Nonlinear Resonances
Nonlinear Resonances

Author: Shanmuganathan Rajasekar

Publisher: Springer

Published: 2015-11-30

Total Pages: 417

ISBN-13: 3319248863

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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.

Nonlinear Resonances in the Motion of Rolling Reentry Bodies
Nonlinear Resonances in the Motion of Rolling Reentry Bodies

Author: Ali Hasan Nayfeh

Publisher:

Published: 1971

Total Pages: 52

ISBN-13:

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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 Resonance Analysis
Nonlinear Resonance Analysis

Author: Elena Kartashova

Publisher: Cambridge University Press

Published: 2010-10-21

Total Pages: 241

ISBN-13: 1139493086

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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.

The Mechanics of Nonlinear Systems with Internal Resonances
The Mechanics of Nonlinear Systems with Internal Resonances

Author: Arkadiy I. Manevich

Publisher: World Scientific

Published: 2005

Total Pages: 278

ISBN-13: 1860945104

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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.

Normal Modes and Localization in Nonlinear Systems
Normal Modes and Localization in Nonlinear Systems

Author: Alexander F. Vakakis

Publisher: John Wiley & Sons

Published: 2008-07-11

Total Pages: 552

ISBN-13: 3527617876

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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.

Linear and Nonlinear Rotordynamics
Linear and Nonlinear Rotordynamics

Author: Yukio Ishida

Publisher: John Wiley & Sons

Published: 2013-03-05

Total Pages: 495

ISBN-13: 3527651918

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A wide-ranging treatment of fundamental rotordynamics in order to serve engineers with the necessary knowledge to eliminate various vibration problems. New to this edition are three chapters on highly significant topics: Vibration Suppression - The chapter presents various methods and is a helpful guidance for professional engineers. Magnetic Bearings - The chapter provides fundamental knowledge and enables the reader to realize simple magnetic bearings in the laboratory. Some Practical Rotor Systems - The chapter explains various vibration characteristics of steam turbines and wind turbines. The contents of other chapters on Balancing, Vibrations due to Mechanical Elements, and Cracked Rotors are added to and revised extensively. The authors provide a classification of rotating shaft systems and general coverage of key ideas common to all branches of rotordynamics. They offers a unique analysis of dynamical problems, such as nonlinear rotordynamics, self-excited vibration, nonstationary vibration, and flow-induced oscillations. Nonlinear resonances are discussed in detail, as well as methods for shaft stability and various theoretical derivations and computational methods for analyzing rotors to determine and correct vibrations. This edition also includes case studies and problems.

Hagenberg Research
Hagenberg Research

Author: Bruno Buchberger

Publisher: Springer Science & Business Media

Published: 2009-05-29

Total Pages: 490

ISBN-13: 3642021271

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BrunoBuchberger This book is a synopsis of basic and applied research done at the various re search institutions of the Softwarepark Hagenberg in Austria. Starting with 15 coworkers in my Research Institute for Symbolic Computation (RISC), I initiated the Softwarepark Hagenberg in 1987 on request of the Upper Aus trian Government with the objective of creating a scienti?c, technological, and economic impulse for the region and the international community. In the meantime, in a joint e?ort, the Softwarepark Hagenberg has grown to the current (2009) size of over 1000 R&D employees and 1300 students in six research institutions, 40 companies and 20 academic study programs on the bachelor, master’s and PhD level. The goal of the Softwarepark Hagenberg is innovation of economy in one of the most important current technologies: software. It is the message of this book that this can only be achieved and guaranteed long term by “watering the root”, namely emphasis on research, both basic and applied. In this book, we summarize what has been achieved in terms of research in the various research institutions in the Softwarepark Hagenberg and what research vision we have for the imminent future. When I founded the Softwarepark Hagenberg, in addition to the “watering the root” principle, I had the vision that such a technology park can only prosper if we realize the “magic triangle”, i.e. the close interaction of research, academic education, and business applications at one site, see Figure 1.

