Numerical and Experimental Response of Free-Standing Art Objects Subjected to Ground Motion

Shaking Table Seismic Experimental Investigation of Lightweight Rigid Bodies

“…In order to extend the features of the Simple Rocking Model, it was upgraded considering the possible occurrence of sliding [14], and also accounting for asymmetric [12,13] or three-dimensional behavior [15]. Finally, a considerable number of studies were devoted to analyze and propose realistic approaches for evaluating the coefficient of restitutions [10,22]. It is worth mentioning that no model, even the most advanced one, can get rid of the chaotic character of the rigid body motion, for which there is strong evidence brought to light in some studies [40][41][42].…”

“…Two suitable vertically aligned points G and P were chosen in correspondence of the center of gravity and the center top of the rigid body, respectively. Then, as proposed in [10], the rotation can be simply retrieved as:…”

“…Sorrentino et al [51], in the interpretation of their experimental campaign, already highlighted a dependency of the estimated coefficient of restitution on the number of impacts accounted for. Alternatively, the formulation proposed in [10], which modifies the formula introduced in [38], aims at assessing instantaneous value of the coefficient of restitution in correspondence of the generic impact, and can also be adopted for asymmetric blocks. Precisely, the coefficient of restitution , c j e at the j-th impact depends on the maximum rotations achieved in the rocking phases before and after the impact and can be evaluated as follows…”

“…Rigid body motion can describe a wide variety of structural systems both in the field of civil engineering [1][2][3] and in the protection of ancient remains [4][5][6] and artworks [7][8][9][10], especially in seismic conditions. In view of the practical implications of the understanding of such systems, starting from the pioneering Housner's study [11] presented in 1963, the rigid motion of rocking blocks was addressed by several experimental studies that aimed to refine the numerical prediction of their response.…”

“…Several authors contributed to improve Housner's model, extending its features by considering asymmetric blocks [12,13], the occurrence of sliding [14], by extending the model to the three-dimensional behavior [15], or by proposing alternative strategy to evaluate the coefficient of restitution [16][17][18][19][20][21], also with reference to experimental evaluations [10,22]. In other cases, alternative numerical models were proposed, considering moment-rotation laws to describe the rocking motion [17,[23][24][25][26].…”