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

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. •The mechanical behavior of a piezoelectric controlled Ziegler column is investigated.•The linear stability diagram of the controlled system is presented.•The role of the coupling and damping parameters on the Hopf load is discussed.•A numerical investigation of the post-critical behavior is carried out.•The effects of the controller on the amplitude of the limit cycle are presented.