Harmonic Balance for Nonlinear Vibration Problems

Harmonic Balance for Nonlinear Vibration Problems PDF Author: Malte Krack
Publisher: Springer
ISBN: 3030140237
Category : Technology & Engineering
Languages : en
Pages : 167

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Book Description
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.

Harmonic Balance for Nonlinear Vibration Problems

Harmonic Balance for Nonlinear Vibration Problems PDF Author: Malte Krack
Publisher: Springer
ISBN: 3030140237
Category : Technology & Engineering
Languages : en
Pages : 167

Get Book Here

Book Description
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 Vibration with Control

Nonlinear Vibration with Control PDF Author: David Wagg
Publisher: Springer Science & Business Media
ISBN: 9048128374
Category : Technology & Engineering
Languages : en
Pages : 361

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Book Description
The authors discuss the interrelationship of linear vibration theory for multi-degree-of-freedom systems; nonlinear dynamics and chaos; and nonlinear control. No other book covers these areas in the same way, so this is a new perspective on these topics.

The Method of Normal Forms

The Method of Normal Forms PDF Author: Ali H. Nayfeh
Publisher: John Wiley & Sons
ISBN: 352741097X
Category : Science
Languages : en
Pages : 344

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Book Description
In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to 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. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.

The Duffing Equation

The Duffing Equation PDF Author: Ivana Kovacic
Publisher: John Wiley & Sons
ISBN: 0470977833
Category : Science
Languages : en
Pages : 335

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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.

Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics

Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics PDF Author: Oleg V. Gendelman
Publisher: Springer Nature
ISBN: 3031569024
Category :
Languages : en
Pages : 277

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Book Description


Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, And Averaging Methods

Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, And Averaging Methods PDF Author: Ronald E Mickens
Publisher: World Scientific
ISBN: 9814466042
Category : Mathematics
Languages : en
Pages : 261

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Book Description
This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of “truly nonlinear” (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods.The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply these technique to the field of nonlinear oscillations.

Nonlinearity in Structural Dynamics

Nonlinearity in Structural Dynamics PDF Author: K Worden
Publisher: CRC Press
ISBN: 0429524986
Category : Science
Languages : en
Pages : 571

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Book Description
Many types of engineering structures exhibit nonlinear behavior under real operating conditions. Sometimes the unpredicted nonlinear behavior of a system results in catastrophic failure. In civil engineering, grandstands at sporting events and concerts may be prone to nonlinear oscillations due to looseness of joints, friction, and crowd movements.

Nonlinear Structures & Systems, Vol. 1

Nonlinear Structures & Systems, Vol. 1 PDF Author: Matthew R. W. Brake
Publisher: Springer Nature
ISBN: 3031694090
Category :
Languages : en
Pages : 151

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Book Description


Nonlinear Structures & Systems, Volume 1

Nonlinear Structures & Systems, Volume 1 PDF Author: Matthew R.W. Brake
Publisher: Springer Nature
ISBN: 3031040864
Category : Technology & Engineering
Languages : en
Pages : 291

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Book Description
Nonlinear Structures & Systems, Volume 1: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Experimental Nonlinear Dynamics Jointed Structures: Identification, Mechanics, Dynamics Nonlinear Damping Nonlinear Modeling and Simulation Nonlinear Reduced-Order Modeling Nonlinearity and System Identification

Advances in Nonlinear Dynamics

Advances in Nonlinear Dynamics PDF Author: Walter Lacarbonara
Publisher: Springer Nature
ISBN: 3030811662
Category : Technology & Engineering
Languages : en
Pages : 579

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Book Description
This second of three volumes includes papers from the second series of NODYCON which was held virtually in February of 2021. The conference papers reflect a broad coverage of topics in nonlinear dynamics, ranging from traditional topics from established streams of research to those from relatively unexplored and emerging venues of research. These include · Nonlinear vibration control · Control of nonlinear systems and synchronization · Experimental dynamics · System identification and SHM · Multibody dynamics