The Critical Velocity and Post-Buckling Behavior of Axially Moving Beams with Poisson’s Ratio

Abstract

In this study, the critical velocity of axially moving beams is calculated and the post-buckling behaviors of beams are investigated. The governing equation of the axially moving beam problem is obtained by using vector approach. This approach is also known as Newton’s second law method. The obtained equations depend on normal force, shear force and moment. The opposite side of the equation depends on the acceleration since the dynamic analysis is done. Using Hook’s law, the normal forces and the moment are rewritten in displacement form, then the governing equation is obtained in displacement form. The dimensionless form of the resulting equation is as obtained. It is solved to provide simple-simple support conditions. Thus, the critical velocity value and the post-buckling graph are obtained depending on the displacement. As a result of these analyzes; the effects of the Poisson ratio on critical velocity and post-buckling behavior are observed. The effect of Poisson's ratio on critical velocity and post-buckling effect in axial moving beam problems are revealed.