Journal of Theoretical
and Applied Mechanics

54, 4, pp. 1205-1217, Warsaw 2016
DOI: 10.15632/jtam-pl.54.4.1205

Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Őzge Őzdemir
In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton’s principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for 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 are calculated and effects of several parameters are investigated.
Keywords: differential transform method, functionally graded beam, Timoshenko beam