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1.
The highly complex rocking response of free-standing statues atop multi-drum columns underground excitation resulting in insuperable difficulties for obtaining reliable solution is reexamined analytically. This is achieved after simulating the columns by monolithic viscoelastic cantilevers having structural damping, based on experiments, equivalent to the energy dissipation due to impact and sliding of multi-drum columns. Subsequently, the conditions of rocking (overturning) instability of free-standing rigid blocks (representing the statues) after their uplift from the top surface of the laterally vibrating cantilevers, are established, including overturning with or without impact. Attention focuses on the minimum amplitude ground acceleration which leads to an escaped motion through the vanishing of the angular velocity and acceleration. Maximization of such a minimum amplitude (implying stabilization) of the rigid block is obtained by seeking the optimum combination of values of the slenderness ratio of the column and its height. Analytically derived results based on linearised analyses are in excellent agreement with those obtained via nonlinear numerical analyses. 相似文献
2.
The classical problem of rocking of a rigid, free-standing block to earthquake ground shaking containing distinct pulses, as is the case of near-fault earthquake motions, is revisited. A rectangular block resting on a rigid base is considered, subjected to a range of idealized single-lobe ground acceleration pulses expressed by a generalized function controlled by a single shape parameter. The problem is treated analytically in the realm of the linearized equations of motion under the assumption of slender block geometry and rocking without slipping. Peak rocking response and overturning criteria for different waveforms are presented in terms of dimensionless closed-form expressions and graphs. Two parameters are employed to this end: dimensionless pulse duration f (i.e., actual pulse duration times characteristic block frequency) and dimensionless uplift strength η (i.e., ratio of minimum required acceleration for initiation of uplift over peak pulse acceleration). The linearized response is compared analytically with the fully non-linear one using an ad hoc energy formulation leading to an approximate closed-form solution. It is shown that the non-linear equations of motion yield more stable response than their linearized counterparts. A brief discussion on scaling laws is provided. 相似文献
3.
An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification 
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下载免费PDF全文 This paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top‐heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non‐dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Marios Apostolou George Gazetas Evangelia Garini 《Soil Dynamics and Earthquake Engineering》2007,27(7):642-654
The rocking of rigid structures uplifting from their support under strong earthquake shaking is investigated. The structure is resting on the surface of either a rigid base or a linearly elastic continuum. A large-displacement approach is adopted to extract the governing equations of motion allowing for a rigorous calculation of the nonlinear response even under near-overturning conditions. Directivity-affected near-fault ground motions, idealized as Ricker wavelets or trigonometric pulses, are used as excitation. The conditions under which uplifting leads to large angles of rotation and eventually to overturning are investigated. A profoundly nonlinear rocking behavior is revealed for both rigid and elastic soil conditions. This geometrically nonlinear response is further amplified by unfavorable sequences of long-duration pulses in the excitation. Moreover, through the overturning response of a toppled tombstone, it is concluded that the practice of estimating ground accelerations from overturning observations is rather misleading and meaningless. 相似文献
5.
Rocking (overturning) instability analyses of rigid blocks based on the assumption that the friction between the block and the ground is sufficiently large to exclude the effect of sliding, are reconsidered by including the effect in question. Both modes of overturning instability – without impact and after one impact – are thoroughly discussed in connection with small sliding, whose value depends on the values of kinetic (dry) friction coefficient and the external frequency excitation. Using an energy approach the analytical derivation of the nonlinear differential equations of motion of free-standing rigid blocks under one-sine ground pulse including the effect of sliding, are comprehensively established. The serious difficulties in solving this problem on one hand the change of the kinetic friction coefficient during the motion and on the other hand the reliable evaluation of the actual friction effect when rocking is included, are effectively confronted. This is achieved through a reliable approximation of an equivalent (reduced) coefficient assuming that the major part of friction takes place from the initiation of motion and terminates shortly after the onset of rocking. In cases of slender blocks closed form solutions for overturning due to simultaneous rocking–sliding without or after one impact, are conveniently derived. Among other findings, it was explored that the single block in question for small values of the external frequency (long periods of excitation) the sliding effect is beneficial (stabilizing the block), while for large values of external frequency this effect is detrimental (destabilizing the block). 相似文献
6.
