Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances

DOI10.1007/s11071-013-1057-7zbMath1281.74012OpenAlexW2058976306MaRDI QIDQ2436159

Cyril Touzé, Simon Benacchio, Mélodie Monteil, Olivier Thomas

Publication date: 21 February 2014

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-013-1057-7

zbMATH Keywords

nonlinear oscillationsinternal resonancemultiple scales

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Parametric resonances for nonlinear problems in mechanics (70K28)

Related Items (6)

Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification ⋮ Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices ⋮ Nonlinear normal modes of a shallow arch with elastic constraints for two-to-one internal resonances ⋮ Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS ⋮ Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study ⋮ A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems

Uses Software

• ManLab

Cites Work

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• Nonlinear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance
• On the nature of turbulence
• Averaging methods in nonlinear dynamical systems
• A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells

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