Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

Alessandra Vizzaccaro, Andrea Opreni, Loic Salles, Attilio Frangi, Cyril Touzé

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.

Original languageEnglish
Title of host publicationNonlinear Structures and Systems, Volume 1 - Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022
EditorsMatthew R.W. Brake, Ludovic Renson, Robert J. Kuether, Paolo Tiso
PublisherSpringer
Pages233-236
Number of pages4
ISBN (Print)9783031040856
DOIs
Publication statusPublished - 2023
Event40th IMAC, A Conference and Exposition on Structural Dynamics, 2022 - Orlando, United States
Duration: 7 Feb 202210 Feb 2022

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Conference

Conference40th IMAC, A Conference and Exposition on Structural Dynamics, 2022
Country/TerritoryUnited States
CityOrlando
Period7/02/2210/02/22

Keywords

  • Direct parametrisation
  • Invariant manifold
  • Large-scale FE models
  • Reduced-order modelling

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