This investigation deals with the rocking response of rigid blocks subjected to earthquake ground motion. A numerical procedure and computer program are developed to solve the non-linear equations of motion governing the rocking motion of rigid blocks on a rigid base subjected to horizontal and vertical ground motion. The response results presented show that the response of the block is very sensitive to small changes in its size and slenderness ratio and to the details of ground motion. Systematic trends are not apparent: The stability of a block subjected to a particular ground motion does not necessarily increase monotonically with increasing size or decreasing slenderness ratio. Overturning of a block by a ground motion of particular intensity does not imply that the block will necessarily overturn under the action of more intense ground motion. In contrast, systematic trends are observed when the problem is studied from a probabilistic point of view with the ground motion modelled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increase in ground motion intensity, increase in slenderness ratio of the block and decrease in its size. It is concluded that probabilistic estimates of the intensity of ground shaking may be obtained from its observed effects on monuments, minarets, tombstones and other similar objects provided suitable data in sufficient quantity is available, and the estimates are based on probabilistic analyses of the rocking response of rigid blocks, considering their non-linear dynamic behaviour. 相似文献
7.
Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified ‘equivalent’ oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
8.
Nikos Gerolymos Marios Apostolot George Gazetas 《地震工程与工程振动(英文版)》2005,4(2):213-228
Under strong seismic excitation, a rigid block will uplift from its support and undergo rocking oscillations which may lead to （complete） overturning. Numerical and analytical solutions to this highly nonlinear vibration problem are first highlighted in the paper and then utilized to demonstrate how sensitive the overturning behavior is not only to the intensity and frequency content of the base motion, but also to thc presence of strong pulses, to their detailed sequence, and even to their asymnletry. Five idealised pulses capable of representing ＂rupture-directivity＂ and ＂fling＂ affected ground motions near the fault, are utilized to this end ： the one-cycle sinus, the one-cycle cosinus, the Ricker wavelet, the truncated （T）-Ricker wavelet, and the rectangular pulse ＂Overturning-Acceleration Amplification＂ and ＂Rotation＂ spectra are introduced and presented. Artificial neural network modeling is then developed as an alternative numerical solution. The neural network analysis leads to closed-form expressions for predicting the overturning failure or survival of a rigid block, as a function of its geometric properties and the characteristics of the excitation time history. The capability of the developed neural network modeling is validated through comparisons with the numerical solution. The derived analytical expressions could also serve as a tool for assessing the destructiveness of near-fault ground motions, for structures sensitive to rocking with foundation uplift. 相似文献
9.
A new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
Klaus-G. Hinzen 《Journal of Seismology》2012,16(4):797-814
Vertically oriented objects, such as tombstones, monuments, columns, and stone lanterns, are often observed to shift and rotate during earthquake ground motion. Such observations are usually limited to the mesoseismal zone. Whether near-field rotational ground motion components are necessary in addition to pure translational movements to explain the observed rotations is an open question. We summarize rotation data from seven earthquakes between 1925 and 2009 and perform analog and numeric rotation testing with vertically oriented objects. The free-rocking motion of a marble block on a sliding table is disturbed by a pulse in the direction orthogonal to the rocking motion. When the impulse is sufficiently strong and occurs at the ‘right’ moment, it induces significant rotation of the block. Numeric experiments of a free-rocking block show that the initiation of vertical block rotation by a cycloidal acceleration pulse applied orthogonal to the rocking axis depends on the amplitude of the pulse and its phase relation to the rocking cycle. Rotation occurs when the pulse acceleration exceeds the threshold necessary to provoke rocking of a resting block, and the rocking block approaches its equilibrium position. Experiments with blocks subjected to full 3D strong motion signals measured during the 2009 L’Aquila earthquake confirm the observations from the tests with analytic ground motions. Significant differences in the rotational behavior of a monolithic block and two stacked blocks exist. 相似文献
11.
