Stability Analysis of Cantilever Cracked Beams Subjected to Follower Forces

Abstract

A stability analysis of a cracked cantilever beam subjected to a follower compressive load is presented by using Adomian modified decomposition method(AMDM). The free end of the cantilever beam is restrained by a translational spring and subjected to a follower force. The crack is modeled as an equivalent massless rotational spring. Based on the AMDM the governing differential equation for this cracked beam becomes a recursive algebraic equation. By using boundary conditions and continuity/jump condition equations at crack location, the dimensionless natural frequencies and corresponding closed-form series solution of mode shapes can be obtained simultaneously. The accurate and effective of the proposed method are verified by comparing the results using the AMDM to those given in the literature. The effect of the location and depth of the crack on the critical compressive load for flutter or buckling instability of the beam is studied. Furthermore, the critical spring stiffness is calculated to determine the different type of instability of the beam under the follower compression. The numerical calculations results show that the maximum changes of the natural frequencies are observed when the crack is located near clamped end. It is also found that the stability of beam may be improved due to crack.