Vibration and Parametric Instability of Functionally Graded Material Plates

Ramu I^1, and Mohanty SC¹

¹Department of Mechanical Engineering, NIT, Rourkela, India

Cite this paper:
Ramu I and Mohanty SC. Vibration and Parametric Instability of Functionally Graded Material Plates. Journal of Mechanical Design and Vibration. 2014; 2(4):102-110. doi: 10.12691/jmdv-2-4-5

Abstract

The present work aims the vibration and parametric instability of functionally graded material rectangular plates with simply supported boundary condition, subjected to a biaxial in-plane periodic loading. First order shear deformation theory is used for theoretical formulation of FGM plates. The properties of the functionally graded material plates are assumed to vary along the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. Hamilton’s principle is employed to convert the governing equations into a linear system of Mathieu–Hill equations from which the boundary of stable and unstable regions are determined by using Floquet’s theory on the parameter space. Natural frequency and buckling analysis are also discussed. Numerical results are presented in both dimensionless parameters and graphical forms for FGM plates made of steel and alumina. The influences of various parameters such as index value, aspect ratio on the buckling load and natural frequencies are examined. Power law index value and aspect ratio effects on the dynamic stability regions also studied in detail.

Keywords:
free vibrations critical buckling load functionally graded material plates finite element method instability regions

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