Title page for ETD etd-2212152639761151


Type of Document Dissertation
Author Liang, Xiaoqing
URN etd-2212152639761151
Title Dynamic Response of Linear/Nonlinear Laminated Structures Containing Piezoelectric Laminas
Degree PhD
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Inman, Daniel J.
Librescu, Liviu
Meirovitch, Leonard
Sun, Shu-Ming
Batra, Romesh C. Committee Chair
Keywords
  • finite element
  • laminated composite structures
  • linear elasticity
  • nonlinear piezoelectric materials
Date of Defense 1997-03-17
Availability unrestricted
Abstract
The three-dimensional linear theory of

piezo-elasticity is used to analyse steady state

vibrations of a simply supported rectangular

laminated composite plate with piezoelectric

(PZT) actuator and sensor patches either

embedded in it or bonded to the its surfaces. It

is assumed that different layers are perfectly

bonded to each other. The method of Fourier

series is used to find an analytical solution of

the problem. The analytical solution is then

applied to study the shape control of a steadily

vibrating composite plate by exciting different

regions of a PZT actuator. Numerical results

for a thin and a thick plate containing one

embedded actuator layer and one embedded

sensor layer are presented. For the former

case, the optimum location of the centroid of

the excited rectangular region that will require

minimum voltage to control the out-of-plane

displacements is determined. Keeping the

location of the centroid and the shape of the

excited region fixed, we ascertain the voltage

required as a function of the length of its

diagonal to nullify the deflections of the plate.

The maximum shear stress at the interface

between the sensor and the lamina is found to

be lower than that between the actuator and

the lamina. The point of maximum output

voltage from the sensor coincides with that of

its peak out-of-plane displacement. The

variations of displacement and stress

components through the thickness for the thin

and thick plates are similar.

The transient finite deformations of a

neo-Hookean beam or plate with PZT patches

bonded to its upper and lower surfaces are

simulated by the finite element method. The

constitutive relation for the piezoelectric

material is taken to be linear in the

Green-Lagrange strain tensor but quadratic in

the driving voltage. A code using 8-noded

brick elements has been developed and

validated by comparing computed results with

either analytical solutions or experimental

observations. The code is then used to study

flexural waves generated by PZT actuators

and propagating through a cantilever beam

both with and without a defect in it. The

computed results are compared with test

observations and with the published results for

the linear elastic beam. The effects of both

geometrical and material nonlinearities are

discussed. A simple feedback control

algorithm is shown to annul the motion of a

neo-Hookean plate subjected to an impulsive

load.

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