Keywords: non-symmetric rigid block, base isolation, security stops, rocking, sliding, seismic excitation.

The model of a rigid block is well known in the scientific literature. Recently this model has been used to describe the behaviour of monolithic bodies subject to earthquake excitation [1]. Almost all papers on rigid blocks subject to base excitation focus their attention on symmetric rigid bodies. With the aim of studying non-symmetric rigid blocks too, in [2] the influence of the eccentricity of the centre of mass on the motion of the system has been studied. In recent years, methods to reduce the effects of seismic excitation on art objects have been studied in some papers. For example, in [3] a base isolation system has been used to protect statues from seismic effects. The art object has been modelled as a symmetric rigid block simply supported on an oscillating base connected to the ground by a visco-elastic device. Finally in [4] the authors have enriched the model developed in [3] by considering the eccentricity of the centre of mass of the rigid body and the presence of security stops that are able to prevent the breakage of the isolation system.

In the present paper the sliding effects, not considered in [3,4], are introduced and the frictional forces have been expressed by using the Coulomb description. A model of non-symmetric rigid block, able to rock and slide, positioned on a oscillating base connected by a linear visco-elastic device to the ground is developed. Security stops, to prevent damage to the base isolation system, are also considered. The behaviour of the whole system is studied under seismic external excitation. Exact nonlinear equations of motion are written by using a Lagrangian approach for the different phases of motion: full-contact, sliding, rocking, slide-rocking; transition phase conditions are also obtained. In conclusion two different kinds of collapse condition have been considered: one describes the fall from the oscillating base of the rigid block, the other, the overturning of the body. The analysis has been conducted in order to indicate the exact influence of the friction coefficient, the eccentricity, the slenderness, the security stops and of the other parameters regarding the behaviour of the system. Comparison between results obtained for isolated rigid body and non-isolated rigid body are also carried out to show the effectiveness of base isolation with respect to the absence of this passive control system. In conclusion, the analysis reveals that base isolation can be more effective for rigid bodies with geometrical parameters similar to those of real works of art.

1

T. Taniguchi, "Non-linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion", Earthquake Engineering and Structural Dynamics, 31, 1481-1500, 2002. doi:10.1002/eqe.170

2

R.L. Boroscheck, 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

I. Caliò, 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

4

A. Contento, A. Di Egidio, "Investigations into Benefits of Base Isolation for Non-Symmetric Rigid Blocks", Earthquake Engineering and Structural Dynamics, 2009. doi:10.1002/eqe.870

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)