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

Abstract

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.

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

“…The structure analyzed by Yasin et al [53] (see Figure 3) is a cantilevered aluminum plate with eight piezoelectric patches, four on the top surface and symmetrically four on the bottom ones. The plate is clamped on one short edge and free on the other three sides.…”

“…This case includes only the pure structural stiffness of the PZT patches and the modal analysis, made by Yasin et al [53], involves the solution of the simplified following eigenvalue problem:…”

“…The governing equations for the free-vibration analysis of plate structures are derived from the PVD, in order to apply the FE method. An isotropic plate with piezoelectric patches is analyzed, and the results, obtained with the different models contained in CUF, are compared with the higher-order type solution given in the literature by Yasin et al [53].…”

Vibration control of two-connected piezoelectric flexible plate using nonlinear algorithm and T-S fuzzy controller

“…Besides analytical methods, the finite element modeling method for smart plate structures was investigated by some researchers (Chandrashekhara and Bhatia, 1993;Lam et al, 1997;Yasin et al, 2010). Lam et al (1997) provided a finite element model for a composite plate bonded with distributed piezoelectric sensors and actuators.…”

“…Chandrashekhara and Bhatia (1993) developed a piezoelectric finite element model using the first-order shear deformation theory in conjunction with linear piezoelectric theory. Yasin et al (2010) used extended Hamilton's principle to build the model of smart plate equipped with patched piezoelectric sensors and actuators. Linear variation of electric potential across the piezoelectric layers in thickness direction was also considered.…”