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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cochelin, B., Vergez, C.: A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions. J. Sound Vib. 324(1–2), 243–262 (2009)
Guillot, L., Cochelin, B., Vergez, C.: A generic and efficient Taylor series based continuation method using a quadratic recast of smooth nonlinear systems, Numerical Methods in Engineering, pp 1–20, (2018). doi:http://10.1002/nme.6049
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Woiwode, L. et al. (2020). Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations. In: Kerschen, G., Brake, M., Renson, L. (eds) Nonlinear Structures and Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12391-8_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-12391-8_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12390-1
Online ISBN: 978-3-030-12391-8
eBook Packages: EngineeringEngineering (R0)