Dynamic Study of a Functionally Graded Material Rotating Conical Shaft Based on a New Model of Variation by Slice in the Material Properties

Abstract

This article is concerned with the dynamic behavior study of a rotating conical shaft bi-supported in functionally graded material (FGM), using the Timoshenko beam theory (FSDBT), with consideration of the gyroscopic effect. The material properties are varied through the thickness direction of the shaft based on a new model which defines the variation per slice in the volume fraction of the two extreme materials according to the exponential law distribution (E-FGM). This dynamic system is examined from a mathematical development and a hierarchical finite element modeling p-version. To validate our model, the numerical results obtained are compared with those available in the literature. Several examples are treated and a discussion is held to determine the influence of the internal properties (FGM), the conicity (α) and the slenderness ratio on the eigen-frequencies and consequently on the dynamic behavior of FGM rotating conical shafts.