When a rigid block resting on a horizontal rigid foundation is shaken by a periodic excitation it can topples if the excitation amplitude is sufficiently high. This question is addressed in this work by the combined use of numerical and analytical tools. Numerical computations are first performed aimed at understanding the overall overturning behavior, and how it is modified by varying relevant parameters, such as the excitation phase and the coefficient of restitution at impacts. Then the problem is addressed from a theoretical point of view, with the objective of analytically detecting the most relevant features highlighted by previous numerical simulations. We succeed in obtaining closed form and manageable criteria for overturning.

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