Dynamic analysis of an axially moving beam subject to inner pressure using finite element method

A dynamic model of an axially moving flexible beam subject to an inner pressure is present. The coupling principle between a flexible beam and inner pressure is analyzed first, and the potential energy of the inner pressure due to the beam bending is derived using the principle of virtual work. A 1D hollow beam element contain inner pressure is established. The finite element method and Lagrange's equation are used to derive the motion equations of the axially moving system. The dynamic responses are analyzed by Newmark-β time integration method. Based on the computed dynamic responses, the effects of inner pressure on beam dynamics are discussed. Some interesting phenomenon is observed.