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.

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators / Papangelo, A.; Fontanela, F.; Grolet, A.; Ciavarella, M.; Hoffmann, N.. - In: JOURNAL OF SOUND AND VIBRATION. - ISSN 0022-460X. - STAMPA. - 440:(2019), pp. 202-211. [10.1016/j.jsv.2018.10.028]

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Papangelo A.;Ciavarella M.;
2019-01-01

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.
2019
Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators / Papangelo, A.; Fontanela, F.; Grolet, A.; Ciavarella, M.; Hoffmann, N.. - In: JOURNAL OF SOUND AND VIBRATION. - ISSN 0022-460X. - STAMPA. - 440:(2019), pp. 202-211. [10.1016/j.jsv.2018.10.028]
File in questo prodotto:
File Dimensione Formato  
Duffing with DOI.pdf

accesso aperto

Descrizione: Submitted version
Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 848.79 kB
Formato Adobe PDF
848.79 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/175770
Citazioni
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 27
social impact