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Nonlinear Resonance Analysis

Author : Elena Kartashova

Publisher : Cambridge University Press

Page : 241 pages

File Size : 27,11 MB

Release : 2010-10-21

Category : Science

ISBN : 1139493086

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Book Description

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.



Nonlinear Resonances

Author : Shanmuganathan Rajasekar

Publisher : Springer

Page : 417 pages

File Size : 31,63 MB

Release : 2015-11-30

Category : Science

ISBN : 3319248863

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Book Description

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.



The Mechanics of Nonlinear Systems with Internal Resonances

Author : Arkadiy I. Manevich

Publisher : World Scientific

Page : 278 pages

File Size : 21,30 MB

Release : 2005

Category : Science

ISBN : 1860945104

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Book Description

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.



Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation

Author : Tribikram Kundu

Publisher : Springer

Page : 761 pages

File Size : 48,5 MB

Release : 2018-10-19

Category : Technology & Engineering

ISBN : 3319944762

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Book Description

This multi-contributed volume provides a practical, applications-focused introduction to nonlinear acoustical techniques for nondestructive evaluation. Compared to linear techniques, nonlinear acoustical/ultrasonic techniques are much more sensitive to micro-cracks and other types of small distributed damages. Most materials and structures exhibit nonlinear behavior due to the formation of dislocation and micro-cracks from fatigue or other types of repetitive loadings well before detectable macro-cracks are formed. Nondestructive evaluation (NDE) tools that have been developed based on nonlinear acoustical techniques are capable of providing early warnings about the possibility of structural failure before detectable macro-cracks are formed. This book presents the full range of nonlinear acoustical techniques used today for NDE. The expert chapters cover both theoretical and experimental aspects, but always with an eye towards applications. Unlike other titles currently available, which treat nonlinearity as a physics problem and focus on different analytical derivations, the present volume emphasizes NDE applications over detailed analytical derivations. The introductory chapter presents the fundamentals in a manner accessible to anyone with an undergraduate degree in Engineering or Physics and equips the reader with all of the necessary background to understand the remaining chapters. This self-contained volume will be a valuable reference to graduate students through practising researchers in Engineering, Materials Science, and Physics. Represents the first book on nonlinear acoustical techniques for NDE applications Emphasizes applications of nonlinear acoustical techniques Presents the fundamental physics and mathematics behind nonlinear acoustical phenomenon in a simple, easily understood manner Covers a variety of popular NDE techniques based on nonlinear acoustics in a single volume



The Duffing Equation

Author : Ivana Kovacic

Publisher : John Wiley & Sons

Page : 335 pages

File Size : 28,27 MB

Release : 2011-02-11

Category : Science

ISBN : 0470977833

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Book Description

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.



Understanding Acoustics

Author : Steven L. Garrett

Publisher : Springer

Page : 913 pages

File Size : 33,68 MB

Release : 2017-02-24

Category : Science

ISBN : 3319499785

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Book Description

This textbook provides a unified approach to acoustics and vibration suitable for use in advanced undergraduate and first-year graduate courses on vibration and fluids. The book includes thorough treatment of vibration of harmonic oscillators, coupled oscillators, isotropic elasticity, and waves in solids including the use of resonance techniques for determination of elastic moduli. Drawing on 35 years of experience teaching introductory graduate acoustics at the Naval Postgraduate School and Penn State, the author presents a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation that can incorporate attenuation mechanisms and complex media. This view provides a consistent and reliable approach that can be extended with confidence to more complex fluids and future applications. Understanding Acoustics opens with a mathematical introduction that includes graphing and statistical uncertainty, followed by five chapters on vibration and elastic waves that provide important results and highlight modern applications while introducing analytical techniques that are revisited in the study of waves in fluids covered in Part II. A unified approach to waves in fluids (i.e., liquids and gases) is based on a mastery of the hydrodynamic equations. Part III demonstrates extensions of this view to nonlinear acoustics. Engaging and practical, this book is a must-read for graduate students in acoustics and vibration as well as active researchers interested in a novel approach to the material.



Nonlinear Resonances in the Motion of Rolling Reentry Bodies

Author : Ali Hasan Nayfeh

Publisher :

Page : 52 pages

File Size : 50,54 MB

Release : 1971

Category : Body of revolution

ISBN :

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Book Description

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.



Nonlinear Functional Analysis

Author : Klaus Deimling

Publisher : Springer Science & Business Media

Page : 465 pages

File Size : 42,54 MB

Release : 2013-11-11

Category : Mathematics

ISBN : 3662005476

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Book Description

topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.



Nonlinear Resonance Computer Components

Author : Takao Ozawa

Publisher :

Page : 116 pages

File Size : 35,23 MB

Release : 1963

Category : Computers

ISBN :

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Book Description

A mathematical analysis of the series resonant circuit is given. The principle of harmonic balance is applied to the differential equations for the circuit in order to obtain the steady state responses. It is shown that the circuit is a threshold device with respect to the amplitude of the driving voltage. A three phase clock system is used to drive the basic resonant circuits, which are coupled to form threshold logic. Various types of coupling between the circuits are considered. The transient response of the circuit which is closely related to the switching speed is analyzed by a series method. Two basic resonant circuits are coupled to form a flip-flop. The conditions for bistability of the coupled circuits are investigated. Possible realizations of the resonant circuit and the logic circuits are suggested, with the assumption that all necessary devices are available. (Author).



Homotopy Analysis Method in Nonlinear Differential Equations

Author : Shijun Liao

Publisher : Springer Science & Business Media

Page : 566 pages

File Size : 45,93 MB

Release : 2012-06-22

Category : Mathematics

ISBN : 3642251323

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Book Description

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.