Dynamic analysis of sliding structures with unsynchronized support motions

The dynamic analysis of sliding structures is complicated due to the presence of friction. Synchronization of the kinematics of all the isolation bearings is often granted to simplify the task. This, however, may lead to inaccurate prediction of the structural responses under certain circumstances. Stepped structures or continuous bridges with seismic isolation are notable examples where unsynchronized bearing motions are expected. In this paper, a logically simple and numerically efficient procedure is proposed to solve the dynamic problem of sliding systems with unsynchronized support motions. The motion equations for the sliding and non‐sliding modes of the isolated structure are unified into a single equation that is represented as a difference equation in a discrete‐time state‐space form and the base shear forces between the sliding interfaces can be determined through simple matrix algebraic analysis. The responses of the sliding structure can be obtained recursively from the discrete‐time version of the motion equation with constant integration time step even during the transitions between the non‐sliding and sliding phases. Therefore, both accuracy and efficiency in the dynamic analysis of the highly non‐linear system can be enhanced to a large extent. Rigorous assessment of seismic structures with unsynchronized support motions has been carried out for both a stepped structure and a continuous bridge. Effectiveness of friction pendulum bearings for earthquake protection of such structures has been verified. Moreover, evident unsynchronized sliding motions of the friction bearings have been observed, confirming the necessity to deal with each of the bearings independently in the analytical model. Copyright © 2000 John Wiley & Sons, Ltd.     

Time domain identification of hybrid base isolation systems using free vibration tests

A procedure for the dynamic identification of the physical parameters of coupled base isolation systems is developed in the time domain. The isolation systems considered include high damping rubber bearings (HDRB) and low friction sliding bearings (LFSB). A bi‐linear hysteretic model is used alone or in parallel with a viscous damper to describe the behavior of the HDRB system, while a constant Coulomb friction device is used to model the LFSB system. After deriving the analytical dynamical solution for the coupled system under an imposed initial displacement, this is used in combination with the least‐squares method and an iterative procedure to identify the physical parameters of a given base isolation system belonging to the class described by the models considered. Performance and limitations of the proposed procedure are highlighted by numerical applications. The procedure is then applied to a real base isolation system using data from static and dynamic tests performed on a building at Solarino. The results of the proposed identification procedure have been compared to available laboratory data and the agreement is within ±10%. However, the need for improvement both in models and testing procedures also emerges from the numerical applications and results obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response analysis of bridges isolated with friction pendulum bearings

A systematic method is developed for the dynamic analysis of the structures with sliding isolation which is a highly non-linear dynamic problem. According to the proposed method, a unified motion equation can be adapted for both stick and slip modes of the system. Unlike the traditional methods by which the integration interval has to be chopped into infinitesimal pieces during the transition of sliding and non-sliding modes, the integration interval remains constant throughout the whole process of the dynamic analysis by the proposed method so that accuracy and efficiency in the analysis of the non-linear system can be enhanced to a large extent. Moreover, the proposed method is general enough to be adapted for the analysis of the structures with multiple sliding isolators undergoing independent motion conditions simultaneously. The superiority of the proposed method for the analysis of sliding supported structures is verified by a three-span continuous bridge subjected to harmonic motions and real earthquakes. In addition, the side effect of excessive displacement of the superstructure induced by the sliding isolation is eliminated by replacing one of the roller supports on the abutments with hinge support. Therefore, both reductions in the forces of the substructure and the displacements of the superstructure can be achieved simultaneously. © 1998 John Wiley & Sons, Ltd.     

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.     

Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability‐based design (SRBD)

The paper deals with the seismic reliability of elastic structural systems equipped with friction pendulum isolators (friction pendulum system). The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the friction pendulum system device behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. With reference to medium soil condition, the uncertainty in the seismic inputs is taken into account by considering a set of artificial records, obtained through Monte Carlo simulations within the power spectral density method, with different frequency contents and characteristics depending on the soil dynamic parameters and scaled to increasing intensity levels. The sliding friction coefficient at large velocity is also considered as random variable modeled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities exceeding different limit states related to both r.c. superstructure and isolation level defining the seismic fragility curves through an extensive parametric study carried out for different structural system properties. Finally, considering the seismic hazard curves related to a site near L'Aquila (Italy), the seismic reliability of the r.c. superstructure systems is evaluated, and seismic reliability‐based design abacuses are derived with the aim to define the radius in plan of the friction pendulum devices in function of the structural properties and reliability level expected. Copyright © 2016 John Wiley & Sons, Ltd.     

Shake table testing on restoring capability of double concave friction pendulum seismic isolation systems

After an earthquake, non‐negligible residual displacements may affect the serviceability of a base isolated structure, if the isolation system does not possess a good restoring capability. The permanent offset does not affect the performance unless the design is problematic for utilities, also considering possible concerns related to the maintenance of the devices. Starting from experimental and analytical results of previous studies, the restoring capability of Double Concave Friction Pendulum bearings is investigated in this paper. A simplified design suggestion for the estimation of maximum expected residual displacements for currently used friction pendulum systems is then validated. The study is based on controlled‐displacement and seismic input experiments, both performed under unidirectional motion. Several shaking table tests have been carried out on a three‐dimensional isolated specimen structure. The same sequence of seismic inputs was applied considering three different conditions of sliding surfaces corresponding to low, medium and high friction. The accumulation of residual displacements is also investigated by means of nonlinear dynamic analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

