## Enhancement of the Dynamic Buckling Load and Analysis of Active Constrained Layer Damping with Extension and Shear Mode Piezoceramic Actuators

##### Abstract

We consider geometric and material nonlinearities when studying numerically, by
the 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.

##### Collections

- Doctoral Dissertations [12751]

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