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Dynamic Analysis of Structures With Nonlinear Bolted Joints by Using an Adaptive Harmonic Balance Method

[+] Author Affiliations
Vincent Jaumouillé

EADS Innovation Works, Suresnes, France

Jean-Jacques Sinou

Ecole Centrale de Lyon, Ecully, France

Paper No. DETC2009-87162, pp. 355-364; 10 pages
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4898-2 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME


Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute non linear response functions in the frequency domain. The basic idea is to develop the response as a Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus the aim of this study is to develop an adaptive HBM which appreciates numerically the contribution of each harmonic on the dynamic response. For a given precision, the number of retained harmonics is adapted by an algorithm which integrates a numerical criterion based on an approximate strain energy. The application case is an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. Condensation and continuation methods are used to accelerate calculation. Adaptive HBM shows that, for a given value of the criterion, the number of harmonics may increase on resonances indicating that non linear effects are predominant.

Copyright © 2009 by ASME



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