Harmonic Balance for Nonlinear Vibration Problems

✍ Scribed by Malte Krack, Johann Gross

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 167
• Series: Mathematical Engineering
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Introduction (Malte Krack, Johann Gross)....Pages 1-10
Theory of Harmonic Balance (Malte Krack, Johann Gross)....Pages 11-46
Application to Mechanical Systems (Malte Krack, Johann Gross)....Pages 47-79
Solving the Harmonic Balance Equations (Malte Krack, Johann Gross)....Pages 81-103
Solved Exercises and Homework Problems (Malte Krack, Johann Gross)....Pages 105-130
Back Matter ....Pages 131-159

✦ Subjects

Engineering; Engineering Mathematics; Fourier Analysis; Vibration, Dynamical Systems, Control