Strong Nonlinear Oscillators

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Author :
Publisher : Springer
ISBN 13 : 3319588265
Total Pages : 317 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Strong Nonlinear Oscillators by : Livija Cveticanin

Download or read book Strong Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2017-05-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Strongly Nonlinear Oscillators

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Author :
Publisher : Springer
ISBN 13 : 3319052721
Total Pages : 239 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Strongly Nonlinear Oscillators by : Livija Cveticanin

Download or read book Strongly Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2014-05-22 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

The Duffing Equation

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Publisher : John Wiley & Sons
ISBN 13 : 0470977833
Total Pages : 335 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis The Duffing Equation by : Ivana Kovacic

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.

Fluctuating Nonlinear Oscillators

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Author :
Publisher : Oxford University Press
ISBN 13 : 019969138X
Total Pages : 446 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Fluctuating Nonlinear Oscillators by : Mark Dykman

Download or read book Fluctuating Nonlinear Oscillators written by Mark Dykman and published by Oxford University Press. This book was released on 2012-07-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a unifying insight into a broad range of phenomena displayed by vibrational systems of current interest. The chapters complement each other to give an account of the major fundamental results and applications in quantum information, condensed matter physics, and engineering.

Nonlinear Oscillations

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 3527617590
Total Pages : 720 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Nonlinear Oscillations by : Ali H. Nayfeh

Download or read book Nonlinear Oscillations written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.

Fluctuating Nonlinear Oscillators

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Author :
Publisher : OUP Oxford
ISBN 13 : 0191637548
Total Pages : 432 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Fluctuating Nonlinear Oscillators by : Mark Dykman

Download or read book Fluctuating Nonlinear Oscillators written by Mark Dykman and published by OUP Oxford. This book was released on 2012-07-26 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a unifying insight into fluctuation phenomena in a broad variety of vibrational systems of current interest. It consists of individual chapters written by leading experts in the field. The chapters are self-contained and complement each other. The ongoing rapid development of well-characterized mesoscopic vibrational systems has made it possible to address fundamental physics problems and to explore new approaches to quantum and classical measurements, with applications to quantum information, condensed matter physics, and engineering. The book gives an account of major results in this direction. The topics include dynamics and quantum control of microcavity modes coupled to qubits, measurements with bifurcation-based amplifiers and new types of such amplifiers; switching rate scaling and new quantum mechanisms of metastable decay; wave mixing and parametric excitation in the quantum regime; collective phenomena and the interaction-induced discrete time symmetry breaking; and back-action and shot noise in electron-vibrational systems.

Lectures on Nonlinear Dynamics

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Author :
Publisher : Springer Nature
ISBN 13 : 3031451015
Total Pages : 352 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Lectures on Nonlinear Dynamics by : José Roberto Castilho Piqueira

Download or read book Lectures on Nonlinear Dynamics written by José Roberto Castilho Piqueira and published by Springer Nature. This book was released on 2024-01-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, nonlinear modal analysis and model reduction, synchronization, and strongly nonlinear dynamics. Interwoven seamlessly, these groups cover a wide range of topics, from fundamental concepts to practical applications, catering to both introductory and advanced readers. The first group, consisting of chapters 1 and 2, serves as an introduction to the theory of parametric resonance and the dynamics of parametrically excited slender structures. Chapters 3, 4, and 5 form the second group, offering insights into normal forms, nonlinear normal modes, and nonlinear system identification. Chapters 6 and 7 delve into asynchronous modes of structural vibration and master-slave topologies for time signal distribution within synchronous systems, respectively, representing the third group. Finally, the last four chapters tackle the fourth group, exploring nonlinear dynamics of variable mass oscillators, advanced analytical methods for strong nonlinear vibration problems, chaos theory, and dynamic integrity from the perspectives of safety and design. This book harmoniously combines theoretical depth and practical relevance to provide a comprehensive understanding of nonlinear dynamics.

Galileo Unbound

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Publisher : Oxford University Press
ISBN 13 : 0192528505
Total Pages : 384 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Galileo Unbound by : David D. Nolte

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Theory of Oscillators

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Author :
Publisher : Elsevier
ISBN 13 : 1483194728
Total Pages : 848 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Theory of Oscillators by : A. A. Andronov

Download or read book Theory of Oscillators written by A. A. Andronov and published by Elsevier. This book was released on 2013-10-22 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.

Nonlinear Dynamics

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Author :
Publisher : World Scientific
ISBN 13 : 9789810229825
Total Pages : 254 pages
Book Rating : 4.2/5 (298 download)

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Book Synopsis Nonlinear Dynamics by : Ard‚shir Guran

Download or read book Nonlinear Dynamics written by Ard‚shir Guran and published by World Scientific. This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.

Modern Trends in Structural and Solid Mechanics 2

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Publisher : John Wiley & Sons
ISBN 13 : 1119831849
Total Pages : 306 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Modern Trends in Structural and Solid Mechanics 2 by : Noel Challamel

Download or read book Modern Trends in Structural and Solid Mechanics 2 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media

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Publisher : Springer Science & Business Media
ISBN 13 : 1461547997
Total Pages : 415 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media by : Ludmilla A. Uvarova

Download or read book Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media written by Ludmilla A. Uvarova and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are derived from the Third International Conference of the same name, held June 29-July 3, 1998. Topics include: nonlinear exaltations in condensed systems, evolution of complex systems, dynamics and structure of molecular and biomolecular systems, mathematical models of transfer processes in nonlinear systems and numerical modeling and algorithms.

Partial Differential Equations and Solitary Waves Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 364200251X
Total Pages : 700 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Partial Differential Equations and Solitary Waves Theory by : Abdul-Majid Wazwaz

Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Nonlinear Dynamics and Chaos

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Author :
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Dynamics of Mechanical Systems with Non-Ideal Excitation

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Author :
Publisher : Springer
ISBN 13 : 3319541692
Total Pages : 229 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Dynamics of Mechanical Systems with Non-Ideal Excitation by : Livija Cveticanin

Download or read book Dynamics of Mechanical Systems with Non-Ideal Excitation written by Livija Cveticanin and published by Springer. This book was released on 2017-07-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame – non-ideal source system, non-ideal rotor system, planar mechanism – non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called ‘Sommerfeld effect’, resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.

Nonlinear Dynamics of Structures, Systems and Devices

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Author :
Publisher : Springer Nature
ISBN 13 : 3030347133
Total Pages : 592 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Nonlinear Dynamics of Structures, Systems and Devices by : Walter Lacarbonara

Download or read book Nonlinear Dynamics of Structures, Systems and Devices written by Walter Lacarbonara and published by Springer Nature. This book was released on 2020-01-29 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics.

Truly Nonlinear Oscillations

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Author :
Publisher :
ISBN 13 : 9814466042
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Truly Nonlinear Oscillations by :

Download or read book Truly Nonlinear Oscillations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: