Dynamic behaviors of a deploying beam with a non-linear coupled effect

Abstract

This paper considers the dynamic behaviors of an axial moving beam with a non-linear coupled effect. A dynamic model for a deploying beam is proposed, in which the Euler-Bernoulli beam theory and the von Karman strain theory are adopted. The beam is deployed from a rigid wall. It can be divided into two parts: one part is outside of the wall and the other is within the wall. The beam out of the wall, which is the deployed part, has transverse and longitudinal deflections; however, the beam inside the wall has only a longitudinal deflection. Using Hamilton's principle, the equations of motion and the corresponding boundary conditions are derived. Based on the equations for the longitudinal and transverse motions, time responses of the deploying beam are investigated when the beam is subjected to an external force. In addition, a non-linear effect is also studied.