Open AccessNatural frequencies of a Timoshenko beam subjected to axial forces by the differential transform method
Author(s) -
Omar Bensabri,
Jingjun Yu
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/576/1/012027
Subject(s) - timoshenko beam theory , eigenvalues and eigenvectors , beam (structure) , differential (mechanical device) , mathematical analysis , hamiltonian (control theory) , differential equation , natural frequency , mathematics , rotational speed , physics , classical mechanics , vibration , acoustics , mathematical optimization , optics , quantum mechanics , thermodynamics
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.