IOP Conference Series: Materials Science and Engineering, Volume 576, 2019 International Conference on Advances in Materials, Mechanical and Manufacturing (AMMM 2019) 22–24 March 2019, Beijing, China, 2019
Rotating beams are extensively used in different mechanical and aeronautical installations. In th... more 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. 1. Introduction Rotating structures can be found in turning machinery systems such as motors, engines, and turbines. The bending vibrations analysis of the beams aroused considerable interest for the engineers. The natural frequencies and mode shapes of such systems are indispensable in the design of structures. Zu and Han [1] analytically solved the free flexural vibration of a spinning Timoshenko beam with classical boundary conditions. Zhang [2] studied the free vibration of axially loaded shear beam column and obtained a very simple frequency equation to utilize for axially loaded beam as well as to obtain the buckling loads by setting the natural frequencies to disappear. Farchaly and Shebl [3] determined two sets of exact general frequency and mode shape equations to study the vibration and stability of a Timoshenko beam that carries an end masses of finite length. Lee [4] enclosed the constant axial force and found that it had a considerable effect on the magnitude of the dynamic response. Ouyang [5] established a dynamic model for a rotating Timoshenko beam subjected to three force components acting on the surface. The deflection of the beam examined and found it had proportional increases with respect to the deflection and the frequency components when the axial force component is included. The effect of such parameters such as moving velocity, the skew force angle, and the rotating speed on the system dynamic response is investigated by utilizing the global assumes mode method by considering boundary conditions [6]. The dynamic green function is used to introduce the free vibration of elastically supported Timoshenko beam on a partly Winkler foundation [7]. The finite element method is used the investigate the behaviour of the natural frequencies and to determine the influence of the rotating speed profile on the vibration of the cantilevered beam based on the dynamic modelling method by using the stretch deformation [8].
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