Nonlinear Vibrations in Mechanical and Electrical Systems
Nonlinear Vibrations in Mechanical and Electrical Systems

Author: J. J. Stoker

Publisher: Wiley-Interscience

Published: 1992-01-24

Total Pages: 300

ISBN-13:

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Presents underlying principles and theories using an easily understood approach. Focuses specifically on those features of the problems in which nonlinearity results in a variety of distinctive new phenomena that can be treated by techniques both interesting and instructive in themselves and which do not require the use of sophisticated mathematics. Recent work discussed includes the endeavors of Levinson and Smith on the existence and uniqueness of the periodic solution in a general case of the self-excited type, Haag and Dorodnitsyn on asymptotic developments and quantities associated with relaxation oscillations. Along with 5 appendices containing rigorous existence and uniqueness proofs, readers are both implicitly and explicitly supplied with hints regarding new problems to be tackled plus numerous ideas and techniques that can be used to solve them.

The Behaviour of Nonlinear Vibrating Systems
The Behaviour of Nonlinear Vibrating Systems

Author: Wanda Szemplinska

Publisher: Springer Science & Business Media

Published: 1990-06-30

Total Pages: 370

ISBN-13: 9780792303695

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The purpose of this book is to provide students, practicing engineers and scientists with a treatment of nonlinear phenomena occurring in physical systems. Although only mechanical models are used, the theory applies to all physical systems governed by the same equations, so that the book can be used to study nonlinear phenomena in other branches of engineering, such as electrical engineering and aerospace engineering, as well as in physics. The book consists of two volumes. Volume I is concerned with single degree-of-freedom systems and it presents the fundamental concepts of nonlinear analysis. Both analytical methods and computer simulations are included. The material is presented in such a manner that the book can be used as a graduate as well as an undergraduate textbook. Volume II deals with multi-degree-of-freedom systems. Following an introduc tion to linear systems, the volume presents fundamental concepts of geometric theory and stability of motion of general nonlinear systems, as well as a concise discussion of basic approximate methods for the response of such systems. The material represents a generalization of a series of papers on the vibration of nonlinear multi-degree-of-freedom systems, some of which were published by me and my associates during the period 1965 - 1983 and some are not yet published.

Nonlinear Vibration with Control
Nonlinear Vibration with Control

Author: David Wagg

Publisher: Springer

Published: 2014-11-03

Total Pages: 461

ISBN-13: 3319106449

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This book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader themes cut across these application areas: (i) vibration suppression – or active damping – and, (ii) adaptive structures and machines. In this expanded 2nd edition, revisions include: An additional section on passive vibration control, including nonlinear vibration mounts. A more in-depth description of semi-active control, including switching and continuous schemes for dampers and other semi-active systems. A complet e reworking of normal form analysis, which now includes new material on internal resonance, bifurcation of backbone curves and stability analysis of forced responses. Further analysis of the nonlinear dynamics of cables including internal resonance leading to whirling. Additional material on the vibration of systems with impact friction. The book is accessible to practitioners in the areas of application, as well as students and researchers working on related topics. In particular, the aim is to introduce the key concepts of nonlinear vibration to readers who have an understanding of linear vibration and/or linear control, but no specialist knowledge in nonlinear dynamics or nonlinear control.

Harmonic Balance for Nonlinear Vibration Problems
Harmonic Balance for Nonlinear Vibration Problems

Author: Malte Krack

Publisher: Springer

Published: 2019-03-23

Total Pages: 167

ISBN-13: 3030140237

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This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.

Nonlinear Dynamical Systems in Engineering
Nonlinear Dynamical Systems in Engineering

Author: Vasile Marinca

Publisher: Springer Science & Business Media

Published: 2012-01-05

Total Pages: 403

ISBN-13: 364222735X

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This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Advances in Applied Nonlinear Dynamics, Vibration and Control -2021
Advances in Applied Nonlinear Dynamics, Vibration and Control -2021

Author: Xingjian Jing

Publisher: Springer Nature

Published: 2021-09-23

Total Pages: 1210

ISBN-13: 9811659125

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This book is to provide readers with up-to-date advances in applied and interdisciplinary engineering science and technologies related to nonlinear dynamics, vibration, control, robotics, and their engineering applications, developed in the most recent years. All the contributed chapters come from active scholars in the area, which cover advanced theory & methods, innovative technologies, benchmark experimental validations and engineering practices. Readers would benefit from this state-of-the-art collection of applied nonlinear dynamics, in-depth vibration engineering theory, cutting-edge control methods and technologies, and definitely find stimulating ideas for their on-going R&D work. This book is intended for graduate students, research staff and scholars in academics, and also provides useful hand-up guidance for professional and engineers in practical engineering missions.