A freestanding rigid block subjected to base excitation can exhibit complicated motion described by five response modes: rest, pure rocking, pure sliding, combined sliding-rocking, and free flight. Previous studies on the dynamics of a rocking block have assumed that the block does not interact with neighboring objects. However, there are many applications in which the block may start or come in contact with an adjacent boundary during its motion, for example, a bookcase or cabinet colliding with a partition wall in an earthquake. This paper investigates the dynamics of a sliding-rocking block considering impact with an adjacent wall. A model is developed in which the base and wall are assumed rigid, and impact is treated using the classical impulse and momentum principle. The model is verified by comparing its predictions in numerical simulations against those of an existing general-purpose rigid-body model in which impact is treated using a viscoelastic impact model. The developed model is used to investigate the effects of different parameters on the stability of a block subjected to analytical pulse excitations. It is found that wall placement (left or right) has a dominant effect on the shape of the overturning acceleration spectra for pulse excitations. In general, decreasing the gap distance, base friction coefficient, and wall coefficient of restitution enhance the stability of the block. Similar observations are made when evaluating the overturning probability of a block using earthquake floor motions. 相似文献
12.
Irving J. Oppenheim 《地震工程与结构动力学》1992,21(11):1005-1017
The dynamic response of an unreinforced masonry arch is examined, modelling the rigid body motions of arch segments under the influence of gravitational and inertial forces. This extends earlier studies of single rocking blocks, stacked blocks, and portal mechanisms of blocks; the masonry arch is analysed as another kinematic form of such a system. In this first effort a part-circular planar arch ring is studied and excitation is restricted to horizontal ground acceleration of the base. The mechanism kinematics are presented and the governing equation of motion is derived in non-linear form. The instantaneous form is determined for small rotations about the initial geometry and is used to study the conditions for the onset of mechanism motion. Possible failure conditions are posed and bounding principles are stated. One possible failure condition, direct overturning as a four-link mechanism, is studied for one simplified base motion. The results show that an arch geometry establishes good resistance to earthquake excitation in that ground acceleration must exceed a rather high threshold before any mechanism motion would develop; however, once that threshold has been passed the arch has relatively modest resistance before failure. Other possible failure conditions are discussed; one emerges from pounding effects between segments at impact, and another develops from sliding of blocks over one another as the internal forces (normal and tangential to the masonry joint) vary with the inertial forces. 相似文献
13.
The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning. 相似文献
14.
Dynamic analysis of stacked rigid blocks 总被引：1，自引：0，他引：1
Pol D. Spanos Panayiotis C. Roussis Nikolaos P. A. Politis 《Soil Dynamics and Earthquake Engineering》2001,21(7):472
The dynamic behavior of a structural model of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The derivation of the equations of motion accounts for the consecutive transition from one pattern of motion to another, each being governed by a set of highly nonlinear differential equations. The system behavior is described in terms of four possible patterns of response and impact between either the two blocks or the base block and the ground. The equations governing the rocking response of the system to horizontal and vertical ground accelerations are derived for each pattern, and an impact model is developed by conservation of angular momentum considerations. Numerical results are obtained by developing an ad hoc computational scheme that is capable of determining the response of the system under an arbitrary base excitation. This feature is demonstrated by using accelerograms from the Northridge, CA, 1994, earthquake. It is hoped that the two-blocks model used herein can facilitate the development of more sophisticated multi-block structural models. 相似文献
15.
