Dynamic analysis of functionally graded rotor-blade system using the classical version of the finite element method

Abstract

In this paper, we analyze the dynamic behavior of a functionally graded (FG) rotor-blade system using the classical version of the finite element method (h-FEM). The Euler-Bernoulli beam theory is used to model the rotor-blade system and the governing equation of motion is obtained using Lagrange’s equation. The gradation of materials proprieties is described using the power-law distribution, and a new expression of the volume fraction is developed to express the gradation of the material properties in both the thickness and the width direction of the blade.

The natural frequencies of the studied model are determined using a program developed in MATLAB and the obtained results are verified with previously published works.

A comparative study is conducted between the functionally graded and pure metallic rotor-blade system. The comparison is based on the influence of the blade’s numbers, rotating speed and power law index on the natural frequencies of the rotor-blade system. The obtained results demonstrate the advantage of using functionally graded materials over the metallic materials for the design and conception of rotor-blade systems.

Keywords:

• Rotor
• blade
• h-FEM
• functionally graded material
• natural frequency
• flap-wise frequency
• chord-wise frequency