Vibration and stability of a cracked shaft simultaneously subjected to a follower force with an axial force

An analysis is presented for the vibration and stability of a non-uniform shaft with a crack by use of the transfer matrix approach. The shaft is simultaneously subjected to a tangential follower force, which is distributed over the center line, with an axial force. For this purpose, the governing equations of the shaft are written as a coupled set of first order differential equations by using the transfer matrix of the shaft. Once the matrix has been determined by the numerical integration of equations, the eigenvahies of vibration and the critical flutter loads are obtained. The method is applied to shafts with linearly varying radii, subjected toa concentrated follower force, and the natural frequencies and flutter loads are calculated numerically, to provide information about the effects of them of varying cross-section, span and stiffnesses of intermediate supports, and the position and depth of the crack. © 1998 Elsevier Science Ltd. All rights reserved.