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International audience; This paper investigates the rocking behavior of rigid bodies seismically protected by means of lead rubber bearings and high damping rubber bearings, which are the most popular kinds of elastomeric isolators in the market. The complex nonlinear force-displacement relationship displayed by such devices is predicted by a phenomenological model based on a small set of parameters having a clear mechanical meaning. The algebraic nature of the proposed hysteretic model makes it suitable for a design procedure, using an energy-based approach, that allows one to obtain the hysteretic model parameters on the basis of the mass and the isolation period. Overturning spectra are evaluated and discussed to illustrate the effect of the isolation devices on the rigid bodies' rocking behavior. Furthermore, nonlinear time history analyses associated with six real earthquakes are carried out on six of Michelangelo's sculptures, located in the Galleria dei Prigioni at the Accademia Gallery of Florence, in order to examine their actual behavior under real strong ground motions.

Complexity of dynamical systems are increasing more and more as well as their mathematical models. At the same time, simulation of system behaviour assumes a key role to assure the fulfillment of requirements as performances, quality, safety, and robustness. Therefore, due to model complexity, it is often very complex to assess a system behaviour but a reduction of model complexity could enhance the simulation aimed to specific characteristics of the system. Several useful model order reduction (MOR) techniques exist but each of them is often powerful for specific applications. This review paper deals with MOR by critically comparing the most popular MOR techniques from the fields of structural dynamics, numerical mathematics and systems and control. In particular, after different reduction techniques have been presented, a table summarizing their most important features is proposed, for comparison purpose. The motivation for such comparison stems from the fact that the insight obtained by the comparison allows to make a motivated choice for a particular model reduction technique, on the basis of the desired properties retained in the reduced model. Particular attention is paid on reduction techniques from the area of structural dynamics. Finally, the differences among some of the presented reduction techniques are illustrated, on a quantitative level, by means of their application to the case of a slewing flexible beam. In particular, in the application of the different reduction techniques, a consistent-mass finite element model, with only translational degrees of freedom, is employed as beam full model.