On the effectiveness of a rod-like distributed piezoelectric controller in preventing the Hopf bifurcation of the visco-elastic Beck’s beam

Abstract The linear stability of a piezo-electro-mechanical (PEM) system subject to follower force is here discussed. mechanical subsystem constituted by visco-elastic cantilever beam, loaded at the free end. It suffers from Hopf bifurcation, whose critical load strongly affected damping, according well-known Ziegler’s paradox. On other hand, electrical consists distributed array piezoelectric patches attached beam and connected properly designed second-order analog circuit, aiming possibly enhancing PEM system. partial differential equations motion are discretized Galerkin method. Linear analysis then carried out numerically solving associated eigenvalue problem, for different significant values parameters. A suitable perturbation method also adopted detect role parameters discuss effectiveness controller.