Stability of parametric vibrations of functionally graded plate

A study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented. The rectangular plate described by geometrically non-linear partial differential equations is studied Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The parametric vibrations or dynamic stability of functionally graded plate are analysed using the direct Liapunov method. Due to a small thickness coupling, and rotary inertia terms are neglected. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. Studies of parametric vibrations of functionally graded shells made up of steel – zirkonia, nickel – SiN and aluminum - TiC are presented. An oscillating temperature causes generation of in-plane time-dependent forces destabilizing the plane state of the plate equilibrium.