Download or read book Nonlinear Resonances written by Shanmuganathan Rajasekar and published by Springer. This book was released on 2015-11-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.
Download or read book Nonlinear Resonances in the Motion of Rolling Reentry Bodies written by Ali Hasan Nayfeh and published by . This book was released on 1971 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of multiple scales has been used to analyze the motion of rolling reentry bodies under the influence of nonlinear pitch, damping, and Magnus moments. Each of these moments is assumed to be a cubic function of angle of attack.
Download or read book Nonlinear Resonance Analysis written by Elena Kartashova and published by Cambridge University Press. This book was released on 2010-10-21 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.
Download or read book The Mechanics of Nonlinear Systems with Internal Resonances written by Arkadiy I. Manevich and published by World Scientific. This book was released on 2005 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.
Download or read book Nonlinear Waves In Bounded Media The Mathematics Of Resonance written by Seymour Brian R and published by World Scientific. This book was released on 2017-01-18 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.
Download or read book Nonlinear Vibrations and Stability of Shells and Plates written by Marco Amabili and published by Cambridge University Press. This book was released on 2008-01-14 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.
Download or read book The Mechanics Of Nonlinear Systems With Internal Resonances written by Leonid Manevitch and published by World Scientific. This book was released on 2005-05-12 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied./a
Download or read book Evolution of Extreme Waves and Resonances written by Shamil U. Galiev and published by CRC Press. This book was released on 2020-06-10 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of waves is generalized on cases of strongly nonlinear waves, multivalued waves, and particle–waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects. Extreme waves emerging in different artificial and natural systems from atom scale to the Universe are explored. Vast amounts of experimental data and comparisons of them with the results of the developed theory are presented. The book was written for graduate students as well as for researchers and engineers in the fields of geophysics, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It is designed as a professional reference for those working in the wave analysis and modeling fields.
Download or read book Principles of Magnetic Resonance written by Charles P. Slichter and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a source of great pleasure to help launch the new Springer Series in Solid-State Sciences. Some years aga I wrote my book, Principles of Magnetic Resonance. I have been eager to publish a new book concerned with spin temperature, double resonance, and spin-flip line narrowing, topics basic to important trends in present-day magnetic resonance which were not treated in my earlier book. Invitations to lecture in Osaka, Japan, in Leuven, Belgium, and Lausanne, Switzerland, had provided occasion to prepare first drafts of the new topics and to get student feedback. My plans were changed, however, when I learned that Principles of M agnetic Resonance was no longer available. Dr. Lotsch, Physics Editor of Springer-Verlag, and I decided it made sense to combine the new book with a modified old one, thereby continuing to make available a complete text in basic magnetic resonance written with a philosophy of presenting a thorough treatment of a small number of concepts which are key to large areas of magnetic res on an ce. In addition to adding three new chapters, I have added new material to the original chapters, have added two new appendices-one on the use of Bloch equations to describe rate processes, the other on the effect of diffusion on spin echoes-and have augmented the collection of homework problems.
Download or read book Adiabatic Evolution and Shape Resonances written by Michael Hitrik and published by American Mathematical Society. This book was released on 2022-11-10 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Nonlinear Photonics Devices written by Luigi Sirleto and published by MDPI. This book was released on 2021-01-11 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first nonlinear optical effect was observed in the 19th century by John Kerr. Nonlinear optics, however, started to grow up only after the invention of the laser, when intense light sources became easily available. The seminal studies by Peter Franken and Nicolaas Bloembergen, in the 1960s, paved the way for the development of today’s nonlinear photonics, the field of research that encompasses all the studies, designs, and implementations of nonlinear optical devices that can be used for the generation, communication, and processing of information. This field has attracted significant attention, partly due to the great potential of exploiting the optical nonlinearities of new or advanced materials to induce new phenomena and achieve new functions. According to Clarivate Web of Science, almost 200,000 papers were published that refer to the topic “nonlinear optic*”. Over 36,000 papers were published in the last four years (2015–2018) with the same keyword, and over 17,000 used the keyword “nonlinear photonic*”. The present Special Issue of Micromachines aims at reviewing the current state of the art and presenting perspectives of further development. Fundamental and applicative aspects are considered, with special attention paid to hot topics that may lead to technological and scientific breakthroughs.
Download or read book Fano Resonances in Optics and Microwaves written by Eugene Kamenetskii and published by Springer. This book was released on 2018-11-20 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the development of Fano-based techniques and reveals the characteristic properties of various wave processes by studying interference phenomena. It explains that the interaction of discrete (localized) states with a continuum of propagation modes leads to Fano interference effects in transmission, and explores novel coherent effects such as bound states in the continuum accompanied by collapse of Fano resonance. Originating in atomic physics, Fano resonances have become one of the most appealing phenomena of wave scattering in optics, microwaves, and terahertz techniques. The generation of extremely strong and confined fields at a deep subwavelength scale, far beyond the diffraction limit, plays a central role in modern plasmonics, magnonics, and in photonic and metamaterial structures. Fano resonance effects take advantage of the coupling of these bound states with a continuum of radiative electromagnetic waves. With their unique physical properties and unusual combination of classical and quantum structures, Fano resonances have an application potential in a wide range of fields, from telecommunication to ultrasensitive biosensing, medical instrumentation and data storage. Including contributions by international experts and covering the essential aspects of Fano-resonance effects, including theory, modeling and design, proven and potential applications in practical devices, fabrication, characterization and measurement, this book enables readers to acquire the multifaceted understanding required for these multidisciplinary challenges.
Download or read book Global Transversality Resonance and Chaotic Dynamics written by Albert C. J. Luo and published by World Scientific. This book was released on 2008 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics.
Download or read book Oscillations and Resonances written by Sergey G. Glebov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
Download or read book Nonlinear Vibrations of Cantilever Beams and Plates written by Mohammad Amin Rashidifar and published by Anchor Academic Publishing (aap_verlag). This book was released on 2015-05-12 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering problems can be solved using a linear approximation. In the Finite Element Analysis (FEA) the set of equations, describing the structural behaviour is then linear K d = F (1.1) In this matrix equation, K is the stiffness matrix of the structure, d is the nodal displacements vector and F is the external nodal force vector. Characteristics of linear problems is that the displacements are proportional to the loads, the stiffness of the structure is independent on the value of the load level. Though behaviour of real structures is nonlinear, e.g. displacements are not proportional to the loads; nonlinearities are usually unimportant and may be neglected in most practical problems.
Download or read book Periodic Orbits Stability and Resonances written by G.E.O. Giacaglia and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subjects of resonance and stability are closely related to the problem of evolution of the solar system. It is a physically involving problem and the methods available to mathematics today seem unsatisfactory to produce pure non linear ways of attack. The linearization process in both subjects is clearly of doubtful significance, so that, even if very restrictive, numerical solutions are still the best and more valuable sources of informations. It is quite possible that we know now very little more of the entire problem that was known to Poincare, with the advantage that we can now compute much faster and with much more precision. We feel that the papers collected in this Symposium have contributed a step forward to the comprehension of Resonance, Periodic Orbits and Stability. In a field like this, it would be a surprise if one had gone a long way toward that comprehension, during the short time of two weeks. But we are sure that the joint efforts of all the scientists involved has produced and will produce a measurable acceleration in the process. If this is true it will be a great satisfaction to us that this has happened in Brasil. The Southern Hemisphere in America has now begun to participate actively in the Astro nomical Society and for this, we are grateful to everyone who has helped.
Download or read book The Duffing Equation written by Ivana Kovacic and published by John Wiley & Sons. This book was released on 2011-02-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
