Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics

J. B. Rutzmoser, D. J. Rixen*, P. Tiso, S. Jain

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

44 Citations (Scopus)


In this paper, a generalization of the quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is obtained by a linearization of the static force with respect to the generalized coordinates, resulting in a shift of the quadratic behavior from the force to the manifold. In this framework, static derivatives emerge as natural extensions to the modal derivatives for displacement fields other than the vibration modes, such as the Krylov subspace vectors. In the nonlinear projection framework employed here, the dynamic problem is projected onto the tangent space of the quadratic manifold, allowing for a much lower number of generalized coordinates compared to linear basis methods. The potential of the quadratic manifold approach is investigated in a numerical study, where several variations of the approach are compared on different examples, giving a clear indication of where the proposed approach is applicable.

Original languageEnglish
Pages (from-to)196-209
Number of pages14
JournalComputers and Structures
Publication statusPublished - 2017
Externally publishedYes


  • Geometric nonlinearity
  • Modal derivatives
  • Model order reduction
  • Quadratic manifold
  • Structural dynamics


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