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Multi-Point Multi-Harmonic Collocation With Continuation to Compute Branches of Nonlinear Modes of Structural Systems

[+] Author Affiliations
Sean J. Kelly, Matthew S. Allen, Hamid Ardeh

University of Wisconsin - Madison, Madison, WI

Paper No. DETC2015-47333, pp. V006T10A055; 10 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME


Fast numerical approaches have recently been proposed to compute the undamped nonlinear normal modes (NNMs) of discrete and structural systems, and these have enabled remarkable insights into the nonlinear behavior of more complicated systems than are tractable analytically. Ardeh et al. recently proposed the multi-point, multi-harmonic collocation (MMC) method, which finds a truncated harmonic description of a structure’s NNMs. The MMC algorithm resembles harmonic balance but doesn’t require any analytical pre-processing nor the computational expense of the alternating time-frequency method. In a previous work this method showed significantly faster performance than the shooting method and it also allows the possibility of truncating the description of the NNM to avoid having to compute every internal resonance. This work presents a pseudo-arc length continuation version of the MMC algorithm which can compute a branch of NNMs and compares its performance with the shooting/pseudo-arc length continuation algorithm presented by Peeters and Kerschen in 2009. The algorithms are compared for two systems, a two degree-of-freedom (DOF) spring-mass system and a 10-DOF model of a simply-supported beam.

Copyright © 2015 by ASME



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