Dynamics of flexible sliding beams - Non-linear analysis part I: Formulation

Equations of motion for the geometrically non-linear analysis of flexible sliding beams, deployed or retrieved through a rigid channel, are derived through an extension of Hamilton's principle. Based on the assumptions of Euler-Bernoulli beam theory, the equations of motion account for small strains but large rotations. Also provided is an alternative formulation wherein by superposition of a prescribed axial velocity the beam is brought to rest and the channel assumes the prescribed velocity. The consistency of the two formulations is shown through an appropriate transformation of the governing equations to a fixed domain. The fixed domain Provides a very convenient frame work for numerical solution of the equations of motion. Discretization procedures using Galerkin's method, and numerical examples involving large amplitude vibrations of the flexible sliding beam are presented in part II. (C) 1997 Academic Press Limited.