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Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations

Article dans une revue avec comité de lecture
Author
WOIWODE, Lukas
63008 University of Stuttgart = Universität Stuttgart
BALAJI, Nidish Narayanaa
54086 Rice University [Houston]
KAPPAUF, Jonas
253513 University of Kassel
TUBITA, Fabia
126765 École Centrale de Lyon [ECL]
GUILLOT, Louis
300415 École Centrale de Marseille [ECM]
VERGEZ, Christophe
300415 École Centrale de Marseille [ECM]
COCHELIN, Bruno
300415 École Centrale de Marseille [ECM]
GROLET, Aurélien
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
KRACK, Malte
63008 University of Stuttgart = Universität Stuttgart

URI
http://hdl.handle.net/10985/16777
DOI
10.1007/978-3-030-12391-8_34
Date
2019
Journal
Nonlinear Structures and Systems. Conference Proceedings of the Society for Experimental Mechanics Series.

Abstract

In this work we apply and compare two numerical path continuation algorithms for solving algebraic equations arising when applying the Harmonic Balance Method to compute periodic regimes of nonlinear dynamical systems. The first algorithm relies on a predictor-corrector scheme and an Alternating Frequency-Time approach. This algorithm can be applied directly also to non-analytic nonlinearities. The second algorithm relies on a high-order Taylor series expansion of the solution path (the so-called Asymptotic Numerical Method) and can be formulated entirely in the frequency domain. The series expansion can be viewed as a high-order predictor equipped with inherent error estimation capabilities, which permits to avoid correction steps. The second algorithm is limited to analytic nonlinearities, and typically additional variables need to be introduced to cast the equation system into a form that permits the efficient computation of the required high-order derivatives. We apply the algorithms to selected vibration problems involving mechanical systems with polynomial stiffness, dry friction and unilateral contact nonlinearities. We assess the influence of the algorithmic parameters of both methods to draw a picture of their differences and similarities. We analyze the computational performance in detail, to identify bottlenecks of the two methods.

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