Dynamic analysis of a deploying beam with overall translation motion

Abstract

The dynamic behaviors of an axially deploying beam are analyzed when the deploying beam has overall translation motion. After a dynamic model is established by using the Euler-Bernoulli beam theory and the von Karman strain theory, the equations of motion and the corresponding boundary conditions are derived by Hamilton's principle. In order to obtain the discretized equations, the Galerkin's method is applied to the equations of motion. To analyze the dynamic behaviors of the beam, the time responses for the displacement of the beam are computed by applying a time integration method. The effects of the overall translation motion on the dynamic behavior of the deploying beam are investigated. In addition, nonlinear behaviors are also studied in this study.