###### Abstract
In recent years, a 3D rocking model of a block on an elastic foundation (modeled with a concentrated spring at the corners, as well as with Winkler's spring model) was introduced in [29]. In order to deal with problems of non-smooth contact dynamics, two categories of methods have been developed over the years: event-tracking time-stepping schemes and event-capturing time-stepping schemes. Event-driven schemes [30] involve the accurate detection of events that cause discontinuities. For this reason, in more complex problems, where many different contacts may be established or the density of contacts with respect to time is high, event-driven schemes may quickly lead to time-steps in a time-integrating procedure that are far too small for the analysis to proceed with reasonable efficiency. On the other hand, event-capturing algorithms [31; 32; 33] turn out to be more appropriate. Effectively, these algorithms stem from the physical fact that even though an instantaneous contact force is infinitely large, its impulse is finite. In a numerical time-integration scheme necessarily involving finite time-step sizes, this naturally leads to a finite algorithmic contact force. Therefore, in event-capturing time-stepping schemes, the time-step may be kept constant throughout the simulation, even when a contact is detected, which makes them efficient and robust for complex problems involving a multitude of contact events. As originally developed, the accuracy of these algorithms is limited to the first order, which leaves ample space for further improvement, as shown, e.g., in [34; 35; 36]. Experiences with such advanced schemes in complex practical applications can be significantly expanded, and their performance accordingly analyzed, which leaves room for the identification of potentially needed improvements. The rocking-on-a-beam problem is representative of more complex rigid-flexible mechanical systems, for which an event-capturing algorithm is preferred. In this work, the non-smooth contact dynamics method described in [32; 33; 37] is applied to the problem of a rigid block rocking on a beam structure. The simulations are performed using a code developed in Matlab, and the algorithm for the contact interaction solution is an event-capturing type of numerical scheme. For the flexible beam structure, the finite element method (FEM) is used for space discretization [38; 39]. The convergence of the event-capturing algorithm employed is analyzed in terms of the block's rotation angle, measured in laboratory experiments. The objective is to simulate a realistic scenario of a rigid body rocking on a flexible structure, which is here represented as an elastic beam. Details regarding the numerical solution procedure for this specific problem are presented. Numerical simulations are performed for a rigid and flexible beam structure. Rigid base rocking results are validated against experimental data. Possible algorithm application ranges and limitations are identified. The studied problem is described in Section 2, which is followed by the numerical solution approach to the problem in Section 3. Details regarding the calculation of the contact forces in the setting laid out in the previous two sections are provided in Section 4. In Section 5, the experimental setup is described. In Section 6, we proceed with the experimental and numerical tests' description, validation, and analysis. In Section 7, conclusions are drawn and future work is outlined.