Nonlinear dynamics of uncertain multi-joint structures

The present investigation is part of a long-term effort focused on the development of a methodology for the computationally efficient prediction of the dynamic response of structures with multiple joints. The first part of this thesis reports on the dynamic response of nominally identical beams with a single lap joint (“Brake-Reuss” beam). The observed impact responses at different levels clearly demonstrate the occurrence of both micro- and macro-slip, which are reflected by increased damping and a lowering of natural frequencies. Significant beam-to-beam variability of impact responses is also observed.

Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.

The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.

The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.