(University of Dschang, Cameroon)(2) G. Serges Mbouna Ngueuteu
(University of Yaounde I, Cameroon)*corresponding author
AbstractNonlinear analysis of a forced geometrically nonlinear Hinged-Clamped beam involving three modes interactions with internal resonance and submitted to thermal and mechanical loadings is investigated. Based on the extended Hamilton’s principle, the PDEs governing the thermoelastic vibration of planar motion is derived. Galerkin’s orthogonalization method is used to reduce the governing PDEs of motion into a set of nonlinear non-autonomous ordinary differential equations. The system is solved for the three modes involved by the use of the multiple scales method for amplitudes and phases. For steady states responses, the Newton-Raphson shooting technique is used to solve the three systems of six parametric nonlinear algebraic equations obtained. Results are presented in terms of influences of temperature variations on the response amplitudes of different substructures when each of the modes is excited. It is observed for all substructures and independent of the mode excited a shift within the frequency axis of the temperature influenced amplitude response curves on either side of the temperature free-response curve. Moreover, it is found that thermal loads diversely influence the interacting substructures. Depending on the directly excited mode, higher oscillation amplitudes are found in some substructures under negative temperature difference, while it is observed in others under positive temperature change and in some others for temperature free-response curves.
KeywordsThermal loadings; Nonlinear vibrations; Multimodal interactions; Internal resonance; Frequency response curves
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DOIhttps://doi.org/10.31763/ijrcs.v1i3.422 |
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