• 한국안전학회지
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• 제15권1호
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• pp.1-10
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• 2000

This paper deals with rocking response behavior of rigid block structure subjected to horizontal excitation. A strict consideration of impact and sliding between the block and base is essential to investigate the rocking vibration characteristics because the rocking behavior were greatly influenced by the impact and sliding motion. Therefore, not only restitution coefficient between the block and base but also the energy dissipation rate which is associated with sliding motion, and the static and kinetic friction coefficient between those should be included in the modeling of rocking system. The analytic program was developed to be able to simulate the experimental responses of the block subjected to horizontal sinusoidal excitations. By using this program, rocking responses were numerically calculated by the nonlinear equations for rocking system. From the response simulation and rocking vibration experiment, the following results were obtained. The rocking responses are affected by the impact motion due to energy dissipation and friction and provide very complex behavior. The toppling condition of the block is also influenced by the impact motion and sliding motion.

• 대한기계학회논문집A
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• 제27권6호
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• pp.879-889
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• 2003

This research deals with the nonlinearities of rocking vibration associated with impact and sliding on the rocking behavior of rigid block under two dimensional sinusoidal excitation which has different frequencies in two excitation direction. The varied excitation direction influences not only the rocking response but also the sliding motion and the rocking response shape. Chaotic responses are observed in wider excitation amplitude region, when the frequencies in each excitation direction are different. The complex behavior of chaotic response, in the phase space, is related with the trajectory of base excitation and sliding motion.

• Journal of Mechanical Science and Technology
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• 제16권9호
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• pp.1040-1053
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• 2002

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2010년도 추계 학술발표회 3차
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• pp.61-65
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• 2010

The performance of slopes during earthquake is often accessed in terms of permanent deformation. In the assessment of permanent deformation, Newmark-type rigid block analysis is widely used. Original Newmark-type block approach, however, assumes the potential sliding mass to be rigid, and has been criticized to be potentially unconservative. The paper reviews analytically the impact of this noncompliance assumption on computed permanent deformations. The results indicate that there is a simple criterion that can be used to determine the level of conservativeness of the rigid block approach in cases of gently-sloping slip surfaces and retaining walls.

• Structural Engineering and Mechanics
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• 제9권1호
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• pp.1-16
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• 2000

To study the dynamic response of a rigid block standing unrestrained on a rigid foundation which shakes horizontally, four modes of motion can be identified, i.e., rest, slide, rock, and slide and rock. The occurrence of each of these four modes and the transition between any two modes depend on the parametric values specified, the initial conditions, and the magnitude of ground acceleration. In this paper, a general two-dimensional theory is presented for dealing with the various modes of a free-standing rigid block, considering in particular the impact occurring during the rocking motion. Through selection of proper values for the system parameters, the occurrence of each of the four modes and the transition between different modes are demonstrated in the numerical examples.

• 한국지반공학회논문집
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• 제23권12호
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• pp.117-124
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• 2007

지진으로 인해 사면에 발생한 영구적 변형 계산시 고려된 공간평균과 유연도의 영향을 조사하였다. 현재 변위계산에는 Newmark이 제안한 강체블럭해석기법이 이 기법의 효율적인 계산능력으로 인해 광범하게 사용되고 있다. 그러나 이 해석기법은 지진응답해석과 변위해석을 별도로 수행하는 소위 분리해석법을 채택하고 있다. 당초의 Newmark 해석기법은 활동토사를 강성체로 가정했으며 이로 인하여 비보수적 결과가 도출될 수 있다는 비판을 받아왔다. 본 논문은 Newmark-형식의 해석에서 강성체 가정의 영향을 검토하였다. 활동토사에 작용하는 지진하중의 전체 효과를 공간평균기법을 사용하여 평가하였으며 그 결과를 주파수 영역에서 분석하였다. 해석결과로부터 활동토사의 유연도 수준을 결정하는 경우 사용할 수 있는 단순한 지표를 제시하였다.

