Comportement dynamique d’un tube fonctionnellement gradué

Abstract

In this thesis, an in-depth numerical study is conducted on the free vibrational analysis and static bending of tubes made from functionally graded materials (FGM), taking into account porosity properties under the influence of thermal variations. The power-law is used to model the gradation of FGM materials, while a nonlinear temperature distribution is adopted to better reflect real-world conditions. This work is based on two classical beam theories: Euler-Bernoulli theory and Timoshenko theory, allowing for a comparative analysis of mechanical behavior. The equations of motion are derived by applying Lagrange’s principle through two distinct methods: a numerical method based on classical finite elements and an analytical approach using the Galerkin method. The natural frequencies are then calculated by solving the eigenvalue problem, considering various influencing parameters such as the FGM tube geometry, the power-law index associated with material gradation, temperature variations, porosity index, and different combinations of FG materials. This research aims to provide a deeper understanding of the vibrational and mechanical performance of FGM structures in complex environments.