Nonlinear dynamic behaviors of an axially deploying beam

Abstract

The purpose of this paper is to analyze the dynamic behaviors of an axially moving beam that is extruded from a rigid hub. For analysis, the moving beam can be divided into two parts: One is the part inside the rigid hub and the other is the part outside the hub. The beam inside the hub has only longitudinal motions; however, the beam outside the hub has both longitudinal and transverse motions. Therefore, in this study, the equations of motion are independently derived for the beams inside and outside the hub. In particular, the longitudinal and transverse motions of the beam are coupled to each other, and these motions lead to nonlinear behaviors of the beam. We conclude that the nonlinear behavior should be considered to obtain more accurate analysis results. In addition, the responses of the nonlinear equations are compared to those of the corresponding linear equations.