Dynamics of Rotors Made by Porous Materials (Dynamique des rotors en matériaux poreux)

Abstract

This thesis presents a comprehensive investigation into the dynamic vibration behavior of rotating shafts fabricated from advanced porous materials, including Porous Functionally Graded Materials (PFGM) and Functionally Graded Porous (FGP) structures. The primary objective is to develop a robust computational framework to accurately predict how engineered porosity influences critical rotor characteristics such as natural frequencies, mode shapes, and critical speeds. The methodology is founded on a modified Timoshenko Beam Theory (TBT), which accounts for shear deformation and rotary inertia, implemented within a hierarchical p-version Finite Element Method (p-FEM) to ensure high accuracy and convergence. Extensive parametric studies were conducted to analyze the effects of material gradation, porosity distribution models (even, uneven, symmetric, and non-symmetric), geometric parameters, and boundary conditions. Key findings reveal that while increasing porosity generally reduces stiffness and lowers natural frequencies, its effect is highly dependent on the spatial distribution. Notably, symmetric porosity distributions in FGP shafts can enhance dynamic performance by optimizing the stiffness-to-mass ratio, leading to an increase in critical speed. Conversely, non-symmetric and uneven distributions can introduce complex, non-monotonic behaviors and degrade stability, particularly when interacting with bearing stiffness and disk mass. The results underscore that porosity can be a deliberate design feature for creating lightweight, high-performance rotors, but its architecture must be precisely controlled. This research contributes valuable design guidelines for engineering advanced rotor systems with tailored dynamic properties, which is significant for applications in the aerospace, automotive, and energy industries where operational reliability is critical.