Electrodynamics Of Continua
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| Author | : A. Cemal Eringen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461232260 |
The electrodynamics of continua is a branch ofthe physical sciences concerned with the interaction of electromagnetic fields with deformable bodies. De formable bodies are considered to be continua endowed with continuous distributions of mass and charge. The theory of electromagnetic continua is concerned with the determination of deformations, motions, stress, and elec tromagnetic fields developed in bodies upon the applications of external loads. External loads may be of mechanical origin (e.g., forces, couples, constraints placed on the surface of the body, and initial and boundary conditions arising from thermal and other changes) and/or electromagnetic origin (e.g., electric, magnetic, and current fields). Because bodies of different constitutions respond to external stimuli in a different way, it is imperative to characterize properly the response functions relevant to a given class of continua. This is done by means of the constitutive theory. For example, an elastic dielectric responds to electromagnetic fields in a totally different way than a magnetic fluid. The present book is intended to present a unified approach to the subject matter, based on the principles of contemporary continuum physics.
| Author | : A.Cemal Eringen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461232368 |
This is the second volume of a two-volume set presenting a unified approach to the electrodynamics of continua, based on the principles of contemporary continuum of physics. The first volume was devoted mainly to the development of the theory and applications to deformable solid media. This volume extends the developments of the first volume to richer and newer grounds. It contains discussions on fluid media, magnetohydrodynamics, eletrohydrodynamics and media with more complicated structures. With the discussion, in the last two chapters, of memory-dependent materials and non-local E-M theory, the authors account for the nonlocal effects arising from motions and fields of material points at past times and at spatially distant points. This discussion is included here to stimulate further research in these important fields, which are presently in development stages. The second volume is self-contained and can be studied without the help of volume I. A section summarizing the constitutive equations and the underlying physical ideas, which were presented in more detail in the first volume, is included. This volume may be used as a basis for several graduate courses in engineering schools, applied mathematics and physics departments. It also contains fresh ideas and will stimulate further research in the directions the authors outline.
| Author | : J.S. Yang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 300 |
| Release | : 2003-10-31 |
| Genre | : Science |
| ISBN | : 9781402075797 |
The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to extend our sincere thanks to Professor David Y. Gao of Virginia Tech for suggesting the symposium, and to the authors for their time and effort invested in preparing their manuscripts. We are also grateful to Professor Daining Fang of Tsinghua University for co-chairing the symposium with J. S. Yang. Our special thanks belong to Kluwer for preparing this book for publication. J. S. Yang G. A. Maugin PIEZOELECTRIC VIBRATORY GYROSCOPES J. S.
| Author | : G.A. Maugin |
| Publisher | : Elsevier |
| Total Pages | : 621 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483290107 |
This volume is a rigorous cross-disciplinary theoretical treatment of electromechanical and magnetomechanical interactions in elastic solids. Using the modern style of continuum thermomechanics (but without excessive formalism) it starts from basic principles of mechanics and electromagnetism, and goes on to unify these two fields in a common framework. It treats linear and nonlinear static and dynamic problems in a variety of elastic solids such as piezoelectrics, electricity conductors, ferromagnets, ferroelectrics, ionic crystals and ceramics. Chapters 1-3 are introductory, describing the essential properties of electromagnetic solids, the essentials of the thermomechanics of continua, and the general equations that govern the electrodynamics of nonlinear continua in the nonrelativistic framework (e.g. Maxwell's equations, the fundamental balance laws of continuum mechanics, basic thermodynamical inequalities for electromagnetic continua, jump relations for studying the propagation of shock waves, nonlinear constitutive equations for large classes of materials).The remainder of the text presents in detail special cases, applications, solved problems, and more complex schemes of electromagnetic matter. Chapters 4 and 5 examine material schemes whose description relies on the above-mentioned equations. Chapters 6 and 7 are more advanced, reporting on recent progress in the field.Suitable for graduate teaching, the volume will also be useful to research workers and engineers in the field of electromagnetomechanical interactions, and to those interested in the basic principles, mathematical developments and applications of electroelasticity and magnetoelasticity in a variety of solid materials, such as crystals, polycrystals, compounds and alloys.
