Active Vibration Suppression of Piezoelectric Laminated Beam based on Efficient Finite Element Model using LQG Controller

摘要

This paper presents an efficient finite element model for the active vibration suppression of smart laminated beam with different end conditions. Piezoelectric layers are used as actuation and sensing elements. The FE model is based on an efficient layerwise theory with two noded beam element having four mechanical and a variable number of electric degrees of freedom at each node. Cubic Hermite interpolation is used for the deflection & electric potentials and linear interpolation is used for the axial displacement & the shear rotation. Un-damped natural frequencies and the corresponding mode shapes are obtained by solving the Eigen Value problem using Subspace iteration method for various end conditions. The finite element equations derived are converted in modal model to represent them in the state space form. LQG controller is designed for controlling the lateral vibrations of the beam which is based on the optimal control technique. The control model assumes that the upper layer acts as sensor and the bottom layer as actuator, and the signal generated through is used as a feedback reference in the closed loop control system. The results are presented for the Composite and Sandwich Beams with Cantilever and simply supported end conditions. The 1D-FE results are compared with the 2D-FE results, obtained using ABAQUS. The results demonstrate the accuracy and efficiency of the present approach in the vibration control of piezoelectric laminated beam.