Practical Aspects of Ion Trap Mass Spectrometry
Practical Aspects of Ion Trap Mass Spectrometry

Author: Raymond E. March

Publisher: CRC Press

Published: 1995-09-18

Total Pages: 452

ISBN-13: 9780849344527

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Fundamentals of Ion Trap Mass Spectrometry presents an account of the development and theory of the quadrupole ion trap and its utilization as an ion storage device, a reactor for ion/molecular reactions, and a mass spectrometer. It also expands the appreciation of ion traps from that of a unique arrangement of electrodes of hyperbolic form (and having a pure quadrupole field) to a series of ion traps having fields with hexapole and octopole components and introduces the practical ion trapping device in which electrode spacing has been increased. The fundamentals of ion trap are covered in four chapters, beginning with the origin of the ion trap, its development and operating principles, and improvements in performance. The second part focuses on the environment within the ion trap -- the movement of ions within the trap -- and how this movement is modified by repeated collisions of the ions with buffer gas atoms of helium, and on the collisions of ions with molecules that lead to chemical change. The critical role of collisions in focusing the ion cloud for subsequent operations is emphasized. This important reference presents a coherent picture of the present status of research in the ion trapping field to facilitate the entree of potential ion trappers and provide a backdrop for ion trap research and development in the future.

Practical Aspects of Ion Trap Mass Spectrometry, Volume I
Practical Aspects of Ion Trap Mass Spectrometry, Volume I

Author: Raymond E. March

Publisher: CRC Press

Published: 2024-11-01

Total Pages: 450

ISBN-13: 1040290981

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Fundamentals of Ion Trap Mass Spectrometry presents an account of the development and theory of the quadrupole ion trap and its utilization as an ion storage device, a reactor for ion/molecular reactions, and a mass spectrometer. It also expands the appreciation of ion traps from that of a unique arrangement of electrodes of hyperbolic form (and having a pure quadrupole field) to a series of ion traps having fields with hexapole and octopole components and introduces the practical ion trapping device in which electrode spacing has been increased. The fundamentals of ion trap are covered in four chapters, beginning with the origin of the ion trap, its development and operating principles, and improvements in performance. The second part focuses on the environment within the ion trap -- the movement of ions within the trap -- and how this movement is modified by repeated collisions of the ions with buffer gas atoms of helium, and on the collisions of ions with molecules that lead to chemical change. The critical role of collisions in focusing the ion cloud for subsequent operations is emphasized. This important reference presents a coherent picture of the present status of research in the ion trapping field to facilitate the entree of potential ion trappers and provide a backdrop for ion trap research and development in the future.

Stability of Gyroscopic Systems
Stability of Gyroscopic Systems

Author: Ard‚shir Guran

Publisher: World Scientific

Published: 1999

Total Pages: 438

ISBN-13: 9810226306

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The motion of mechanical systems undergoing rotation about a fixed axis has been the subject of extensive studies over a few centuries. These systems are generally subject to gyroscopic forces which are associated with coriolis accelerations or mass transport and render complex dynamics.The unifying theme among topics presented in this book is the gyroscopic nature of the system equations of motion. The book represents comprehensive and detailed reviews of the state of art in four diverse application areas: flow-induced oscillations in structures, oscillations in rotating systems or rotor dynamics, dynamics of axially moving material systems, and dynamics of gyroelastic systems. The book also includes a chapter on dynamics of repetitive structures. These systems feature spatial periodicity and are generally subject to considerable gyroscopic forces. ?Gyroelastic systems? and ?repetitive structures? are the topics with very recent origins and are still in their infancies compared to the other examples represented in this book. Thus, the contributions on gyroelastic systems and repetitive structures are limited to only modeling, localization and linear stability analysis results.This book covers many important aspects of recent developments in various types of gyroscopic systems. Thus, at last, a comprehensive book is made available to serve as a supplement and resource for any graduate level course on elastic gyroscopic systems, as well as for a course covering the stability of mechanical systems. Moreover, the inclusion of an up-to-date bibliography attached to each chapter will make this book an invaluable text for professional reference.