Investigation of Subcombination Internal Resonances in Cantilever Beams | Zendy

Haider N. Arafat | Zendy; Ali H. Nayfeh | Zendy

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Investigation of Subcombination Internal Resonances in Cantilever Beams

Author(s) -

Haider N. Arafat,

Ali H. Nayfeh

Publication year - 1998

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/1998/649527

Subject(s) - quasiperiodic function , cantilever , multiple scale analysis , amplitude , inertia , physics , mode (computer interface) , nonlinear system , work (physics) , equations of motion , classical mechanics , resonance (particle physics) , excited state , mechanics , excitation , differential equation , optics , quantum mechanics , engineering , condensed matter physics , structural engineering , computer science , operating system

Activation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. Frequency- and force-response curves are generated for the case ω ≈ ω4 ≈ 1/2(ω2 + ω5). There are two possible responses: single-mode and three-mode responses. The single-mode periodic response is found to undergo supercritical and subcritical pitchfork bifurcations, which result in three-mode interactions. In the case of three-mode responses, there are conditions where the low-frequency mode dominates the response, resulting in high-amplitude quasiperiodic oscillations

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