Integral equations and model reduction for fast computation of nonlinear periodic response

Gergely Buza, George Haller, Shobhit Jain*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


We propose a reformulation for a recent integral equations approach to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation results in additional speed-up and better convergence. We show that the solutions of the reformulated equations are in one-to-one correspondence with those of the original integral equations and derive conditions under which a collocation-type approximation converges to the exact solution in the reformulated setting. Furthermore, we observe that model reduction using a selected set of vibration modes of the linearized system substantially enhances the computational performance. Finally, we discuss an open-source implementation of this approach and demonstrate the gains in computational performance using three examples that also include nonlinear finite-element models.

Original languageEnglish
Pages (from-to)4637-4659
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number17
Publication statusPublished - 2021
Externally publishedYes


The authors are thankful to one of the anonymous reviewers of this work for catching significant typos and for providing suggestions that improved this work.


  • integral equations
  • model order reduction
  • nonlinear oscillations
  • periodic response
  • structural dynamics


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