Finite Element Method for Vibration Analysis of Timoshenko Beams

In industry and lots of engineering applications, rotating components, turbines, helicopter blades, rotors belong to large usage area. Design, material properties and dynamic properties of these structures or components are so significant with respect to efficiency. Frequencies and mode shapes are used to identify the dynamic properties of structures. In this study, three different models were researched. A theoretical investigation in free vibration of a functionally graded beam (FGB) which vary along the beam thickness and axial direction and double tapered beam model are presented with using Finite Element Model. It is assumed that material properties vary according to power law distributions. Timoshenko beam theory is studied and the FGB and double tapered beam are modeled according to this theorem. Free vibration analysis of flap wise bending is studied at symmetrical beam. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Analytical solutions of the natural frequencies are obtained with finite element method which the properties of beam distribution shape functions are used for exponential double tapered and FG beams with clamped-free end supports. MATLAB code is developed to analyze the free vibration of the tapered and functionally graded rotating Timoshenko beam. In the process, finite element formulation (FE) is used and the calculated results are validated with the ones in open literature.