Harmonic Balance for Nonlinear Vibration Problems
Title | Harmonic Balance for Nonlinear Vibration Problems PDF eBook |
Author | Malte Krack |
Publisher | Springer |
Pages | 159 |
Release | 2019-03-23 |
Genre | Technology & Engineering |
ISBN | 3030140237 |
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
Title | Nonlinear Vibration with Control PDF eBook |
Author | David Wagg |
Publisher | Springer Science & Business Media |
Pages | 361 |
Release | 2009-12-03 |
Genre | Technology & Engineering |
ISBN | 9048128374 |
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.
A Filtered High-dimensional Harmonic Balance Method for Problems in Nonlinear Dynamics
Title | A Filtered High-dimensional Harmonic Balance Method for Problems in Nonlinear Dynamics PDF eBook |
Author | Allen Russell LaBryer |
Publisher | |
Pages | 156 |
Release | 2009 |
Genre | Dynamics |
ISBN |
Incremental Harmonic Balance Method for Nonlinear Structural Vibrations
Title | Incremental Harmonic Balance Method for Nonlinear Structural Vibrations PDF eBook |
Author | Sai-ling Lau |
Publisher | |
Pages | 244 |
Release | 1982 |
Genre | Nonlinear theories |
ISBN |
Incremental Harmonic Balance Method for Nonlinear Structural Vibrations
Title | Incremental Harmonic Balance Method for Nonlinear Structural Vibrations PDF eBook |
Author | Sai-Ling Lau |
Publisher | |
Pages | |
Release | 2017-01-27 |
Genre | |
ISBN | 9781374772502 |
On the Analysis of Superharmonic Oscillations
Title | On the Analysis of Superharmonic Oscillations PDF eBook |
Author | J. J. Wu |
Publisher | |
Pages | 10 |
Release | 1992 |
Genre | |
ISBN |
This paper presents an analysis for the superharmonics of a forced nonlinear vibration problem involving small parameters, using a generalized harmonic balance method. A nonlinear ordinary differential equation with several nonlinear terms and a periodic forcing function is considered. For the case of superharmonic oscillations of order 2, the key equations for the obtaining the information on the superharmonics will be derived, including a new, nonlinear ordinary differential equation of a slow varying function compared with the original dependent variable. Using these equations, the steady state solution and its stability behavior can be calculated. Results for a special set of parameters are obtained, including a stable node for the steady state solution and the associated van del Pol plane.
The Behaviour of Nonlinear Vibrating Systems
Title | The Behaviour of Nonlinear Vibrating Systems PDF eBook |
Author | Wanda Szemplinska |
Publisher | Springer Science & Business Media |
Pages | 370 |
Release | 1990-06-30 |
Genre | Technology & Engineering |
ISBN | 9780792303695 |
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.