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Perturbation Methods
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper E...
Nonlinear Oscillations
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.
Applied Nonlinear Dynamics
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Linear and Nonlinear Structural Mechanics
* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Provides ready-to-use governing equations.
Introduction to Perturbation Techniques
Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.
Problems in Perturbation
This self-contained volume explains perturbation techniques by means of solved problems. Ideal for self-study, it provides 360 solved problems and an almost equal number of supplementary problems.
Nonlinear Interactions
Nonlinear Interactions provides a coherent and unified treatment of analytical, computational, and experimental methods and concepts of modal interactions. This book is an obvious extension of Ali Nayfeh's well-known book Applied Nonlinear Dynamics (with Bala Balachandran). These methods are used to explore and unfold in a unified manner the fascinating complexities in nonlinear dynamical systems. The systems discussed are drawn from fluid mechanics and structural dynamics. Nonlinear interactions between high-frequency and low-frequency modes are of great practical importance. Through the mechanisms discussed in this book, energy from high-frequency sources can be transferred to the low-frequency modes of supporting structures and foundations, and the result can be harmful large-amplitude oscillations that decrease their fatigue lives. On the other hand, these mechanisms can be exploited to transfer the energy from a system to a sacrificial subsystem and hence decrease considerably the vibrations of the main system and increase its fatigue life.
Nonlinear Oscillations in Mechanical Engineering
"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.
Nonlinear Structural Mechanics
This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
The Method of Normal Forms
Based on a successful text, this second edition presents different concepts from dynamical systems theory and nonlinear dynamics. The introductory text systematically introduces models and techniques and states the relevant ranges of validity and applicability. New to this edition: 3 new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems Key features: Retarded Systems has become a topic of major importance in several applications, in mechanics and other areas Provides a clear operational framework for conscious use of concepts and tools Presents a rich variety of examples, including their final outcome For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging Explains and compares different applications of the considered concepts and techniques Assumes knowledge of basic calculus as well as the elementary properties of ordinary-differential equations
