Analysis of impact with friction for bars

The study of impact is focused on the reaction forces that develop during collision and the dynamic response of structures to these reaction forces. In the literature, most of the cases studied involved simple cases of impact, such as the planar impact of a rigid bar with a surface and planar collision of slender bars with different geometric and physical properties.; In the beginning of this work, the three-dimensional impact with friction of a rigid bar is studied. The equations of motion are calculated using Kane method. For simplification, the relationship between the reference frames is deduced at the moment of impact, when the reference frames have a coincident origin. The generalized momentum and impulse equations are considered to find the equations of motion of the rigid bar. For the case of impact without slipping, it is assumed that the tangential component of the velocity of separation is null. In the case with slipping, the tangential impulse (at the plane of impact) is computed. The assumptions permit the prediction of the direction of post-impact velocity of the rigid bar and the direction of the impulse at impact. A simulation of the impact of the rigid bar with a rigid surface is developed using Mathematica and the impulse at impact and the kinetic energy of the bar after impact are studied for different incident angles of the bar. The incident angle is varied from 0° to 45°. The numerical results show a dependence of the vertical impulse at impact and the kinetic energy loss with the incident angle of the bar.; Also, in this work, the study of frictional impact is extended to flexible bars. The study of the impact of flexible bars introduces the elastic coordinates and thus the system that must be solved includes more equations. For simplification, most of the computations are made in the mobile reference frame attached to the beam and then transferred in the fixed reference frame. Considering that the generalized velocities before impact are known, the impulse at impact and the kinetic energy loss at impact with no slipping and with slipping are found. For different incident angles of the flexible bar, a simulation of the impact is developed. The numerical results show again a dependence of the vertical impulse at impact and the kinetic energy loss with the incident angle of the flexible bar. (Abstract shortened by UMI.)...