Post-critical behavior of damped beam columns with variable cross section subjected to distributed follower forces

Abstract

In this paper the post-critical behavior of beam columns with variable mass and stiffness proper- ties subjected to follower forces arbitrarily distributed along their length in the presence of damping (both in- ternal and external) is investigated using a complete nonlinear dynamic analysis. Although the static non- linear analysis is more economical in computational cost, it is associated only with the loss of local stability via flutter or divergence. Thus, the nonlinear dynamic analysis is adopted in order to examine the global sta- bility of the system. The governing equations of hyper- bolic type are derived in terms of the displacements by considering (a) nonlinear response including the axial deformation, (b) nonlinear response excluding the axial deformation and (c) linear response. More- over, as the cross-sectional properties of the beam vary along its axis, the resulting coupled nonlinear differ- ential equations have variable coefficients. Their so- lution is achieved using the analog equation method (AEM) of Katsikadelis. Besides its accuracy and ef- fectiveness, this method overcomes the shortcoming of a possible FEM solution which may experience a lack of convergence. The problems treated in this in-