• 한국안전학회지
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• 제14권4호
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• pp.3-12
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• 1999

This research concentrates on the influence of non-linearities associated with impact for the nonlinear rocking behavior of rigid block subjected to one dimensional sinusoidal excitation of horizontal direction. The transition of two governing rocking equations, the abrupt reduction in the kinetic energy associated with impact, and sliding motion of block. In this study, two type of rocking vibration system are considered. One is the undamped rocking vibration system, disregarding energy dissipation at impact and the other is the damped rocking system, including energy dissipation and sliding motion. The response analysis using non-dimensional rocking equation is carried out for the change of excitation parameters and friction coefficient. The chaos responses were discovered in the wide response region, particularly, for the case of high excitation amplitude and their chaos characteristics were examined by the time history, Poincare map, power spectra and Lyapunov Exponent of rocking responses. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map. The bifurcation diagram and Poincare map were shown to be effective in order to understand chaos of rocking system.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2000년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2000
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• pp.448-454
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• 2000

Piled multi-block system has been frequently adopted in the historic structures or monuments of cultural heritage. It is well known that such a structural system is very vulnerable to the earthquake shaking. If the structure is of slender type, then it may experience overturning at very low level intensity of ground shaking. One of the methods used to protect such structures from earthquake is seismic isolation system. But the behavior of multi-block systems mounted on the isolated basis is not well understood yet. In this paper we investigate the dynamic behavior of single slender rigid block mounted on the three different isolation systems, i.e., P-F system, FPS and LRB system. Sliding at the isolation interface of P-F system and FPS is formulated based on Coulomb friction. The mounted single block is assumed undergoing rocking or sticking only. Impacting of a single block is described using distinct element method (DEM). Free vibrations due to a prescribed initial conditions are studied. Responses to the harmonic excitation and earthquake motions are calculated

• Structural Engineering and Mechanics
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• 제23권3호
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• pp.293-308
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• 2006

This paper presents a complete and consistent formulation to study the seismic response of a free-standing ship supported by an arrangement of n keel blocks which are all located in a dry dock. It is considered that the foundation of the system is subjected to both horizontal and vertical in plane excitation. The motion of the system is classified in eight different modes which are Rest (relative), Sliding of keel blocks, Rocking of keel blocks, Sliding of the ship, Sliding of both keel blocks and the ship, Sliding and rocking of keel blocks, Rocking of keel blocks with sliding of the ship, and finally Sliding and rocking of keel blocks accompanied with sliding of the ship. For each mode of motion the governing equations are derived, and transition conditions between different modes are also defined. This formulation is based on a number of fundamental assumptions which are 2D idealization for motion of the system, considering keel blocks as the rigid ones and the ship as a massive rigid block too, allowing the similar motion for all keel blocks, and supposing frictional nature for transmitted forces between contacted parts. Also, the rocking of the ship is not likely to take place, and the complete ship separation from keel blocks or separation of keel blocks from the base is considered as one of the failure mode in the system. The formulation presented in this paper can be used in its entirety or in part, and they are suitable for investigation of generalized response using suitable analytical, or conducting a time-history sensitivity analysis.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1991년도 봄 학술발표회 논문집
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• pp.84-90
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• 1991

Underground structures usually consist of rock masses or concretes which can be cracked or have cracks. This study aims to develop an analysis program which can deal with the effect of discontinuous behavior due to those cracks using the block theory. It is assumed that rock masses form blocks along the discontinuity lines, and deformation within the block is relatively small. The behavior of discontinuity plane of the structures is divided into sliding along the discontinuity plane. separation of discontinuity by tensile force, and degradation of asperity angle of discontinuity plane by external force with sliding of rock Basses. These behaviors are implemented using constitutive relation and relevent load-displacement relation defined through normal and shear stiffnesses. Time varying displacements and block velocities are calculated by explicit time stepping algorithm. The effect of rock supports including rockbolts is also considered, and the tending effects which occurs in relatively thin lining is also considered.