Harmonic Balance for Nonlinear Vibration Problems

  • Malte Krack
  • Johann Gross

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Malte Krack, Johann Gross
    Pages 1-10
  3. Malte Krack, Johann Gross
    Pages 11-46
  4. Malte Krack, Johann Gross
    Pages 47-79
  5. Malte Krack, Johann Gross
    Pages 81-103
  6. Malte Krack, Johann Gross
    Pages 105-130
  7. Back Matter
    Pages 131-159

About this book


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.


structural dynamics mechanical vibrations oscillations nonlinearity simulation numerical path continuation Fourier methods

Authors and affiliations

  • Malte Krack
    • 1
  • Johann Gross
    • 2
  1. 1.University of StuttgartStuttgartGermany
  2. 2.University of StuttgartStuttgartGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-030-14022-9
  • Online ISBN 978-3-030-14023-6
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site