Abstract

The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.

Highlights

  • 1.1 IntroductionFunctionally Graded Material (FGM) are a class of composites characterised by a change in composition through its volume, resulting in properties that vary spatially throughout the material [1]

  • The beam is assumed to be made of aluminium and the frequency results are compared against classical methods and the Dynamic Stiffness Method (DSM) method

  • The Dynamic Finite Element (DFE) results were compared with ’exact’ results from DSM and those obtained from Finite Element Method (FEM) and sources from literature

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Summary

Introduction

Graded Material (FGM) are a class of composites characterised by a change in composition through its volume, resulting in properties that vary spatially throughout the material [1]. These materials were designed for use as heat shields to protect spacecrafts during re-entry. In this chapter FEM and DFE formulations for functionally graded Euler-Bernoulli beams are presented. In the previous chapter the DFE formulation for FGM beams was presented and the vibration characteristics were investigated under various conditions. To further validate and build confidence in the results presented, a FGM beam model will be analyzed using the commercial FEM software package, ANSYS R.

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