Comparison of two algorithms for Harmonic Balance and path continuation. (February 2020)

• Record Type: Journal Article
• Authors: Woiwode, Lukas; Balaji, Nidish Narayanaa; Kappauf, Jonas; Tubita, Fabia; Guillot, Louis; Vergez, Christophe; Cochelin, Bruno; Grolet, Aurélien; Krack, Malte
• Is Part Of: Mechanical systems and signal processing. Volume 136(2020)
• Publication Date: 2020-02
• Subjects: Harmonic Balance Method -- Non-linear vibration -- Periodic solution -- Continuation method -- Friction damping -- Geometric nonlinearity; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.106503
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: A1: Alternating Frequency-Time scheme, Predictor-Corrector Continuation (AFT-PreCo). A2: classical Harmonic Balance, Asymptotic Numerical Method (cHB-ANM). Benefits cHB-ANM: continuous repr. of solution path, robust step length control. Benefits AFT-PreCo: suitable for non-smooth problems, computationally efficient. Abstract: In this work we apply and compare two algorithms for setting up Harmonic Balance equations and numerical continuation of the solution path for harmonically driven mechanical systems. The first algorithm relies on a predictor-corrector scheme and an Alternating Frequency-Time approach (AFT-PreCo). The second algorithm relies on a high-order Taylor series expansion of the solution path (asymptotic numerical method) and classical Harmonic Balance formulated entirely in the frequency domain (cHB-ANM). We conclude that the cHB-ANM is suited for smooth nonlinearities, for instance geometrically nonlinear finite element models. Here, cHB-ANM avoids aliasing errors and convinces with a numerically robust adjustment of the continuation step length and a continuous representation of the solution path. For non-smooth nonlinearities such as stick-slip friction or unilateral constraints, AFT-PreCo is better suited, and convinces with high numerical robustness and efficiency.