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Smooth Decomposition Analysis and Order Reduction of Nonlinear Mechanical Systems Under Random Excitation

[+] Author Affiliations
Sergio Bellizzi

Aix-Marseille Université, Marseille, France

Rubens Sampaio

Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

Paper No. IMECE2012-87496, pp. 905-911; 7 pages
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME


This paper presents a possible alternative procedure to the Karhunen-Loève approach to construct reduced order models which capture accurately the dynamics of nonlinear discrete mechanical systems under random excitation. This procedure combines the Smooth Decomposition method and the Petrov-Galerkin approximation. The smooth decomposition method is a multivariate-data analysis method characterizing coherent structures (the smooth modes) as the eigenvectors of the generalized eigenproblem defined from the covariance matrix of the displacement field and the covariance matrix of the velocity field. The Petrov-Galerkin approximation is used to project the dynamics in a subspace generated by a set of the smooth modes. The Petrov-Galerkin approximation preserves the second order structure of the equations of motion. The procedure is considered for a mechanical system including a strongly nonlinear end-attachment. The efficiency of the approach is analyzed comparing the power spectral density functions of the reduced-order model and of the original system.

Copyright © 2012 by ASME



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