Stability analysis of an axially moving free-free beam

This study investigates the stability of an axially moving free-free beam as a function of moving speed, modulus of elasticity, and axial tensile force. The mode shapes of the beam under different axial tensile forces are also discussed. In this study, we derive the equations of motion of a flexible free-free beam with a uniformly circular cross section that moves axially at a constant speed. Using Galerkin’s technique, we dicretize and reduce the nonlinear partial differential equation of motion to a set of ordinary differential equations by choosing the shape functions to be the eigenfunctions of a free beam. The state-space method is used to investigate the stability of an axially moving free beam for different cases. Numerically, the stability of the system is influenced by different cases in various ways and degrees. The transverse vibration modes with different tensile forces are also considered in this study.