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Strongly Nonlinear Oscillators
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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.
Book Synopsis Averaging of Strongly Nonlinear Oscillators Using Elliptic Functions by : Vincent Timothy Coppola
Download or read book Averaging of Strongly Nonlinear Oscillators Using Elliptic Functions written by Vincent Timothy Coppola and published by . This book was released on 1989 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Book Synopsis On Approximations of First Integrals for Strongly Nonlinear Oscillators by : S. B. Waluya
Download or read book On Approximations of First Integrals for Strongly Nonlinear Oscillators written by S. B. Waluya and published by . This book was released on 2002 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Phase Shift for Strongly Nonlinear Slowly Varying Oscillators with Perturbations by : Richard Haberman
Download or read book Phase Shift for Strongly Nonlinear Slowly Varying Oscillators with Perturbations written by Richard Haberman and published by . This book was released on 1988 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Periodic Solutions of a Certain Non-Linear Differential Equations by : Gamal Ismail
Download or read book Periodic Solutions of a Certain Non-Linear Differential Equations written by Gamal Ismail and published by LAP Lambert Academic Publishing. This book was released on 2012-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear oscillators equations is of great importance not only in all areas of physics but also in engineering and other disciplines, since most phenomena in our word are nonlinear and are described by nonlinear equations. Recently, considerable attention has been direct towards the analytical solutions for nonlinear oscillators, for example, elliptic homotopy averaging method, amplitude-frequency formulation, homotopy perturbation method, parameter-expanding method, energy balance method, and others. The aim of this thesis is to study the periodic solutions for some physical systems which the mathematical formulation of these systems leads to a certain set of nonlinear ordinary differential equations of the second order.
Book Synopsis Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators by : F. J. Bourland
Download or read book Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators written by F. J. Bourland and published by . This book was released on 1989 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Dynamics by : Valery N. Pilipchuk
Download or read book Nonlinear Dynamics written by Valery N. Pilipchuk and published by Springer Science & Business Media. This book was released on 2010-05-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.
Book Synopsis Normal Modes and Localization in Nonlinear Systems by : Alexander F. Vakakis
Download or read book Normal Modes and Localization in Nonlinear Systems written by Alexander F. Vakakis and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.
Book Synopsis Variation of Wave Action: Modulations of the Phase Shift for Strongly Nonlinear Dispersive Waves with Weak Dissipation. A New Adiabatic Invariant Involving the Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators. The Modulated Phase Shift for Weakly Dissipated Nonlinear Oscillatory Waves of the Korteweg-de Vries Type by : F. J. Bourland
Download or read book Variation of Wave Action: Modulations of the Phase Shift for Strongly Nonlinear Dispersive Waves with Weak Dissipation. A New Adiabatic Invariant Involving the Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators. The Modulated Phase Shift for Weakly Dissipated Nonlinear Oscillatory Waves of the Korteweg-de Vries Type written by F. J. Bourland and published by . This book was released on 1987 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations for the spatial and temporal modulations of the phase shift for slowly varying strongly nonlinear oscillators and dispersive waves have been determined for the first time. The effects of dissipative perturbations have been investigated for nonlinear oscillatory solutions of ordinary and partial differential equations (described by Klein-Gordon and Korteweg-de Vries type equations). The phase shift equations were derived using the method of multiple scales by evaluating the small perturbations to the exact action equation, a somewhat simpler technique than usual elimination of secular terms at an even higher order in the asymptotic expansion. It has been shown that, for dissipative perturbations, the frequency and action equations are valid to higher order and that their variations are only due to perturbations in the wave number and the averaged amplitude parameters. For second-order ordinary differential equations, the phase shift is determined from initial conditions in straight-forward manner since it was shown that there exists a new adiabatic invariant.
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.
Book Synopsis An Analytical Approach to Investigation of Nonlinear Dynamical Systems by : Mohammad Molla-Alipour
Download or read book An Analytical Approach to Investigation of Nonlinear Dynamical Systems written by Mohammad Molla-Alipour and published by LAP Lambert Academic Publishing. This book was released on 2012-07 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most common oscillations of the mechanical systems are inherently nonlinear. These systems are important in engineering because many practical engineering components consist of vibrating systems that can be modeled using oscillator systems such as elastic beams supported by two springs or mass-on-moving belt or nonlinear pendulum and vibration of a milling machine. Therefore, investigating the nonlinear oscillations is important for many practical engineering components. The fluctuation, stability and the natural frequencies are very important items in oscillations of the mechanical systems, and investigating the influence of different parameters on these items is important in the design step. In the present book, nonlinear oscillation and stability analyses of dynamical systems are analyzed using an analytical approach. The results show that this method is very effective and work very well for the wide range of time and boundary conditions for various strongly nonlinear oscillators.
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.
Book Synopsis Asymptotic Methods in the Theory of Non-linear Oscillations by : Nikolaĭ Nikolaevich Bogoli︠u︡bov
Download or read book Asymptotic Methods in the Theory of Non-linear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by CRC Press. This book was released on 1961 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Oscillators and Oscillatory Signals from Smooth to Discontinuous by : Valery N. Pilipchuk
Download or read book Oscillators and Oscillatory Signals from Smooth to Discontinuous written by Valery N. Pilipchuk and published by Springer Nature. This book was released on 2023-09-23 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.
Book Synopsis Nonlinear Approaches in Engineering Applications by : Liming Dai
Download or read book Nonlinear Approaches in Engineering Applications written by Liming Dai and published by Springer. This book was released on 2018-01-29 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes the updated principles and applications of nonlinear approaches to solve engineering and physics problems. The knowledge on nonlinearity and the comprehension of nonlinear approaches are inevitable to future engineers and scientists, making this an ideal book for engineers, engineering students, and researchers in engineering, physics, and mathematics. Chapters are of specific interest to readers who seek expertise in optimization, nonlinear analysis, mathematical modeling of complex forms, and non-classical engineering problems. The book covers methodologies and applications from diverse areas such as vehicle dynamics, surgery simulation, path planning, mobile robots, contact and scratch analysis at the micro and nano scale, sub-structuring techniques, ballistic projectiles, and many more.
