Effects of Nonunique Residual Traction on the Non-repeatability of the Dynamics of Jointed Structures

The tangential friction force of a permanently sticking contact (referred to as residual traction) can have an arbitrary (nonunique) value within the limits defined by the Coulomb cone. However, the actual value of residual traction is unknown due to its dependence on the load history. This uncertainty can introduce significant variability, ranging from 20 to 300 percent, in the level of resonant vibration, as observed in experiments of structures with friction dampers. In this study, we systematically investigate, for the first time, the influence of nonunique residual traction on the vibration response variability of a system with bolted joints. The selected benchmark consists of an L-shaped beam and a cross beam (stiffener) connected by two joints. The joints are aligned under 90-degree angle, establishing a structural coupling between the tangential and normal directions of the contacts. Both experimental and numerical analyses are conducted to assess the effects in detail. In the experimental phase, phase-locked-loop testing is employed to measure the amplitude-dependent modal parameters. On the computational side, the structure is modelled using commercial finite element software, and quasi-static modal analysis is employed. The results show to what extent the nonuniqueness of residual traction contributes to the non-repeatability of the vibration response and the accuracy of the correlation between experiments and numerical analyses.