"The study of the behaviour of rigid block had a continuous evolution in time, starting from the first simplified models [1]. In latest years, the complexity of the models of rigid blocks has been widely increased and different phenomena associated to the motion of rigid bodies have been discovered. However only few three-dimensional models, mainly dedicated to bodies with circular shape have been studied; formulations are mainly dedicated to circular shaped tanks and the interaction with their inner liquids. The same authors of the present work extensively investigated the behaviour of the rigid block, representative of a monolithic object of art, with a two-dimensional model, both in the case of free-standing rigid block and in the case of isolated rigid body with different kinds of constraint [2, 3]. . In the present paper a three-dimensional model has been developed: the rigid body has been taken as non-symmetric and rectangular based, thus the rocking can occur on one edge or on a corner, according to the direction of the initial input. The rigid body is assumed able only to rock since its slenderness does not allow occurrence of sliding between the base and the ground. Exact nonlinear equations of motion describing the rocking motion are obtained from the general balance principle; starting, ending and impact conditions of the motion are found. Impacts have been modelled taking into account the conservation of the angular momentum; however also the case of perfect elastic impacts, where the conservation of the mechanical energy holds, have been taken into account. . The effects of a pulse-type excitation, which approximates the leading kinematic characteristics of near source ground motions, have been studied as in [4]. Several analyses have been carried out in order to highlight the influence of different geometrical parameters in the motion. The direction of the input has been varied continuously to analyse the effects of the eccentricity and of the slenderness of the rigid body on the minimum acceleration amplitude that needs to overturn the rigid block. Great attention has been also devoted to the role of the period of the impulsive excitation. Preliminary analyses for near-square based non-symmetric bodies (human-like statues) have been conducted to verify the existence of particular directions of the input, where the amplitude of the overturning excitation is lower than the one obtained for a classical two-dimensional model. This phenomenon is strictly related to the eccentricity of the body in the direction orthogonal to the plane of the two-dimensional models.. Analyses have been done using the program Mathematica as main ambient and Fortran language for the numerical integration where particular attention has been devoted to the choice of the algorithm of integration and of the minimum time step. Currently the validity and the results of the model are going to be checked.. . References. [1] HW. Shenton and NP. Jones. Base excitation of rigid bodies. I: Formulation, Journal of Engineering Mechanics, 117(10), 2286-306, 1991.. [2] A. Di Egidio and A. Contento. Base isolation of sliding-socking non-symmetric rigid blocks subjected to impulsive and seismic excitations. Engineering Structures, 31, 2723-2734, 2009.. [3] A. Di Egidio and A. Contento. Seismic response of a non-symmetric rigid block on a constrained oscillating base. Engineering Structures, 32, 3028-3039, 2010.. [4] Makris N, Black CJ. Dimensional analysis of bilinear oscillators under pulse-type Excitations. Journal of Engineering Mechanics (ASCE), 130(9), 1019-1031, 2004."

The dynamics of three-dimension al non-symmetric rigid bodies subject to one-sine pulse excitations

ZULLI, Daniele;CONTENTO, ALESSANDRO;DI EGIDIO, ANGELO
2011-01-01

Abstract

"The study of the behaviour of rigid block had a continuous evolution in time, starting from the first simplified models [1]. In latest years, the complexity of the models of rigid blocks has been widely increased and different phenomena associated to the motion of rigid bodies have been discovered. However only few three-dimensional models, mainly dedicated to bodies with circular shape have been studied; formulations are mainly dedicated to circular shaped tanks and the interaction with their inner liquids. The same authors of the present work extensively investigated the behaviour of the rigid block, representative of a monolithic object of art, with a two-dimensional model, both in the case of free-standing rigid block and in the case of isolated rigid body with different kinds of constraint [2, 3]. . In the present paper a three-dimensional model has been developed: the rigid body has been taken as non-symmetric and rectangular based, thus the rocking can occur on one edge or on a corner, according to the direction of the initial input. The rigid body is assumed able only to rock since its slenderness does not allow occurrence of sliding between the base and the ground. Exact nonlinear equations of motion describing the rocking motion are obtained from the general balance principle; starting, ending and impact conditions of the motion are found. Impacts have been modelled taking into account the conservation of the angular momentum; however also the case of perfect elastic impacts, where the conservation of the mechanical energy holds, have been taken into account. . The effects of a pulse-type excitation, which approximates the leading kinematic characteristics of near source ground motions, have been studied as in [4]. Several analyses have been carried out in order to highlight the influence of different geometrical parameters in the motion. The direction of the input has been varied continuously to analyse the effects of the eccentricity and of the slenderness of the rigid body on the minimum acceleration amplitude that needs to overturn the rigid block. Great attention has been also devoted to the role of the period of the impulsive excitation. Preliminary analyses for near-square based non-symmetric bodies (human-like statues) have been conducted to verify the existence of particular directions of the input, where the amplitude of the overturning excitation is lower than the one obtained for a classical two-dimensional model. This phenomenon is strictly related to the eccentricity of the body in the direction orthogonal to the plane of the two-dimensional models.. Analyses have been done using the program Mathematica as main ambient and Fortran language for the numerical integration where particular attention has been devoted to the choice of the algorithm of integration and of the minimum time step. Currently the validity and the results of the model are going to be checked.. . References. [1] HW. Shenton and NP. Jones. Base excitation of rigid bodies. I: Formulation, Journal of Engineering Mechanics, 117(10), 2286-306, 1991.. [2] A. Di Egidio and A. Contento. Base isolation of sliding-socking non-symmetric rigid blocks subjected to impulsive and seismic excitations. Engineering Structures, 31, 2723-2734, 2009.. [3] A. Di Egidio and A. Contento. Seismic response of a non-symmetric rigid block on a constrained oscillating base. Engineering Structures, 32, 3028-3039, 2010.. [4] Makris N, Black CJ. Dimensional analysis of bilinear oscillators under pulse-type Excitations. Journal of Engineering Mechanics (ASCE), 130(9), 1019-1031, 2004."
978-1-905088-47-8
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/89355
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