| Author | : Alexander L. Fetter |
| Publisher | : Courier Corporation |
| Total Pages | : 596 |
| Release | : 2003-12-16 |
| Genre | : Science |
| ISBN | : 0486432610 |
This two-part text fills what has often been a void in the first-year graduate physics curriculum. Through its examination of particles and continua, it supplies a lucid and self-contained account of classical mechanics — which in turn provides a natural framework for introducing many of the advanced mathematical concepts in physics. The text opens with Newton's laws of motion and systematically develops the dynamics of classical particles, with chapters on basic principles, rotating coordinate systems, lagrangian formalism, small oscillations, dynamics of rigid bodies, and hamiltonian formalism, including a brief discussion of the transition to quantum mechanics. This part of the book also considers examples of the limiting behavior of many particles, facilitating the eventual transition to a continuous medium. The second part deals with classical continua, including chapters on string membranes, sound waves, surface waves on nonviscous fluids, heat conduction, viscous fluids, and elastic media. Each of these self-contained chapters provides the relevant physical background and develops the appropriate mathematical techniques, and problems of varying difficulty appear throughout the text.
| Author | : Friedrich W Hehl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 405 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461200512 |
In this book we display the fundamental structure underlying classical electro dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro magnetics and of the chapter "Charge and Magnetic Flux" of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .
| Author | : Holm Altenbach |
| Publisher | : Springer |
| Total Pages | : 521 |
| Release | : 2019-03-06 |
| Genre | : Science |
| ISBN | : 3030116654 |
This book presents a collection of chapters on the current problems of the theory of dynamical processes in generalized continua and structures, and has been compiled to commemorate the 70th birthday of Prof. Dmitry Indeitsev – a leading specialist in the field of dynamical processes in solids, fluids and structures. It discusses various applications related to Prof. Indeitsev’s contributions, including various discrete and continuous dynamic models of structures and media, as well as a number of dynamical processes in generalized media.
| Author | : Xiaohong Chen |
| Publisher | : World Scientific |
| Total Pages | : 326 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 184816663X |
Fracture Mechanics of Electromagnetic Materials provides a comprehensive overview of fracture mechanics of conservative and dissipative materials, as well as a general formulation of nonlinear field theory of fracture mechanics and a rigorous treatment of dynamic crack problems involving coupled magnetic, electric, thermal and mechanical field quantities. Thorough emphasis is placed on the physical interpretation of fundamental concepts, development of theoretical models and exploration of their applications to fracture characterization in the presence of magneto-electro-thermo-mechanical coupling and dissipative effects. Mechanical, aeronautical, civil, biomedical, electrical and electronic engineers interested in application of the principles of fracture mechanics to design analysis and durability evaluation of smart structures and devices will find this book an invaluable resource.
| Author | : Gérard A. Maugin |
| Publisher | : Springer |
| Total Pages | : 268 |
| Release | : 2016-09-24 |
| Genre | : Science |
| ISBN | : 9811024340 |
This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.
| Author | : Bernd Markert |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 231 |
| Release | : 2011-07-15 |
| Genre | : Science |
| ISBN | : 3642227384 |
Modern computational techniques, such as the Finite Element Method, have, since their development several decades ago, successfully exploited continuum theories for numerous applications in science and technology. Although standard continuum methods based upon the Cauchy-Boltzmann continuum are still of great importance and are widely used, it increasingly appears that material properties stemming from microstructural phenomena have to be considered. This is particularly true for inhomogeneous load and deformation states, where lower-scale size effects begin to affect the macroscopic material response; something standard continuum theories fail to account for. Following this idea, it is evident that standard continuum mechanics has to be augmented to capture lower-scale structural and compositional phenomena, and to make this information accessible to macroscopic numerical simulations.
