Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations
Article dans une revue 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.
A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems Article dans une revue avec comité de lectureGUILLOT, Louis; LAZARUS, Arnaud; THOMAS, Olivier; VERGEZ, Christophe; COCHELIN, Bruno (Elsevier BV, 2020-09)Since the founding theory established by G. Floquet more than a hundred years ago, computing the stability of periodic solutions has given rise to various numerical methods, mostly depending on the way the periodic solutions ...
Article dans une revue avec comité de lectureCOGNET, Bruno; PERNOT, Jean Philippe; RIVEST, Louis; DANJOU, Christophe (Inderscience Publishers, 2021-11-29)The fourth industrial revolution is forcing companies to define their digital strategy, making it imperative that they assess their digital maturity as a basis for improvements. As a result, a variety of maturity models ...
Article dans une revue avec comité de lectureDEBERTRAND, Louis; FAYOLLE, Bruno; RÉGNIER, Gilles; PARIS, Christophe; CINQUIN, Jacques; BRULÉ, Benoît (Wiley, 2019)Since poly(ether ketone ketone) (PEKK) is a good candidate as a matrix for composite structural parts, the mechanical properties of PEKK copolymers prepared from diphenyl ether, terephthalic acid (T), and isophthalic acid ...
Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods Article dans une revue avec comité de lectureFONTANELA, Filipe; GROLET, Aurélien; SALLES, Loïc; HOFFMANN, Norbert (Elsevier, 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 Article dans une revue avec comité de lecturePAPANGELO, Antonio; FONTANELA, Filipe; GROLET, Aurélien; CIAVARELLA, Michele; HOFFMANN, Norbert (Elsevier, 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 ...