Mathematical Problems in Engineering
Volume 2005 (2005), Issue 4, Pages 411-424
doi:10.1155/MPE.2005.411
Dynamic stability of functionally graded plate under
in-plane compression
Warsaw University of Technology, Narbutta 84, Warszawa 02-524, Poland
Received 2 March 2004
Copyright © 2005 Andrzej Tylikowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Functionally graded materials have gained considerable attention
in the high-temperature applications. A study of parametric
vibrations of functionally graded plates subjected to in-plane
time-dependent forces is presented. Moderately large deflection
equations taking into account a coupling of in-plane and
transverse motions are used. Material properties are graded in the
thickness direction of the plate according to volume fraction
power law distribution. An oscillating temperature causes
generation of in-plane time-dependent forces destabilizing the
plane state of the plate equilibrium. The asymptotic stability and
almost-sure asymptotic stability criteria involving a damping
coefficient and loading parameters are derived using Liapunov's
direct method. Effects of power law exponent on the stability
domains are studied.