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

• 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.

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.