| Description |
1 online resource : illustrations |
| Series |
Mathematical engineering |
|
Mathematical engineering.
|
| Contents |
Intro; Preface; References; Contents; Symbols and Abbreviations; 1 Introduction; 1.1 What Can Harmonic Balance Do?; 1.2 Example: Duffing Oscillator; 1.3 Scope and Outline of This Book; References; 2 Theory of Harmonic Balance; 2.1 Fourier Analysis; 2.2 The Periodic Boundary Value Problem; 2.3 Weighted Residual Approaches; 2.4 Harmonic Balance and Other Fourier Methods; References; 3 Application to Mechanical Systems; 3.1 Range of Utility of Harmonic Balance; 3.2 Harmonic Balance Equations; 3.3 Treatment of Nonlinear Forces; 3.4 Selection of the Harmonic Truncation Order |
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3.5 Why is Harmonic Balance Faster than Numerical Integration?3.6 Stability Analysis; 3.7 Quasi-periodic Oscillations; 3.8 Brief Historical Perspective; 3.9 Current Challenges; References; 4 Solving the Harmonic Balance Equations; 4.1 Problem Statement; 4.2 Solution Strategies; 4.3 Computing a Solution Point Near a Good Initial Guess; 4.4 Computing a Branch of Solution Points; 4.5 Finding a Good Initial Guess; 4.6 Handling of Branching Points and Isolated Branches; References; 5 Solved Exercises and Homework Problems; References; A Topelitz Structure of the Jacobian |
| Summary |
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 |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed March 26, 2019) |
| Subject |
Nonlinear mechanics.
|
|
Vibration -- Mathematical models
|
|
Differential equations, Nonlinear.
|
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SCIENCE -- Mechanics -- General.
|
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SCIENCE -- Mechanics -- Solids.
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Differential equations, Nonlinear
|
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Nonlinear mechanics
|
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Vibration -- Mathematical models
|
| Form |
Electronic book
|
| Author |
Gross, Johann, author
|
| ISBN |
9783030140236 |
|
3030140237 |
|
9783030140243 |
|
3030140245 |
|
9783030140250 |
|
3030140253 |
|
