Dynamic Behavior of The Rotor Structure By the Finite Element Method P- Version

Abstract

This work concerning the vibration behavior analysis of Rotor. Using Finite Element Method p- version 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. System of equation resolved by program of calculus developed in MATLAB software for obtention the natural frequencies and eigenvalues. FEM p- version convergence presented with three boundary conditions and three various materials. The validation of numerical method and our program devised in two parts, the first for natural frequencies we validate with result viable in literature, and the last part for associated eigenvalue we use three boundary conditions, Simply Supported (Pinned-Pinned), Clamped-pinned and Pinned-free validate with exact values. In the result we study four fist mode of natural frequency with the objective of show the influence of various boundary condition (we take a same precedent boundary conditions) for three materials Stainless Steel, Nickel and Zirconia, after that a result of the first mode of natural frequency in function of rotating speed and the critical rotating speed for model of shaft used (Campbell’s graph).