Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform

This study introduces the concept of a differential transform to solve the free vibration problems of a rotating twisted Timoshenko beam under axial l oading. First, the concept of differential transform is briefly introduced. Second taking a differential transform of a Timoshenko beam vibration prob lem, a set of difference equations is derived. Performing some simple algeb raic operations on these equations, we can determine the jth natural-freque ncy, the closed form series solution of the jth mode shape. Finally, three cases-twist, axial force and rotation-are investigated to illustrate the ac curacy and efficiency of the present method. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.