Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators. (3rd February 2019)

• Record Type: Journal Article
• Authors: Papangelo, A.; Fontanela, F.; Grolet, A.; Ciavarella, M.; Hoffmann, N.
• Is Part Of: Journal of sound and vibration. Volume 440(2019)
• Page Start: 202
• Page End: 211
• Publication Date: 2019-02-03
• Subjects: Nonlinear vibrations -- Nonlinear normal modes -- Multistability -- Localization; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2018.10.028
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: 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.