Vibration Analysis of Rotating Timoshenko Beams With Different Material Distribution Properties

Abstract

In this study, vibration characteristics of functionally graded rotating Timoshenko beams that undergoes flapwise bending vibration are analysed. Beam models with different material distribution properties are considered. The energy expressions are derived by introducing several explanotary figures and tables. Applying the Hamilton's Principle to the derived energy expressions, governing differential equations of motion and the boundary conditions are obtained. Related formulation is coded by using MATLAB and in the solution part, the equations of motion, including the parameters for the rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies of the modeled beams are obtained. Increasing effects of the slenderness ratio and the rotational speed and the decreasing effect of the power-law index on the natural frequencies are investigated. Moreover, differences between the natural frequencies of the beam models with different material distribution characteristics is noticed and examined. Obtained results are distributed in several tables.

Vibration Characteristics of Nonuniform Blades Made of Functionally Graded Material

“…Details of the derivation can be found in Ref. [14][15][16] in great detail by using several explanatory figures and tables.…”