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Vibrations forcées de structures minces, élastiques, non linéaires

Abstract : this work is devoted to the study of nonlinear vibration of thin structures, by both numerical and experimental approaches. First, we developed a numerical tool to calculate the harmonic forced response of thin structures including geometrical nonlinearities. The Finite Element Method is used to treat the large displacements elastodynamic problem, taking into account a shape default and a prestressed initial state. Periodical solutions are obtained thanks to the Harmonic Balance Method and branches continuation is performed with the Asymptotic Numerical Method. These two methods are implemented in an existent Finite Element software, Eve. At the end, the unknowns, displacements and stresses, are expressed in terms of the amplitude and pulsation of the excitation. This work results in a quite general numerical tool, able to deal with a large range of structures (beams, plates and shells). Typical nonlinear behaviors, such as hysteresis or secondary resonances and bifurcation branches are presented on several instances. Moreover, the response simulated for a weak excitation amplitude, leads to structural nonlinear modes. At the same time, we proceeded with an experimental study. An experimental set-up has been designed and built, to observe the forced response of plates or shells, fitted with a prestress mechanism in order to obtain modal interaction. Previously, we observed nonlinear behaviors on a clamped-clamped beam under harmonic excitation.
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Contributor : Franck Pérignon <>
Submitted on : Friday, November 26, 2004 - 3:40:21 PM
Last modification on : Thursday, January 23, 2020 - 6:22:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:25:40 PM


  • HAL Id : tel-00007535, version 1


Franck Pérignon. Vibrations forcées de structures minces, élastiques, non linéaires. Modélisation et simulation. Université de la Méditerranée - Aix-Marseille II, 2004. Français. ⟨tel-00007535⟩



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