Development of Isoparametric, Degenerate Constrained Layer Element
for Plate and Shell Structures
AIAA JOURNAL, 39 (10):
1997 -- 2005 (October 2001)Abstract
An isoparametric, degenerate element for constrained layer damping
treatments is presented. The element is valid for either plate or
shell structures. The element is an 18-node degenerate element with
nine nodes located on the base shell (or plate) structure and nine
nodes on the constraining layer. Each node has ? ve degrees of freedom:
translations in x, y, and z and bending rotationsВ® and ВЇ about
the midsurface where the node is located. The displacement ? eld
of the viscoelastic layer is interpolated linearly from the nodal
displacements; therefore, the viscoelastic layer allows both shear
and normal deformations. The base shell (or plate) structure and
the constraining layer can be linearly elastic or piezoelectric for
passive or active applications.The viscoelastic layer is assumed
to be linearly viscoelastic. The equation of motion is derived through
use of the principle of virtual work.
For thin plate structures, numerical results show that the isoparametric
element can predict natural frequencies, loss factors, andmechanical
impedances that are as accurate as NASTRAN with substantially fewer
elements. For thin shell structures, locking and spurious modes need
to be resolved to yield reasonable results.