# Effect of Functionally Graded Material on the Dynamic Stability of Three-Layered Annular Plates

## TL;DR

This paper studies how functionally graded materials affect the dynamic stability of three-layered annular plates under in-plane forces.

## Contribution

The study introduces a detailed analysis of dynamic stability using functionally graded materials in annular plates.

## Key findings

- Modeling with appropriate material functions significantly affects dynamic stability.
- Critical parameters like load and deflection are influenced by material gradation.
- Finite difference and finite element methods yield consistent results.

## Abstract

This study considers the dynamic stability of a three-layered annular plate, whose facings are made of functionally graded material in the radial direction. The plate is subjected to linearly increasing in-plane forces applied at either the inner or outer edge. The effect of the heterogeneity of the plate-facing material on the dynamic response is analyzed in detail. The main parameters defining the stability state—such as critical dynamic load, critical time, maximum deflection, and buckling mode—are specifically evaluated. The problem is analyzed using two approximation methods: the finite difference method and the finite element method. Numerical calculations were carried out using two approaches: the author’s program following analytical calculations, and the ABAQUS system. The results show the importance of modeling the plate with an appropriate material function describing the radial gradation, which significantly affects the plate’s dynamic stability response and critical parameters.