Analytical Methods In Nonlinear Oscillations

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Analytical Methods in Nonlinear Oscillations

Author : Ebrahim Esmailzadeh
Publisher : Springer
ISBN 13 : 9402415424
Total Pages : 286 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Analytical Methods in Nonlinear Oscillations by : Ebrahim Esmailzadeh

Download or read book Analytical Methods in Nonlinear Oscillations written by Ebrahim Esmailzadeh and published by Springer. This book was released on 2018-06-29 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.

ANALYTICAL METHODS IN THE THEORY OF NONLINEAR OSCILLATIONS.

Author : Timothy Patrick Coffey
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (682 download)

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Book Synopsis ANALYTICAL METHODS IN THE THEORY OF NONLINEAR OSCILLATIONS. by : Timothy Patrick Coffey

Download or read book ANALYTICAL METHODS IN THE THEORY OF NONLINEAR OSCILLATIONS. written by Timothy Patrick Coffey and published by . This book was released on 1967 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author : John Guckenheimer
Publisher : Springer Science & Business Media
ISBN 13 : 1461211409
Total Pages : 475 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer

Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Strongly Nonlinear Oscillators

Author : Livija Cveticanin
Publisher : Springer
ISBN 13 : 3319052721
Total Pages : 241 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 241 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.

Nonlinear Oscillations

Author : Ali H. Nayfeh
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.

Introduction to Non-linear Mechanics

Author : Nicolai Minorsky
Publisher :
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Non-linear Mechanics by : Nicolai Minorsky

Download or read book Introduction to Non-linear Mechanics written by Nicolai Minorsky and published by . This book was released on 1947 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Asymptotic Methods in Nonlinear Oscillations

Author : Yuri A. Mitropolsky
Publisher : Springer Science & Business Media
ISBN 13 : 9401588473
Total Pages : 352 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Applied Asymptotic Methods in Nonlinear Oscillations by : Yuri A. Mitropolsky

Download or read book Applied Asymptotic Methods in Nonlinear Oscillations written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.

Analytical Methods for Nonlinear Oscillators and Solitary Waves

Author : Chu-Hui He
Publisher : Frontiers Media SA
ISBN 13 : 2832539637
Total Pages : 132 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Analytical Methods for Nonlinear Oscillators and Solitary Waves by : Chu-Hui He

Download or read book Analytical Methods for Nonlinear Oscillators and Solitary Waves written by Chu-Hui He and published by Frontiers Media SA. This book was released on 2023-11-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.

Introduction to Nonlinear Oscillations

Author : Vladimir I. Nekorkin
Publisher : John Wiley & Sons
ISBN 13 : 3527685421
Total Pages : 264 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Introduction to Nonlinear Oscillations by : Vladimir I. Nekorkin

Download or read book Introduction to Nonlinear Oscillations written by Vladimir I. Nekorkin and published by John Wiley & Sons. This book was released on 2015-04-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.

Oscillations in Nonlinear Systems

Author : Jack K. Hale
Publisher : Courier Dover Publications
ISBN 13 : 0486803260
Total Pages : 192 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Oscillations in Nonlinear Systems by : Jack K. Hale

Download or read book Oscillations in Nonlinear Systems written by Jack K. Hale and published by Courier Dover Publications. This book was released on 2015-03-24 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.

Nonlinear Oscillations of Hamiltonian PDEs

Author : Massimiliano Berti
Publisher : Springer Science & Business Media
ISBN 13 : 0817646809
Total Pages : 191 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Nonlinear Oscillations of Hamiltonian PDEs by : Massimiliano Berti

Download or read book Nonlinear Oscillations of Hamiltonian PDEs written by Massimiliano Berti and published by Springer Science & Business Media. This book was released on 2007-10-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

An Introduction to Nonlinear Oscillations

Author : Ronald E. Mickens
Publisher : CUP Archive
ISBN 13 : 9780521222082
Total Pages : 234 pages
Book Rating : 4.2/5 (22 download)

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Book Synopsis An Introduction to Nonlinear Oscillations by : Ronald E. Mickens

Download or read book An Introduction to Nonlinear Oscillations written by Ronald E. Mickens and published by CUP Archive. This book was released on 1981 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory account of the equations describing nonlinear oscillations & the methods for solving them.

Nonlinear Random Vibration

Author : Cho W.S. To
Publisher : CRC Press
ISBN 13 : 1482287269
Total Pages : 257 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Nonlinear Random Vibration by : Cho W.S. To

Download or read book Nonlinear Random Vibration written by Cho W.S. To and published by CRC Press. This book was released on 2000-01-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.

Nonlinear System Analysis

Author : Austin Blaquiere
Publisher : Elsevier
ISBN 13 : 0323151663
Total Pages : 409 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Nonlinear System Analysis by : Austin Blaquiere

Download or read book Nonlinear System Analysis written by Austin Blaquiere and published by Elsevier. This book was released on 2012-12-02 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Analysis focuses on the study of systems whose behavior is governed by nonlinear differential equations. This book is composed of nine chapters that cover some problems that play a major role in engineering and physics. The opening chapter briefly introduces the difference between linear and nonlinear systems. Considerable chapters are devoted to engineering and physics related problems and their applications to particle accelerators, frequency measurements, and masers. Included in these chapters are important practical problems, such as synchronization, stability of systems with periodic coefficients, and effect of random disturbances. The remaining chapters examine random fluctuations of the motion and self-oscillators. This book is intended primarily for engineers and physicists.

Nonlinear Oscillations

Author : Ivana Kovacic
Publisher : Springer Nature
ISBN 13 : 3030531724
Total Pages : 278 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Nonlinear Oscillations by : Ivana Kovacic

Download or read book Nonlinear Oscillations written by Ivana Kovacic and published by Springer Nature. This book was released on 2020-08-14 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.

Strong Nonlinear Oscillators

Author : Livija Cveticanin
Publisher : Springer
ISBN 13 : 3319588265
Total Pages : 320 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 320 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.

Nonlinear Oscillations in Mechanical Engineering

Author : Alexander Fidlin
Publisher : Springer Science & Business Media
ISBN 13 : 3540281169
Total Pages : 367 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Nonlinear Oscillations in Mechanical Engineering by : Alexander Fidlin

Download or read book Nonlinear Oscillations in Mechanical Engineering written by Alexander Fidlin and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Nonlinear Oscillations in Mechanical Engineering" explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused by dry friction and collisions. Another important source of nonlinearity which is covered is that caused by rotating unbalanced parts common in various machines as well as variable inertias occurring in all kinds of crank mechanisms. This book is written for advanced undergraduate and postgraduate students, but it may be also helpful and interesting for both theoreticians and practitioners working in the area of mechanical engineering at universities, in research labs or institutes and especially in the R and D departments within industrial firms.