DYNAMICS OF FLEXIBLE SLIDING BEAMS - NONLINEAR-ANALYSIS PART I - FORMULATION

Equations of motion for the geometrically non-linear analysis of flexi ble sliding beams, deployed or retrieved through a rigid channel, are derived through an extension of Hamilton's principle. Based on the ass umptions of Euler-Bernoulli beam theory, the equations of motion accou nt for small strains but large rotations. Also provided is an alternat ive formulation wherein by superposition of a prescribed axial velocit y the beam is brought to rest and the channel assumes the prescribed v elocity. The consistency of the two formulations is shown through an a ppropriate 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 vi brations of the flexible sliding beam are presented in part II. (C) 19 97 Academic Press Limited.