On the effects of a beam-like piezoelectric passive controller on the linear stability of the visco-elastic Beck's beam

The linear stability of the visco-elastic Beck's beam is investigated in this paper. The mechanical system is equipped with a piezoelectric distributed controller, whose governing equation of motion in linear dynamics resembles that of the beam, in except for the second-order spatial derivative term related to the follower force. Suitable passive control strategies are explored with the aim to increase the Hopf bifurcation critical load, triggered by the presence of the follower force in the mechanical sub-system. The equations of motion of the resultant Piezo-Electro-Mechanical (PEM) system are derived via a variational approach and discretized through the Galerkin method. The linear stability analysis of the PEM system is carried out by solving the descending eigenvalue problem. In this framework, parametric investigations are developed in order to investigate the effects of the electrical parameters on the stability of the system.