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 incorporated using the linear equations of piezothermoelasticity. Inclusion of temperature and electric potential as state variables along with mechanical displacement permits a unified representation of multiple fields coupling in finite element formulations. A two noded 3-D beam element is derived using first order shear deformation theory to model direct and coupled effects. Eigenstructure assignment technique using output feedback is employed in the controller design, which is subsequently adopted to actively control the first three modes of a cantilever PZT/Steel/PZT beam. The desired eigenfrequencies are placed exactly and the tip motion of the beam is significantly reduced by shaping the eigenvectors of the closed-loop system. Control spillover effect is minimized by optimally selecting the actuator/sensor locations and optimizing the damping factors of the desired closed-loop eigenvalues.