Structural Control of Piezoelectric Laminated Beams under Thermal Load

Abstract

The dynamic analysis and the active vibration control of piezoelectric laminated beams under thermal load are presented. The beam is modeled using two noded finite elements with four mechanical and a variable number of electric potential degrees of freedom at each node. In the thickness direction, the thermal and the electric fields are approximated as piecewise linear across an arbitrary number of sublayers in a layer. Cubic Hermite interpolation is used for the deflection and electric potentials at the sublayers and linear interpolation is used for the axial displacement and the shear rotation. The thermal field is computed using a consistent six-noded thermal finite element with a quadratic interpolation along longitudinal direction and a linear interpolation along thickness direction. The temperature distribution and undamped natural frequencies are obtained for composite and sandwich beam under cantilever and clamped-clamped boundary conditions and compared with 2D-FE Abaqus results. The finite element equations derived are converted into modal model to represent them in the state space form. This model is then reduced using Hankel norm for designing the LQG controller. Optimal control technique is used to control the vibration of the beam. The designed LQG controller controls the tip deflection of composite and sandwich cantilever beams and midpoint deflection of clamped-clamped beams.