Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2019

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

L. Woivode
  • Fonction : Auteur
N.N. Balaji
  • Fonction : Auteur
F. Tubita
  • Fonction : Auteur
Bruno Cochelin

Résumé

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.
Fichier principal
Vignette du fichier
37i_4495_Extended_Abstract.pdf (252.33 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02310523 , version 1 (03-01-2020)

Licence

Paternité

Identifiants

Citer

L. Woivode, N.N. Balaji, Johannes Kappauf, F. Tubita, Louis Guillot, et al.. Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations. 37th IMAC, A Conference and Exposition on Structural Dynamics 2019, Jan 2019, Orlando, United States. ⟨10.1007/978-3-030-12391-8_34⟩. ⟨hal-02310523⟩
150 Consultations
146 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More