Download or read book Nonlinear Effects on Wave Propagation in a Cylindrical Elastic Body written by Roger Dalke and published by . This book was released on 1986 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Some Effects of Nonlinearity and Nonuniformity in Wave Propagation and Vibration elastic Strings and Discs written by Peter Zane Bulkeley and published by . This book was released on 1961 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Effects in Fluids and Solids written by Michael M. Carroll and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of scientific papers is dedicated with gratitude and esteem to Ronald Rivlin and is offered as a token of appreciation by former students, col laborators, and friends. Ronald Rivlin's name is synonymous with modem developments in contin uum mechanics. His outstanding pioneering theoretical and experimental re ·search in finite elasticity is a landmark. From his work there has followed a spate of developments in which he played the leading role-the theory of fiber-rein forced materials, the developments of the theory of constitutive equations, the theory of materials with memory, the theory of the fracture of elastomers, the theory of viscoelastic fluids and solids, the development of nonlinear crystal physics, the theory of small deformations superimposed on large, and the effect of large initial strain on wave propagation. It is in Rivlin's work that universal relations were first recognized. Here also are to be found lucid explanations of physical phenomena such as the Poynting effect for elastic rods in torsion. Addi tionally, he and his co-workers predicted the presence of secondary flows for viscoelastic fluids in straight pipes of noncircular cross section under a uniform pressure head. While some others may have displayed a cavalier lack of concern for physical reality and an intoxication with mathematical idiom, Rivlin has al ways been concerned with genuine mathematical and physical content. All of his papers contain interesting and illuminating material-and may be read with profit by anyone interested in continuum mechanics.
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.
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.
Download or read book Waves in Nonlinear Pre Stressed Materials written by M. Destrade and published by Springer Science & Business Media. This book was released on 2007-11-08 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers in this book provide a state-of-the-art examination of waves in pre-stressed materials. You’ll gain new perspectives via a multi-disciplinary approach that interweaves key topics. These topics include the mathematical modeling of incremental material response (elastic and inelastic), an analysis of the governing differential equations, and boundary-value problems. Detailed illustrations help you visualize key concepts and processes.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Nonlinear Waves in Solids written by A. Jeffrey and published by Springer. This book was released on 2014-05-04 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Beside fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up to date account of the current state of research in the theory and practice of nonlinear waves in solids.
Download or read book Time domain Solutions for Nonlinear Elastic 1 D Plane Wave Propagation written by and published by . This book was released on 1998 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-domain solutions are obtained for 1-D nonlinear elastic wave propagation problems using a five-constant nonlinear theory. The assumption of weak attenuation was used throughout the development. The strongest nonlinear effects are obtained for the case of single compressional wave propagation, for single compressional or shear wave propagation through a longitudinally pre-stressed elastic material, and for shear wave propagation in a shear pre-stressed elastic material. Estimates of the size of these effects indicate that nonlinear phenomena are likely to be observable in real seismic data. The results may be useful for the measurement of nonlinear constants in elastic materials, for explaining the frequency content of seismograms, and for monitoring strain fields in the earth's crust.
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:
Download or read book Nonlinear Elastic Waves in Materials written by Jeremiah J. Rushchitsky and published by Springer. This book was released on 2016-09-03 with total page 0 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.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1986 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Bibliography of Scientific and Industrial Reports written by and published by . This book was released on 1969 with total page 1020 pages. Available in PDF, EPUB and Kindle. Book excerpt:
