Static and dynamic analysis of laminated composite plates with integrated piezoelectrics

Abstract

A Finite Element model based on First-order Shear Deformation Theory is developed for the static shape control and vibration control of la minated composite plates integrated with piezoelectric sensors and actuators. A nine-node isoparametric rectangular element with 45 degrees of freedom for the generalized displacements and 2 electrical degrees of freedom is implemented for the static and dynamic analyses. The model is validated by comparing with existing results documented in the literature. Some numerical results are presented. It is concluded that the shape of the piezoelectric laminated composite plates can reach the desired shape through passive control or active control. The influence of stacking sequence of composite plates and position of piezoelectric layers and sensors/actuators patches on the response of the piezoelectric composite plates is evaluated.

Optimal Placement and Active Vibration Control of Composite Plates Integrated Piezoelectric Sensor/Actuator Pairs

“…The constitutive relations for the piezoelectric composite materials of k th layer are given by [7,8]:…”

“…The equations of motion for the laminated composite plate with integrated piezoelectric sensors and actuators can be derived using the Hamilton's principle [7,10,8]:…”

Dynamic Stability Analysis of Laminated Composite Plates With Piezoelectric Layers

“…Based on the first-order shear deformation theory, the displacement fields at any point in the plate are [11,12] u (x, y, z, t) = u 0 (x, y, t) + zθ y (x, y, t) , v (x, y, z, t) = v 0 (x, y, t) − zθ x (x, y, t) , w (x, y, z, t) = w 0 (x, y, t) , (1) where u, v and w are the displacements of a general point (x, y, z) in the laminate along x, y and z directions, respectively. u 0 , v 0 , w 0 , θ x and θ y are the displacements and rotations of a midplane transverse normal about the y-and x-axes respectively.…”

“…The equation of bending vibrations with out-of-plane loads is [1,3,12]; {φ} is the overall electric potential vector; {F (t)} is the in-plane load vector, {R} is the normal load vector, {Q el } is the vector containing the nodal charges and in-balance charges. The element coefficient matrices are [8,11,15] [M …”

Dynamic stability analysis of laminated composite plates with piezoelectric layers

“…Based on the first-order shear deformation theory, the displacement fields at any point in the plate are [11,12] u (x, y, z, t) = u 0 (x, y, t)…”