为探讨自复位桥墩的地震反应,以某简支梁桥为工程背景,设计并制作了一个缩尺的模型桥梁。通过白噪声扫频获得了自复位桥墩的动力特性及其变化规律,选取El-Centro、Mexico和Chi-Chi强震记录作为地震动输入,进行振动台模型试验。试验记录了墩顶的加速度和位移反应,考查了地震动强度、频谱特性及预应力钢筋及其初始预加力对模型桥墩动力特性及摇摆反应的影响。试验结果表明:墩顶水平加速度反应随地震动强度及初始预加力的提高而增大,墩顶位移反应受地震动的强度、频谱特性及初始预加力大小影响较大。墩底提离面轻微损伤会明显降低体系的整体水平刚度,初始预加力则能提高体系整体水平刚度,桥墩的阻尼比随体系的水平刚度增大而减小。强震下自复位桥墩发生了预期的提离摇摆,震后墩底提离面出现轻微损伤,墩身无裂缝产生,结构具有良好的抗震及自复位性能。振动台试验结果验证已有文献的数值分析结论,振动台试验数据可用于数值模型校核或修正。 相似文献
16.
Dynamic response analysis of solitary flexible rocking bodies: modeling and behavior under pulse‐like ground excitation 下载免费PDF全文
下载免费PDF全文 Results obtained for rigid structures suggest that rocking can be used as seismic response modification strategy. However, actual structures are not rigid: structural elements where rocking is expected to occur are often slender and flexible. Modeling of the rocking motion and impact of flexible bodies is a challenging task. A non‐linear elastic viscously damped zero‐length spring rocking model, directly usable in conventional finite element software, is presented in this paper. The flexible rocking body is modeled using a conventional beam‐column element with distributed masses. This model is verified by comparing its pulse excitation response to the corresponding analytical solution and validated by overturning analysis of rocking blocks subjected to a recorded ground motion excitation. The rigid rocking block model provides a good approximation of the seismic response of solitary flexible columns designed to uplift when excited by pulse‐like ground motions. Guidance for development of rocking column models in ordinary finite element software is provided. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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为了研究近断层地震动速度脉冲及强竖向地震动对风机塔地震响应的影响,以某陆上风电场1.5 MW风机塔为研究对象开展了结构在水平向脉冲型地震动、水平向非脉冲型地震动、水平与竖向地震动组合3种地震输入工况的时程分析。通过3种工况下塔顶位移时程、加速度时程、塔底剪力、弯矩及轴力的对比分析发现:近断层速度脉冲对结构塔顶水平位移、塔顶水平加速度、塔底剪力与弯矩均影响显著;竖向地震动会加大结构的塔顶竖向加速度响应及塔底轴力响应;随着竖向与水平加速度峰值比增大,塔顶竖向加速度响应增大,最大轴力随着峰值比增大而增大,最小轴力随着峰值比增大而减小。此外,增量动力分析表明,采用自接触的有限元模型可以更真实地预测风机塔的失稳破坏机制。 相似文献
19.
Allowing structures to uplift modifies their seismic response; uplifting works as a mechanical fuse and limits the forces transmitted to the superstructure. However, engineers are generally reluctant to construct an unanchored structure because the system could overturn due to lacking redundancy. Using a safety factor for the design of a flat rocking foundation, ie, designing it wider, goes against the main idea of this seismic modification method as the force demand for the structure increases. We propose to extend the flat base of a rocking block with curved extensions to better protect the block from overturning, yet not prevent its uplifting. After investigating the seismic response of such rocking blocks, we extend the study to investigate the seismic response of rolling and rocking frames comprising columns with curved base extensions. The equations of motion are derived, time history analyses are performed, and rocking spectra are constructed. We draw two important conclusions: (a) the response of a class of rocking oscillators with curved base extensions is equivalent to the response of a flat-base rocking oscillators of the same slenderness, yet larger size; (b) the rotation demand on two negative stiffness rocking and rolling oscillators with the same uplifting acceleration and the same size is roughly the same as long as the rocking oscillators are not close to overturning. The above findings can serve as a basis for the rational seismic design of structures supported on rocking columns with curved bases, a system that has been used since the 1960s. 相似文献