Dynamic modeling and stability analysis of an axially oscillating beam undergoing periodic impulsive force

A dynamic modeling method of an axially oscillating beam undergoing periodic impulsive force is proposed in the present work. An element-specific modeling method using a stretch deformation variable is employed to derive the linear equations of motion. The stiffness variation effect induced by the periodic impulsive force as well as the axially oscillating motion is included in the linear equations of motion. The accuracy of the proposed modeling method is verified by comparing its numerical solutions to those of a nonlinear finite element code. The effects of the impulse magnitude, the oscillating frequency, the oscillating speed amplitude and the modal damping ratio on the dynamic stability of the beam are investigated with the modeling method.