On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I

The dynamic response of a flexible beam subject to large overall motions is traditionally formulated relative to a floating frame, sometimes referred to as the shadow beam. This type of formulation leads to equations of motion of the form g˜(y˙, y, t) = 0, that are implicit, nonlinear and highly coupled in the inertia terms. An alternative approach is proposed whereby all quantities are referred to the inertial frame. As a result, the inertia term enters linearly in the formulation simply as mass times acceleration. Crucial to this formulation is the use of finite strain rod theories capable of treating finite rotations. Numerical examples that involve finite vibrations coupled with large overall motions are presented in Part II of this paper.