SLIDING BEAMS, PART II - TIME INTEGRATION

In this paper we obtain solutions for the discretized incremental syst em equations, as obtained in Part I, under certain initial and boundar y conditions and/or specified applied loads, using the variable domain beam element. As a check on the validity of implementation, we first limit ourselves to linear analysis and obtain results for the axially inextensible sliding beams which we compare with the results reported in the literature. Second we set the axial velocity to zero and solve some special cases when the length of the beam is constant. In this ca se, we check the formulation and its implementation for non-linearitie s in the system due to large displacements. Finally, we solve the slid ing beam problem for small amplitude oscillations; with a non-linear s olver and compare the results with those obtained by the linear Solver used for inextensible sliding beams. With these preliminary tests com pleted, we obtain the transient response of the free and forced large amplitude vibrations of the flexible sliding beam and demonstrate the need for using a nonlinear analysis for this complex system. Finally, we consider the stability of the motion of periodically time varying f lexible sliding beams and show that in the case of parametric resonanc e, the unstable regions obtained in the linear analysis, which imply u nbounded amplitudes, are indeed stable and bounded when non-linear ter ms are taken into account. (C) 1998 John Wiley & Sons, Ltd.