The aim of this work is to analyze the dynamic behavior of axially loaded Timoshenko flexible shafts with cantilevered overhung disk based on the differential transformation analysis. The equations of motion are derived using Hamilton’s principle. The set of the latter consists of four coupled partial differential equations, which can be reduced to a set of two coupled equations by using a complex transformation to further improve the computational effort. An efficient mathematical recursive technique called the differential transformation method (DTM) is then used to solve the differential equations of motion. The natural frequencies of the shaft are obtained, the influence of intrinsic and extrinsic parameters on the natural frequencies is investigated, and the results are compared to those found in the literature. The results reflect the high accuracy and precision of the DTM. The novelty of the work is the application of the DTM to determine the frequency characteristics and the stability of an axially loaded overhung rotor’s free vibration analysis. These results show that the current analysis is accurate and offers an effective approach that is relatively simple and more direct regarding previous modal analyses.

Rotating beams are extensively used in different mechanical and aeronautical installations. In this paper, a systematic approach is presented in order to solve the eigenvalues problem through the Timoshenko beam theory. The equations of motion are deduced by using the Hamiltonian approach. These equations are then solved by the differential transform method (DTM). The obtained numerical results using DTM are compared with the exact solution. Natural frequencies are determined, and the effects of the rotational speed and axial force on the natural frequencies are investigated. Results show high accuracy and efficiency of the differential transform method.