Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force

An analysis is presented of the vibration and stability of a non-uniform cracked Timoshenko beam subjected to a tangential follower force distributed over the center line by use of the transfer matrix approach. For this purpose, the governing equations of the beam are written as a coupled set of first-order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by the numerical integration of equations, the eigenvalues of vibration and the critical flutter loads are obtained. The method is applied to beams with linearly varying radii, subjected to a concentrated follower force, and the natural frequencies and flutter loads are calculated numerically, to provide information about the effects on them of varying cross-section, span and stiffnesses of intermediate supports, and the position and depth of the crack. (C) 1999 Elsevier Science Ltd. All rights reserved.