Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics

When structures are subjected to dynamic loading, such as that caused by an earthquake or working machinery, the rocking behavior of objects located on parts of the loaded structure plays an important role in addressing the protection and stability of non-structural components. In this work, the free rocking of a rigid block on a flexible beam and rigid base was investigated using numerical simulations. To this end, a numerical code based on the non-smooth contact dynamics method was developed for this particular problem, and numerical simulations are compared to experimental tests when a rigid base is considered. The purpose of the study was to investigate the predictive capabilities and limitations of the numerical model and address the effect of introducing beam flexibility on the rocking response. The investigated flexibilities were such that the beam deflection under the static weight of the block remains within the common limit of 1/250 of the beam span. For a rigid base, qualitatively good correlation with the experiments was obtained, and good convergence in terms of the time-step is displayed. With the increase in beam base flexibility, it was observed that the simulation results tend to become more sensitive to mesh density and time-step size. Furthermore, we identify a limited flexibility with respect to which unreliable predictions of the overall free rocking are obtained, which corresponds to the stiffness resulting in the beam deflection under the block weight of beam-span/2500. For stiffnesses higher than that, no significant effect of beam flexibility in comparison to the rigid base was noticed in terms of tilt angle and rocking duration, which indicates the adequacy of a rigid base approximation for beams with low flexibility.