A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.
Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer e.
An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations with the tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.
This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Covering the whole spectrum of vibration theory and itsapplications in both civil and mechanical engineering, Mechanicaland Structural Vibrations provides the most comprehensive treatmentof the subject currently available. Based on the author s manyyears of experience in both academe and industry, it is designed tofunction equally well as both a day-to-day working resource forpracticing engineers and a superior upper-level undergraduate orgraduate-level text. Features a quick-reference format that, Mechanical and StructuralVibrations gives engineers instant access to the specific theory orapplication they need. Saves valuable time ordinarily spent wadingthrough unrelated or extraneous material. And, while they arethoroughly integrated throughout the text, applications to bothcivil and mechanical engineering are organized into sections thatpermit the reader to reference only the material germane to his orher field. Students and teachers will appreciate the book's practical,real-world approach to the subject, its emphasis on simplicity andaccuracy of analytical techniques, and its straightforward,step-by-step delineation of all numerical methods used incalculating the dynamics and vibrations problems, as well as thenumerous examples with which the author illustrates those methods.They will also appreciate the many chapter-end practice problems(solutions appear in appendices) designed to help them rapidlydevelop mastery of all concepts and methods covered. Readers will find many versatile new concepts and analyticaltechniques not covered in other texts, including nonlinearanalysis, inelastic response of structural and mechanicalcomponents of uniform and variable stiffness, the "dynamic hinge,""dynamically equivalent systems," and other breakthrough tools andtechniques developed by the author and his collaborators. Mechanical and Structural Vibrations is both an excellent text forcourses in structural dynamics, dynamic systems, and engineeringvibration and a valuable tool of the trade for practicing engineersworking in a broad range of industries, from electronic packagingto aerospace. Timely, comprehensive, practical--a superior student text and anindispensable working resource for busy engineers Mechanical and Structural Vibrations is the first text to cover theentire spectrum of vibration theory and its applications in bothcivil and mechanical engineering. Written by an author with over aquarter century of experience as a teacher and practicing engineer,it is designed to function equally well as a working professionalresource and an upper-level undergraduate or graduate-level textfor courses in structural dynamics, dynamic systems, andengineering vibrations. Mechanical and Structural Vibrations: * Takes a practical, application-oriented approach to the subject * Features a quick-reference format that gives busy professionalsinstant access to the information needed for the task at hand * Walks readers, step-by-step, through the numerical methods usedin calculating the dynamics and vibration problems * Introduces many cutting-edge concepts and analytical tools notcovered in other texts * Is packed with real-world examples covering everything from thestresses and strains on buildings during an earthquake to thoseaffecting a space craft during lift-off * Contains chapter-end problems--and solutions--that help studentsrapidly develop mastery of all important concepts and methodscovered * Is extremely well-illustrated and includes more than 300diagrams, tables, charts, illustrations, and more
Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics. * Discusses nonlinearity and chaotic phenomena in molecular vibrations* Approaches the complicated highly excited molecular vibration* Provides clear information for students and researchers looking to expand knowledge in this field
An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations with the tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.
