Vibration analysis of a deploying beam with translation

Abstract

This paper presents the vibration analysis of a deploying beam when the beam has an overall translation motion. After establishing a dynamic model for a deploying beam with translation, the partial differential equations of motion are derived by using Hamilton's principle. The derived partial differential equations are discretized by applying the Galerkin method. The discretized equations are transformed to a matrix-vector equation, and then time responses are obtained using the Newmark time integration method. The effects of deploying and translating velocities on the dynamic responses are investigated. In addition, we examine which velocity profiles of the deploying and translating velocities can reduce the residual vibration of a beam.