1. The first numerical example is the beam slider problem that will be used to illustrate the dramatic difference between prismatic and sliding joints when flexible bodies are involved. Fig. 8 depicts the problem configuration: a flexible beam of length L = 2.4 m is pinned at point R by means of a spherical joint, and carries a tip body of mass Mr =40Kg and moments of inertia /11 = 2/22= 2h3= 0.45 Kg .m2. A driver of height h = 1.6 m is pinned at point A by means of a revolute joint with its axis of rotation along Gand is connected to the beam at point B. Two case will be investigated, denoted cases 1 and 2, respectively. The driver is connected to the beam by means of a sliding joint for case 1. and of a prismatic joint followed by a revolute joint ,vith its axis of rotation along f3for case 2. The relative translation at the sliding joint is prescribed as 7/=0.5- 0.25 cos21rt,whereas that ofthe prismatic joint is prescribed as =0.6 (1- cos21rt)rn. Note that the prescribed motions for cases 1 and 2 are identical, the different expressions for and TJreflect their different definitions. The beam and driver were modeled with 12 and 3 cubic beam elements, respectively. The rather fine mesh used for the beam is necessary because the sliding joint corresponds to a point load traveling along the beam. Although this finemesh was not required for case 2which converged with 4 elements only, the same fine mesh was used for both cases. The physical properties of the beam are: axial stiffness EA = 44.0 MN, bending stiffnesses E/22 = 300.0 and h3= 23.0 KN.rn2,torsional stiffness GJ = 28.0 KN.m2,shearing stiffnesses GK22 =2.8and GK33 =14.0 MN, mass per unit span m =1.6 Kg/m, and mass moment of inertia per unit span h2 = 1.0 and h3=11.0mg.m. The properties of the driver are identical to those of
2. The configuration of the second numerical example is identical to that the first example, except for one important difference: the beam is now pre-twisted with a constant twist rate k1= 0.4363 rad/rn. In r:ase 1, the driver is connected to the beam by means of a sliding screw joint which rotates according to the beam twist. The relative translation at the sliding screw joint is prescribed as r, =0.5-0.25 cos 2rrt. For case 2,the driver is connected to the beam by means of a screw joint followed by a universal joint. The relative translation of the screw joint is prescribed as = 0.6 (1 - cos 2rrt) m, and the pitch of the Figure 13: Time history of the driving force. Case 1: solid line; case 2: dashed line.