Research Information System
ADVANCES IN VIBRATION ENGINEERING, vol.12, no.1, pp.89-108, 2013 (SCI-Expanded)
The free vibration analysis of moving Timoshenko beam using DTM has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model by using Differential Transform Method (DTM) in this study. In order to use DTM, it is necessary to derive the governing differential equations of motion of the moving beam. At first, the governing differential equations of motion of the moving Timoshenko beam in free vibration are derived using Hamilton's principle. Parameters for the nondimensionalized multiplication factors for the constant velocity and nondimensionalized multiplication factor for the axial tensile force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of the moving Timoshenko beams with various combinations of boundary conditions using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the fundamental mode shapes are presented in graphs.