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Author: Jeremiah J. Rushchitsky Publisher: Springer Science & Business ISBN: 3319004646 Category : Science Languages : en Pages : 445
Book Description
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.
Author: Jeremiah J. Rushchitsky Publisher: Springer Science & Business ISBN: 3319004646 Category : Science Languages : en Pages : 445
Book Description
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.
Author: M. Destrade Publisher: Springer Science & Business Media ISBN: 3211735720 Category : Technology & Engineering Languages : en Pages : 287
Book Description
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.
Author: A. Bedford Publisher: ISBN: Category : Science Languages : en Pages : 320
Book Description
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.
Author: Gérard A. Maugin Publisher: ISBN: 9780198534846 Category : Mathematics Languages : en Pages : 328
Book Description
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
Author: Anthony Bedford Publisher: Springer Nature ISBN: 3031328752 Category : Technology & Engineering Languages : en Pages : 388
Book Description
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.
Author: Publisher: ISBN: Category : Languages : en Pages : 9
Book Description
The purpose of this paper is to describe a theory of the propagation of elastic waves in hysteretic nonlinear elastic materials, e.g., rock. In the next section, we introduce the Priesach-Mayergoyz (P-M) model [6,7] of hysteretic systems and adapt it to describe the hysteretic mesoscopic elastic units (HMEU) determining the elastic properties of a rock. We combine the P-M model with effective medium theory (EMT) [8] to find the elastic response of a rock that has experienced a specified pressure history. Next, we consider elastic wave propagation in a hysteretic nonlinear elastic system governed by a history dependent equation of state. We consider one-dimensional propagation of compressional waves. The equation of motion for the longitudinal displacement field contains the same hysteretic nonlinear interactions that characterize the equation of state. We solve the equation of motion using the Green function technique developed by McCall [9]. This solution lets us identify the qualitative features in harmonic generation that are signatures of nonlinearity and hysteresis.
Author: Igor V. Andrianov Publisher: CRC Press ISBN: 1000372197 Category : Technology & Engineering Languages : en Pages : 251
Book Description
This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.
Author: D. S. Drumheller Publisher: Cambridge University Press ISBN: 9780521587464 Category : Science Languages : en Pages : 546
Book Description
Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.