###### Abstract  
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. non-smooth contact dynamics; rocking; numerical algorithm; experimental validation 2024202414683 [1]Title:  
be considered small) using an analytical approach [7; 8; 9; 10; 11]. These analyses were usually limited to simple ground motions. Some analyses were conducted using a fully nonlinear equation of motion [11; 12; 13]. Such a solution usually requires the use of a chosen method for the numerical integration of the equation of motion [14; 15]. The restitution coefficient, which usually represents the ratio between the angular velocities immediately after and just before the impact, has been modified to improve [PERSON]'s original assumption that the impact impulse acts at the very edge of the block [14; 16; 17] and takes the material dissipation into account. However, the description of rocking by an equation of motion with a single degree of freedom--the rotation of the block--cannot account for the slipping and jumping of the block [18; 19], which is present in bulky blocks [12]. To tackle this, alternative approaches to modeling rocking, such as the discrete element method (DEM) [20; 21] and the non-smooth contact-dynamics method (NSCD) [22], have been employed. Moreover, rocking fragility analyses for given intensity measures can be used to predict the properties of rocking motion (e.g., peak rotation angle) [23], where an intensity measure that considers excitation characteristics and geometric properties of the rigid block is proposed. Recently, the rocking of rigid blocks was also analyzed using a neural network architecture [24]. In order to protect rigid block-like structures against seismic hazards, protection methods are being developed and investigated [25]. Less investigated are problems of the rocking of rigid blocks lying on a flexible structure, although they possess substantial engineering relevance, such as marble exhibits in museums [26], non-rigidly anchored electrical cabinets in nuclear plants [27], free-standing bookshelves in libraries, furniture, or machinery that is not rigidly connected to its foundation [28]. One of the most important questions is whether the additional flexibility is beneficial or detrimental to the overall rocking stability of the block, which can represent non-structural components.