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Piezoelectric control of Hopf bifurcations: A non-linear discrete case study

Francesco d'Annibale 1 Giuseppe Rosi 2 Angelo Luongo 3
1 International Research Center on Mathematics and Mechanics of Complex Systems, University of L׳Aquila, 67100 L׳Aquila, Italy
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
3 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
Abstract : Linear and non-linear analyses of a piezoelectric controlled non-linear Ziegler column are carried out in this paper. The aim is to evaluate the effects of a linear piezoelectric element on the Hopf bifurcations of the non-linear mechanical system, triggered by the non-conservative follower force. To this end a linear stability analysis, showing the performances of the controller in shifting forward the critical load of the uncontrolled system, is carried out and the role of the electro-mechanical coupling parameter and of the mechanical damping is investigated. The beneficial effects of the controller on the amplitude of the limit cycle occurring in the post-critical field are also discussed.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01595692
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Submitted on : Tuesday, September 26, 2017 - 10:47:45 PM
Last modification on : Tuesday, October 19, 2021 - 4:09:11 PM

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Francesco d'Annibale, Giuseppe Rosi, Angelo Luongo. Piezoelectric control of Hopf bifurcations: A non-linear discrete case study. International Journal of Non-Linear Mechanics, Elsevier, 2016, 80, pp.160-169. ⟨10.1016/j.ijnonlinmec.2015.09.012⟩. ⟨hal-01595692⟩

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