Finite element analysis of actively controlled smart plate with patched actuators and sensors

The active vibration control of smart plate equipped with patched piezoelectric sensors and actuators is presented in this study. An equivalent single layer third order shear deformation theory is employed to model the kinematics of the plate and to obtain the shear strains. The governing equations of motion are derived using extended Hamilton's principle. Linear variation of electric potential across the piezoelectric layers in thickness direction is considered. The electrical variable is discretized by Lagrange interpolation function considering two-noded line element. Undamped natural frequencies and the corresponding mode shapes are obtained by solving the eigen value problem with and without electromechanical coupling. The finite element model in nodal variables are transformed into modal model and then recast into state space. The dynamic model is reduced for further analysis using Hankel norm for designing the controller. The optimal control technique is used to control the vibration of the plate