Dynamics of an axially extending and rotating cantilever beam including the effect of gravity

Abstract

A system of approximate differential equations in matrix form is derived for the dynamics of an axially extending and rotating beam including the effect of gravity using a Lagrangian approach and the assumed mode method. A simple series of single-term functions is used for the assumed mode in place of the beam functions used in the other reported studies. The transverse motions in the two principal orthogonal directions of the cross-section of the beam are coupled when the setting angle, which is the angle between the axis of rotation and one of the principal axes of the cross section of the beam, is not equal to 0° or 90°. Numerical simulations are performed for various combinations of prescribed axial and rotational motions of the beam. © 1995.