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On the Use of the Proper Generalised Decomposition for Solving Nonlinear Vibration Problems

[+] Author Affiliations
Aurelien Grolet, Fabrice Thouverez

Ecole Centrale de Lyon, Ecully, France

Paper No. IMECE2012-87538, pp. 913-920; 8 pages
doi:10.1115/IMECE2012-87538
From:
  • 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

abstract

This paper presents the use of the so called Proper Generalized Decomposition method (PGD) for solving nonlinear vibration problems. PGD is often presented as an a priori reduction technique meaning that the reduction basis for expressing the solution is computed during the computation of the solution itself. In this paper, the PGD is applied in addition with the Harmonic Balance Method (HBM) in order to find periodic solutions of nonlinear dynamic systems. Several algorithms are presented in order to compute nonlinear normal modes and forced solutions. Application is carried out on systems containing geometrical nonlinearity and/or friction damping. We show that the PGD is able to compute a good approximation of the solutions event with a projection basis of small size. Results are compared with a Proper Orthogonal Decomposition (POD) method showing that the PGD can sometimes provide an optimal reduction basis relative to the number of basis components.

Copyright © 2012 by ASME

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