Politecnico di Milano - Department of Mechanical Engineering

Authors: Cigada A., Sabbioni E., Siami A., Zappa E.

The famous statue Pietà Rondanini by Michelangelo Buonarroti (sculpted in the second half of 1500) was recently moved to a new position in a museum in Castello Sforzesco, Milano (FIG. 1). In this new location, vibrations induced by the close presence of underground tracks, has been considered worthy of specific attention: Therefore both the Municipality of Milan and the Cultural Heritage Ministry asked for the design of a new base capable of mitigating the vibration input to the statue. In addition, since Milan is a seismic area (although with moderate risk), it was also required to include in the base design an anti-seismic device. The protection from the underground induced vibrations (which is in the range between 16 and 80 Hz) requires the development of a system with low natural frequency and rather limited damping, to have a steep filtering after resonance (anti-vibration device). However in case of an earthquake, the low frequency range would be strongly excited, with the risk of an extreme event like a fall. A second device (anti-seismic device) is thus introduced to protect the statue from earthquakes, which consists of a low friction slide of the same type as those used to protect buildings from the same kind of events. The coupling between the two types of protection imposed a careful design and testing of the complete system made up of the base and the statue.

FIG. 1: Michelangelo’s Pietà Rondanini in the Castello Sforzesco museum (left) and multibody model of the installation developed using MSC ADAMS/View (right).

The design of the base was developed by means of an experimental and numerical approach. A measuring campaign using a large 6 degrees of freedom shaking table was used to test a full scale prototype of the base supporting a marble 1:1 copy of the statue. A multibody model of the full installation (complete base and statue) was developed using MSC ADAMS/View (FIG. 1), accounting for nonlinear behavior of rubber elements constituting the anti-vibration device and of friction forces of the slide constituting the anti-seismic device. The developed model was validated against the experimental data acquired during the experimental campaign and then used to optimize the system parameters, such as the position and the stiffness/damping distribution of the rubber elements constituting the anti-vibration device. As an example, FIG. 2 shows the sensitivity of isolating device response to stiffness distribution among the rubber elements. By increasing the stiffness of the rubber bearings placed at the corners (FIG. 2-left, blue circles), the peak amplitude of the pitch motion can be significantly reduced at the head of the statue.

FIG. 2: Sensitivity analysis on the rubbers stiffness distribution: FRFs between the acceleration of the seismic base along the horizontal direction and the acceleration of statue support (blue lines) and statue head (black lines).

Acknowledgements
The authors gratefully acknowledge the Municipality of Milano for the financial support and the precious control role, then CESI Ricerche, THK, Miyamoto and the Conservation Institute of the Italian Ministry of Cultural Heritage (ISCR) for the precious cooperation offered through the different activities of the project.

References
Cigada A., Sabbioni E., Siami A., Zappa E. (2016). Modeling and Testing of the Anti-Vibration Base for Michelangelo’s Pietà Rondanini. Conference Proceedings of the Society for Experimental Mechanics Series - Special Topics in Structural Dynamics, 6, pp. 11.21.