Free Vibration Analysis of a Rotating Mori–Tanaka-Based Functionally Graded Beam via Differential Transformation Method

Abstract

In this paper, free vibration analysis of a rotating Mori–Tanaka-based functionally graded (FG) beam is investigated based on Timoshenko beam theory. The physical neutral axis position for the mentioned FG beam is determined. By using a semi-analytical differential transformation method (DTM), the governing differential equations are transformed into recurrence relations and the boundary conditions are converted to algebraic equations. The material properties of the rotating FG beam are supposed to vary across the thickness direction based on Mori–Tanaka micromechanics model. In the classical beam theory, the effects of transverse shear deformation and rotary inertia are not taken into consideration, while the Timoshenko beam model takes these effects into account. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of rotating FG beams. The good agreement between the results of this article and those available in the literature validated the presented approach. The detailed mathematical derivations are presented, and numerical investigations are performed, while the emphasis is placed on investigating the effect of functionally graded microstructure, mode number, slenderness ratios, rotational speed and hub radius and boundary conditions on the normalized natural frequencies of the rotating FG beam in detail. It is explicitly shown that the vibration behavior of a rotating FG beam is significantly influenced by these effects.