Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
Article dans une revue avec comité de lecture
JournalJournal of Sound and Vibration
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 localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.
Files in this item
- post refering version
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 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 ...
Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations Article dans une revue avec comité de lectureWOIWODE, Lukas; BALAJI, Nidish Narayanaa; KAPPAUF, Jonas; TUBITA, Fabia; GUILLOT, Louis; VERGEZ, Christophe; COCHELIN, Bruno; GROLET, Aurélien; KRACK, Malte (Springer International Publishing, 2019)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 ...
Article dans une revue avec comité de lectureHOFFMANN, N.; FONTANELA, Francesco; GROLET, Aurélien; SALLES, Loïc; CHABCHOUB, Amin; CHAMPNEYS, Alan; PATSIAS, Sophoclis; HOFFMANN, Norbert (Elsevier, 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 ...
Article dans une revue avec comité de lectureMAHE, V.; RENAULT, Alexandre; GROLET, Aurélien; MAHE, Hervé; THOMAS, Olivier (Elsevier BV, 2022-09)Rotating machines are often subjected to fluctuating torques, leading to vibrations of the rotor and finally to premature fatigue and noise pollution. This work addresses a new design of centrifugal pendulum vibration ...
On the dynamic stability and efficiency of centrifugal pendulum vibration absorbers with rotating pendulums Article dans une revue avec comité de lectureMAHÉ, V.; RENAULT, Alexandre; GROLET, Aurélien; MAHÉ, Hervé; THOMAS, Olivier (Elsevier BV, 2022-10)The automotive industry uses centrifugal pendulum vibration absorbers (CPVAs) to reduce vibrations of the transmission system. These passive devices are made of several masses oscillating along a given path relative to a ...