Mathematical Problems in Engineering
Volume 2005 (2005), Issue 4, Pages 411-424

Dynamic stability of functionally graded plate under in-plane compression

Andrzej Tylikowski

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.


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.