Type of Document Dissertation Author Geng, Twzen-Shang Author's Email Address tgeng@vt.edu URN etd-05302002-150756 Title Enhancement of the Dynamic Buckling Load and Analysis of Active Constrained Layer Damping with Extension and Shear Mode Piezoceramic Actuators Degree PhD Department Engineering Science and Mechanics Advisory Committee

Advisor Name Title Batra, Romesh C. Committee Chair Hendricks, Scott L. Committee Member Hyer, Michael W. Committee Member Inman, Daniel J. Committee Member Plaut, Raymond H. Committee Member Keywords

- Three-dimensional Deformations
- Piezoceramic Actuators
- Vibration Control
- Buckling Control
- Finite Element Analysis
Date of Defense 2002-04-09 Availability unrestricted AbstractWe consider geometric and material nonlinearities when studying numerically, bythe finite element method, transient three-dimensional electroelastic

deformations of a graphite-epoxy square plate sandwiched between two

piezoceramic (PZT) layers. Points on the four edges of the bottom surface

of the plate are restrained from moving vertically. The two opposite edges

of the plate are loaded

by equal in-plane compressive loads that increase linearly

with time and the other two edges are kept traction free. The plate material

is modeled as orthotropic and neoHookean. For the transversely isotropic

PZT the second Piola-Kirchhoff stress tensor and the electric displacement

are expressed as second degree polynomials in the Green-St. Venant strain

tensor and the electric field. Both direct and converse piezoelectric

effects are accounted for in the PZT. The plate is taken to have buckled

when its centroidal deflection equals three times the plate thickness.

The dynamic buckling load for the plate is found to strongly depend upon the

rate of rise of the applied tractions. With the maximum electric field

limited to

1kV/mm, the buckling load is enhanced by 18.3$\%$ when the PZT elements are

activated. For a peak electric field of 30kV/mm, the buckling load

increased by 58.5$\%$. When more than 60$\%$ of the surface area of the top

and the bottom surfaces of the plate are covered by the PZT layers, then

square PZT elements placed symmetrically about the plate centroid provide

a larger enhancement in the buckling load than rectangular shaped or

cross-shaped PZT elements. An increase in the plate thickness relative

to that of the PZT actuators decreases the effectiveness of

the PZT in enhancing the buckling load for the plate.

The finite element code was modified to also analyze, in time domain, transient

deformations of a viscoelastic material for which the second Piola-Kirchhoff

stress tensor is expressed as a linear functional of the strain history of

the Green-St. Venant strain tensor. It was used to analyze

three-dimensional deformations of a thick laminated plate with layers

made of aluminum, a viscoelastic material and a PZT. The following two

arrangements of layers are considered. In one case a central PZT layer

is surrounded on both sides by viscoelastic layers and aluminum layers

are on the outside surfaces. The PZT is poled in the longitudinal

direction and an electric field is applied in the thickness direction.

Thus shearing deformations of the PZT layer are dominant. In the second

arrangement, the aluminum layer is in the middle and the PZT layers are

on the outside. The poling direction and the electric field are in the

thickness direction; thus its extensional deformations are predominant.

Three indices are used to gauge the damping of motion of plate particles,

and the effectiveness of PZT actuators in enhancing this damping. It is

found that the optimum thickness of the viscoelastic layers for maximum

total energy dissipation is the same for each set-up.

Also, the total thickness of the PZT layers which results in the maximum

value of one of these indices of energy dissipation is the same for the

two set-ups. Both arrangements give the largest value of this index

for a plate of aspect ratio 10.

Buckling behavior of a sandwich plate containing a soft core is

also studied. The effects of the ratio of the elastic moduli

of the outer layers to those of the core, and of the core

thickness on the buckling load are analyzed.

The top and the bottom layers are connected by very stiff blocks on

two opposite edges where in-plane compressive time-dependent tractions

are applied.

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