Timoshenko Beam Application in Dynamic Vibration Analysis for FGM Structural Rotor Using Finite Element Method P- Version

Abstract

This paper study the vibration behaviors analysis of Rotor. Using Finite Element Method pversion with trigonometric shape functions is used to redefine the equation of motion. The beam theory of Timoshenko using for modulization of the rotor system. Through Kinetic and strain energies of shaft, using Euler-Lagrange’s equation for determination of equation of motion. The transverse shear deformation, rotating inertia, and gyroscopic effects is incorporating. The model of Functionally Graded Material (FGM) used these models is the power-law distribution of the volume fraction. System of equation resolved by program of calculus developed in MATLAB software for obtention the natural frequencies. FEM p- version convergence presented with three boundary conditions Pinned-Pinned (Simply Supported), Clampedpinned and Clamped-Clamped. The validation of numerical method and our program has been with result viable in literature. The result contains first backward and forward modes of natural frequency in function of rotating speed so to determine the volume fraction influence for model of shaft used, The FGM type contain the mixer between SUS304 and Nickel.