A rod-like piezoelectric controller for the improvement of the visco-elastic Beck's beam linear stability

The linear stability of a cantilever beam subject to a follower force is investigated. A system of distributed piezoelectric devices is attached to the beam with the purpose of improving the dynamic stability of the structure. They are connected to a second-order network and second-order analog electrical circuit. The assembly of the mechanical and piezoelectric subsystems constitutes a coupled Piezo-Electro-Mechanical (PEM) system, whose equations of motion, derived within a variational approach, are discretized via the Galerkin weighted residual method and the stability of the trivial equilibrium is addressed by numerically solving the associated eigenvalue problem. A sensitivity analysis, carried out on a numerical ground, is thus conducted on a wide range of the electrical parameters to investigate the effectiveness of the proposed controller.