Piezothermoelastic modeling and active vibration control of laminated composite beams

A generalized piezothermoelastic finite element formulation of a laminated beam with embedded piezoelectric material as distributed actuators/sensors is presented. Electromechanical and electrothermal couplings are incorporat ed using the linear equations of piezothermoelasticity. Inclusion of temper ature and electric potential as state variables along with mechanical displ acement permits a unified representation of multiple fields coupling in fin ite element formulations. A two noded 3-D beam element is derived using fir st order shear deformation theory to model direct and coupled effects. Eige nstructure assignment technique using output feedback is employed in the co ntroller design, which is subsequently adopted to actively control the firs t three modes of a cantilever PZT/Steel/PZT beam. The desired eigenfrequenc ies are placed exactly and the tip motion of the beam is significantly redu ced by shaping the eigenvectors of the closed-loop system. Control spillove r effect is minimized by optimally selecting the actuator/sensor locations and optimizing the damping factors of the desired closed-loop eigenvalues.