Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 121, Issue -, Pages 117-134Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2017.05.020
Keywords
Cruciform cross-section; Low torsional stiffness; Nonlinear oscillations; Bifurcations; Instabilities; Multiple internal resonances; Nonlinear interactions
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Funding
- Brazilian research agency FAPERJ [E-26/203.020/2015]
- Brazilian research agency FAPEG
- Brazilian research agency CAPES
- Brazilian research agency CNPq [303321/2013-0]
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The three-dimensional motion of a slender clamped-free beam with a cruciform cross-section of low torsional stiffness, subject to lateral harmonic excitation, is investigated. Special attention is given to the nonlinear oscillations at multiple internal resonances, and to its influence on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on the subject. The nonlinear integro-differential equations describing the flexural-flexural-torsional coupling of the beam are used, together with the Galerkin method, to obtain a minimal (three -degree-of-freedom) reduced order model, whose response is investigated through continuation of the relevant ordinary differential equations. Both inertial and geometric nonlinearities are considered. By varying the stiffness parameters of the beam and using tools of nonlinear dynamics, a complex dynamic behavior is observed around 1:1:1 resonance, where a variety of local bifurcations lead to multiple coexisting solutions which include planar and non planar motions. Notwithstanding the topologically involved portraits of the attractor-basin response, the analysis of system global dynamics may provide hints for safe structural design. (C) 2017 Elsevier Ltd. All rights reserved.
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