Resonances of Nonlinear Mechanical Systems: a Nonlinear Normal Mode Perspective by Loic Salles, July 2021

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Introduction to Harmonic Balance and Continuation Methods Loic Salles July202021
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Resonances of Nonlinear Mechanical Systems: a Nonlinear Normal Mode Perspective

Loic Salles

Imperial College London

July 20, 2021


In the first part of the presentation, the basics of harmonic balance for solving nonlinear vibration problems will be introduced. Definition of Galerkin, Petrov-Galerkin, Collocation, and Spectral methods will be given. The alternating frequency-time procedure will be presented and explained in detail. The second part of the presentation will focus on the continuation methods that permit the path following of parametric response. The concepts of stability and bifurcation will also be introduced, and efficient numerical methods will be shown. Numerical examples will illustrate the proposed methods and an extensive review of past and current researches on the topics will be given to allow the audience to find more information about the presented methods. We will then present the implementation of harmonic balance in finite elements and the challenge linked with it. Finally, we will give a brief overview of the remaining challenges related to those methods and future directions for research.


Loic Salles is a Research Fellow in Rolls-Royce Vibration UTC in the Mechanical Engineering department at Imperial College London. He joined Imperial College in 2012. His research focus in nonlinear vibration and computational methods for large-scale modelling. He works on the development of the in-house harmonic balance code FORSE, which is used by Rolls-Royce for vibration analysis of aircraft engine components.

He obtained his Ph.D. in 2010 conjointly at Ecole Centrale Lyon and Bauman Moscow State Technical University. He graduated as a rocket engineer from BMSTU in 2006 and as a mechanical engineer from Ecole Centrale Lyon in 2006.

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