Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations
TypeArticles dans des revues avec comité de lecture
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.
Files in this item
Showing items related by title, author, creator and subject.
Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods FONTANELA, Filipe; GROLET, Aurélien; SALLES, Loïc; HOFFMANN, Norbert (Elsevier BV, 2019)In this paper we develop a fully numerical approach to compute quasi-periodic vibrations bifurcating from nonlinear periodic states in cyclic and symmetric structures. The focus is on localised oscillations arising from ...
Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators PAPANGELO, Antonio; FONTANELA, Filipe; GROLET, Aurélien; CIAVARELLA, Michele; HOFFMANN, Norbert (Elsevier BV, 2019)Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of ...
HOFFMANN, N.; FONTANELA, Francesco; GROLET, Aurelien; SALLES, Loïc; CHABCHOUB, Amin; CHAMPNEYS, Alan; PATSIAS, Sophoclis; HOFFMANN, Norbert (Elsevier BV, 2019)The emergence of localised vibrations in cyclic and symmetric rotating struc-tures, such as bladed disks of aircraft engines, has challenged engineers in thepast few decades. In the linear regime, localised states ...
On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models GIVOIS, Arthur; GROLET, Aurélien; THOMAS, Olivier; DEÜ, Jean-François (Springer Science and Business Media LLC, 2019)This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is ...
Multiple-correction hybrid k -exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids PONT, Grégoire; PONT, Grégoire; BRENNER, Pierre; BRENNER, Pierre; CINNELLA, Paola; CINNELLA, Paola; MAUGARS, Bruno; MAUGARS, Bruno; ROBINET, Jean-Christophe; ROBINET, Jean-Christophe (Elsevier BVElsevier BV, 2017)A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family ...