the generalized Davey-Stewartson equations are calculated by two different methods. Whİle calculatİng the special solutions by the help of the first method, travelling wave transformations are used in order to reduce the partial differential equations to ordinary differential equations and special solutions are given in terms of Jacobian elliptic functions. It is shown that these solutions reduce to hyperbolic functions for some cases and that they involve sech-tanh-tanh and tanh-tanh-tanh type solutions under some constraints on the parameter values. The second method is based on coupled Riccati equations and their travelling wave transformatİons. By using the second method, the special solutions of the generalized Davey-Stewartson equations are obtained in terms of hyperbolic functions. In the third section, it is observed that the generalized Davey-Stewartson equations are not valid for the long-wave short-wave resonant case. In the case where the phase velocity of the long longitudinal wave is equal to the group velocity of the short transverse wave, new evolution equations are derived characterizing the problem and are called long-wave short-wave interaction equations. The special solutions of the long-wave short-wave interaction equations are obtained by Jacobian elliptic functions and tanh method. In the fourth section, degenerate generalized Davey-Stewartson equations, which are obtained when one of thei,coefficients of the generalized Davey-Stewartson equations becomes zero, are considered. The special solutions of the degenerate generalized Davey-Stewartson equations are obtained by using the two methods given in the second and third sections. ...
Book Synopsis Wave Propagation in Solids and Fluids by : Julian L. Davis
Download or read book Wave Propagation in Solids and Fluids written by Julian L. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.
Book Synopsis Propagation of Cylindrical and Spherical Elastic Waves by Method of Characteristics by : Pei Chi Chou
Download or read book Propagation of Cylindrical and Spherical Elastic Waves by Method of Characteristics written by Pei Chi Chou and published by . This book was released on 1965 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Physics: Proceedings Of The Cp90 International Conference by : Armin G Tenner
Download or read book Computational Physics: Proceedings Of The Cp90 International Conference written by Armin G Tenner and published by #N/A. This book was released on 1991-04-30 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited talks include applications from the fields of solid state physics, plasma physics, hydrodynamics, high-energy physics, thermodymanics, atomic and molecular physics, chemistry, statistical physics, earth sciences, neural networks, meteorology, astrophysics, and presentations on cellular automata and quantum Monte Carlo methods. The emphasis is on methods of software development and engineering, graphic tools, and storage of physical data.
Book Synopsis Wave Propagation in Elastic Solids by : Jan Achenbach
Download or read book Wave Propagation in Elastic Solids written by Jan Achenbach and published by Elsevier. This book was released on 2012-12-02 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treatment necessarily involves considerable mathematical analysis. The pertinent mathematical techniques are, however, discussed at some length.
Book Synopsis Propagation of Spherical Wave in Non-stationary Media by : Frederick Paul Carlson
Download or read book Propagation of Spherical Wave in Non-stationary Media written by Frederick Paul Carlson and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers spherical waves propagating in a non-stationary turbulent media. The method of analysis uses the Rytov approximation and the perturbation technique of J.B. Keller. The resulting integral equations are solved by spectral techniques. The results are then compared with other known plane and spherical wave homogeneous and locally homogeneous results. They are then applied to examine the optimum aperture and resolution results of D.L. Fried. It is concluded that it is essential to allow for a distribution of turbulence in a region. In addition, the optimum aperture results for vertical propagation show a marked dependence on the height of the observer and the parameters which describe the distribution of turbulence in the region. The fact that optimum apertures continue to result is considered important and useful. (Author).
Book Synopsis Nonlinear Elastic Waves in Materials by : Jeremiah J. Rushchitsky
Download or read book Nonlinear Elastic Waves in Materials written by Jeremiah J. Rushchitsky and published by Springer Science & Business. This book was released on 2014-04-23 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”. The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.
