Dynamic analysis of a cantilever beam with deploying and retrieval motions

Abstract

In this paper, we analyze the dynamic responses of a cantilever beam which has deploying motion or retrieval motion. Considering the longitudinal and transverse displacement of the beam, we derive the equations of motion by using the Hamilton principle. During the derivation of the equations, the von Karman strain theory and the Euler beam theory are adopted. The derived equations of motion are nonlinear equations coupled between the longitudinal and transverse motions. After these equations are discretized by the Galerkin method, the time responses are obtained from the discretized equations by using the Newmark time integration method. We do not only analyze the nonlinear effects of the equations on the responses of the beam but we also investigate the effects of the deploying and retrieval motions.