Large Amplitude Free Flexural Vibrations of Functionally Graded Plates

Abstract

The nonlinear formulation developed based on von Karman’s assumptions is employed to study the large free flexural vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature distribution is uniform over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. The nonlinear governing equations obtained using Lagrange’s equations of motion are solved using finite element procedure coupled with the direct iteration technique. The variation of nonlinear frequency ratio with amplitude is highlighted considering various parameters such as gradient index, temperature, thickness and aspect ratios, skew angle and boundary condition. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The results obtained here reveal that the temperature field and gradient index have significant effect on the large amplitude free flexural vibration of the functionally graded plate.