In the past, many papers have been devoted to the study of the dynamic behaviour of rigid blocks. Focusing the attention on the behaviour of this system, subject to base excitations, in [1] a general bi-dimensional 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 museum under seismic excitation. In recent years, methods to reduce the effects of seismic excitation on art objects have been studied in some papers. In particular in [4] a base isolation system constituted by HDRB devices has been studied to protect statues from seismic effects. The work of art has been modelled through an equivalent elastic beam and furthermore hysteretic behaviour for the rubber bearings has been adopted. A parametric analysis has been performed to evaluate the performance of the base isolation. In [5] the same problem has been analyzed, but the art object has been modelled as a symmetric rigid block simply supported on a base which is connected to ground by a visco-elastic device representing the passive control system. Impulsive and earthquake excitations have been considered in the analyses. The behaviour of a base isolated non-symmetric rigid block is the subject of the present paper. In the analysed model a rigid body, which represents works of art, is posed 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 type of excitations, mainly harmonic and seismic external excitations are considered. Exact nonlinear equations of motion are derived for the rocking phase and transition phase conditions are studied under the hypothesis of sliding prevented by special restraints, so that the rigid block is only allowed to rock or remain in a full-contact state with the isolated base. In order to point out the influence of parameters related to the eccentricity and the slenderness of the rigid block and related to the damping and the period of the base isolation system, a suitable nondimensionalization of the equations of motion is done and an extensive parametric analysis is performed via a direct numerical integration of equations of motion. Comparison between results obtained for isolated rigid block and non-isolated rigid block is also carried out to show the effectiveness of base isolation with respect 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 more effective for rigid bodies with geometrical parameters similar to those of real works of art. References [1] HW. Shenton, NP. Jones, Base excitation of rigid bodies. I: Formulation, Journal of Engineering Mechanics ASCE 1991; 117(10):2286-306. [2] RL. Boroscheck, D. Romo, Overturning criteria for non-anchored non-symmetric rigid bodies, 13th World Conference on Earthquake Engineering, Vancouver, 2004, B.C., Canada, August 1-6. [3] MS. Agbabian, FS. Masri, RL. Nigbor, WS. Ginel, Seismic damage mitigation concepts for art objects in museum. In: Proceeding of the 9th World Conference on Earthquake Engineering (Tokyo-Kyoto 1988), 1988,7,235-40. [4] F. Vestroni, S. Di Cinto, Base isolation for seismic protection of statues. In: Proceeding of the 12th World Conference on Earthquake Engineering, New Zeland, 2000. [5] I. Caliò, M. Marletta, Passive control of the seismic response of art objects, Engineering Structures 2003; 25:1009-1018.
Base isolation of a non-s ymmetric rigid block representing a monolithic art object
DI EGIDIO, ANGELO
2007-01-01
Abstract
In the past, many papers have been devoted to the study of the dynamic behaviour of rigid blocks. Focusing the attention on the behaviour of this system, subject to base excitations, in [1] a general bi-dimensional 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 museum under seismic excitation. In recent years, methods to reduce the effects of seismic excitation on art objects have been studied in some papers. In particular in [4] a base isolation system constituted by HDRB devices has been studied to protect statues from seismic effects. The work of art has been modelled through an equivalent elastic beam and furthermore hysteretic behaviour for the rubber bearings has been adopted. A parametric analysis has been performed to evaluate the performance of the base isolation. In [5] the same problem has been analyzed, but the art object has been modelled as a symmetric rigid block simply supported on a base which is connected to ground by a visco-elastic device representing the passive control system. Impulsive and earthquake excitations have been considered in the analyses. The behaviour of a base isolated non-symmetric rigid block is the subject of the present paper. In the analysed model a rigid body, which represents works of art, is posed 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 type of excitations, mainly harmonic and seismic external excitations are considered. Exact nonlinear equations of motion are derived for the rocking phase and transition phase conditions are studied under the hypothesis of sliding prevented by special restraints, so that the rigid block is only allowed to rock or remain in a full-contact state with the isolated base. In order to point out the influence of parameters related to the eccentricity and the slenderness of the rigid block and related to the damping and the period of the base isolation system, a suitable nondimensionalization of the equations of motion is done and an extensive parametric analysis is performed via a direct numerical integration of equations of motion. Comparison between results obtained for isolated rigid block and non-isolated rigid block is also carried out to show the effectiveness of base isolation with respect 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 more effective for rigid bodies with geometrical parameters similar to those of real works of art. References [1] HW. Shenton, NP. Jones, Base excitation of rigid bodies. I: Formulation, Journal of Engineering Mechanics ASCE 1991; 117(10):2286-306. [2] RL. Boroscheck, D. Romo, Overturning criteria for non-anchored non-symmetric rigid bodies, 13th World Conference on Earthquake Engineering, Vancouver, 2004, B.C., Canada, August 1-6. [3] MS. Agbabian, FS. Masri, RL. Nigbor, WS. Ginel, Seismic damage mitigation concepts for art objects in museum. In: Proceeding of the 9th World Conference on Earthquake Engineering (Tokyo-Kyoto 1988), 1988,7,235-40. [4] F. Vestroni, S. Di Cinto, Base isolation for seismic protection of statues. In: Proceeding of the 12th World Conference on Earthquake Engineering, New Zeland, 2000. [5] I. Caliò, M. Marletta, Passive control of the seismic response of art objects, Engineering Structures 2003; 25:1009-1018.Pubblicazioni consigliate
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