, Volume 49, Issue 8, pp 1901–1916 | Cite as

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

  • L. Renson
  • G. Deliége
  • G. Kerschen
Nonlinear Dynamics and Control of Composites for Smart Engi design


This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.


Nonlinear normal modes Invariant manifolds Nonconservative systems Modal analysis Finite element method 



The author L. Renson would like to acknowledge the Belgian National Fund for Scientific Research (FRIA fellowship) for its financial support.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Space Structures and Systems Laboratory, Aerospace and Mechanical Engineering DepartmentUniversity of LiègeLiègeBelgium
  2. 2.Computational Nonlinear Mechanics, Aerospace and Mechanical Engineering DepartmentUniversity of LiègeLiègeBelgium

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