Keywords: base isolation, non-symmetric rigid block, eccentricity, harmonic excitation, seismic excitation, direction of the excitation.

In the past, many papers have been devoted to the study of the dynamic behaviour of rigid blocks. Focusing the attention to base excitations, in [1] a general formulation of the rigid block has been obtained and rocking and slide-rock approximated conditions have been written. With the aim to better represent the behaviour of works of art, which are generally non-symmetric monolithic bodies, in [2] the influence of the eccentricity of the centre of mass on the motion of the system has been studied. In [3] the rigid block model has been used to describe the behaviour of objects of art in museums under seismic excitation. In recent years, methods to reduce the effects of seismic excitation on art objects have been studied in some papers. In [4] a base isolation system has been introduced to protect statues from seismic effects. The art object has been modelled as a symmetric rigid block simply supported on a base which is connected to the ground by a visco-elastic device.

The behaviour of a base isolated non-symmetric rigid block is the subject of the present paper. In the model analysed a rigid body rests on a base connected by a linear visco-elastic device to the ground, representing the base isolation. The behaviour of the whole system is studied under several types of excitation, mainly harmonic and seismic excitations are considered. Exact nonlinear equations of motion are derived for the rocking phase and transition phase conditions, which are studied under the condition that the rigid block is only allowed to rock or remain in a full-contact state. In order to point out the influence of the eccentricity and the slenderness of the rigid block, a suitable non-dimensionalization of the equations of motion is done and an extensive parametric analysis is performed via a direct numerical integration. Comparison between results obtained for isolated and non-isolated rigid blocks is also carried out to show the effectiveness of the base isolation with respect to the absence of this passive control system.

The influence of base isolation on the dynamic behaviour of a rigid block is shown to strongly depend by the considered parameters. In particular, when an eccentricity is considered or when the slenderness of rigid block is increased, the system shows a decay of the performance with respect to the symmetric rigid block and to a less slender body. Also the dependence of the behaviour from the initial direction of the excitation has been highlighted when an eccentricity is considered. Finally, the analysis reveals that base isolation can be very effective for rigid bodies with geometrical parameters similar to those of real works of art.

1

H.W. Shenton, N.P. Jones, "Base excitation of rigid bodies. I: Formulation", Journal of Engineering Mechanics, 117(10), 2286-2306, 1991. doi:10.1061/(ASCE)0733-9399(1991)117:10(2286)

2

R.L. Boroscheck and D. Romo, "Overturning criteria for non-anchored non-symmetric rigid bodies", 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004.

3

M.S. Agbabian, F.S. Masri, R.L. Nigbor, and W.S. Ginel, "Seismic damage mitigation concepts for art objects in museum", in "Proceeding of the 9th World Conference on Earthquake Engineering", Tokyo-Kyoto, Japan, 7, 235-240, 1988.

4

I. Caliò and M. Marletta, "Passive control of the seismic response of art objects", Engineering Structures, 25, 1009-1018, 2003. doi:10.1016/S0141-0296(03)00045-2

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