新型滑移隔震结构模型的振动台试验研究

利用实体软钢棒作为消能限位装置,将一种摩擦性能优良的二硫化钼材料作为隔震支座的滑移材料,提出并制作了一种可以应用于框架结构既能隔震又可以消能的新型摩擦滑移隔震装置。探讨了其设计方法和应用方法,并对安装了该新型摩擦滑移隔震装置的一相似比为1:5的5层框架结构模型进行了振动台试验,测试了框架结构在单向地震波作用下的地震反应规律,分析了摩擦滑移隔震结构的加速度反应、层间剪力反应、隔震层滑移量及隔震层剪力的变化规律。结果表明:一般情况下当设防烈度为8度,Ⅱ类场地时,该隔震结构的加速度响应可降低50%左右,层间剪力响应可降低50%左右,减震效果比较明显。另外,只要确定合理的构造方案和实施方案,这种新型摩擦滑移隔震装置就能满足框架结构的隔震减震要求,可应用于实际工程结构中。     

基于自由振动响应的基础隔震建筑减震能力评估方法研究

目前国内外已修建完成了大量隔震建筑,但仅有少量经受了地震检验,绝大部分隔震结构减震能力能否达到设计目标尚存疑问.本文针对基础隔震建筑,提出了一种基于自由振动响应的减震能力评估方法.首先,对隔震建筑进行多级幅值初位移自由振动原位试验,获取结构的抗震能力曲线;其次,根据地震反应谱建立地震需求曲面,进而确定隔震结构性能点;最...     

Non-linear seismic response analysis of soil-structure interaction systems

This paper presents an effective analysis procedure for the dynamic soil-structure interaction problem considering not only the sliding and separation phenomena but also the non-linear behaviour of soil by the finite element method. Soil is assumed to be an elasto-plastic material and the contact surface between the soil and structure is modelled by the joint element. The load transfer method is adopted to carry out dynamic non-linear response analysis. The method is applied to the response analysis of a nuclear reactor building resting on the ground surface. The effects of non-linear behaviour of soil on the safety against sliding of the structure are examined. The numerical computations reveal the following results: that the non-linear behaviour of soil reduces the response of the system and the magnitude of sliding of the structure, and that the safety against sliding obtained by the proposed method is higher than the safety obtained by classical methods. This implies the possibility of a more rational and economical design of large structures; it can be said that the proposed method provides useful information for the stability analysis of important and large structures.     

VFPI: an isolation device for aseismic design

Sliding isolators with curved surface are effective base isolation systems incorporating isolation, energy dissipation and restoring mechanism in one unit. However, practical utility of these systems, such as friction pendulum system (FPS) has limitations due to constant isolator period and restoring force characteristics. A new isolator called the variable frequency pendulum isolator (VFPI) that overcomes these limitations while retaining all the advantages has been described in this paper. VFPI has oscillation frequency decreasing with sliding displacement, and the restoring force has an upper bound so that the force transmitted to the structure is limited. The mathematical formulations for the response of a SDOF structure and energy balance are also described. Parametric studies have been carried out to critically examine the behaviour of structures isolated with VFPI, FPS and PF system. From these investigations, it is concluded that the VFPI combines the advantages of both FPS and PF system, without their undesirable properties. The VFPI performance is also found to be stable during low‐intensity excitations, and fail‐safe during high‐intensity excitations. VFPI is found to exhibit robust performance for a wide range of structure, isolator and ground motion characteristics clearly demonstrating its advantages. Copyright © 2000 John Wiley & Sons, Ltd.     

A modal procedure for seismic analysis of non-linear base-isolated multistorey structures

A modal procedure for non-linear analysis of multistorey structures with high-damping base-isolation systems was proposed. Two different isolation devices were considered in the analysis: an high-damping laminated rubber bearing and a lead-rubber bearing. Starting from deformational properties verified by tests, the isolation systems were characterized using three different analytical models (an Elastic Viscous, a Bilinear Hysteretic and a Wen's Model) with parameters depending from maximum lateral strain. After non-linear modelling of isolation and lateral-force-resisting systems, the effects of material non-linearities were considered as pseudo-forces applied to the equivalent linear system (Pseudo-Force Method) and the formally linearized equations of motion were uncoupled by the transformation defined by the complex mode shapes. The modal responses were finally obtained with an extension of Nigam–Jennings technique to non-linear and non-classically damped systems, in conjunction with an iterative technique searching for non-linear contributions satisfying equations of motion and constitutive laws. Since the properties of the isolated structure usually change with maximun lateral strain of isolation bearings, the integration of a new set of governing equations was required for each design-displacement value. The procedure proposed was described in detail and then applied for the determination of modal and total seismic responses in some real cases. At first, a very good agreement between non-linear responses obtained with the proposed mode superposition and with a direct integration method was observed. Then a comparison of results obtained with the three different analytical models of the isolation bearings was carried out. At last, the exact modal response obtained with analytical models depending from the design displacement of the isolation bearings was compared with two different approximated solutions, evaluated using mode shapes and isolation properties, respectively, calculated under simplified hypothesis.© 1998 John Wiley & Sons, Ltd.     

Multiple‐slider surfaces bearing for seismic retrofitting of frame structures with soft first stories

A new isolation interface is proposed in this study to retrofit existing buildings with inadequate soft stories as well as new structures to be constructed with soft first story intended for architectural or functional purposes. The seismic interface is an assembly of bearings set in parallel on the top of the first story columns: the multiple‐slider bearings and rubber bearings. The multiple‐slider bearing is a simple sliding device consisting of one horizontal and two inclined plane sliding surfaces based on polytetrafluoroethylene and highly polished stainless steel interface at both ends set in series. A numerical example of a five‐story reinforced concrete shear frame with soft first story is considered and analyzed to demonstrate the efficiency of the proposed isolation system in reducing the ductility demand and damage in the structure while maintaining the superstructure above the bearings to behave nearly in the elastic range with controlled bearing displacement. Comparative study with the conventional system as well as various isolation systems such as rubber bearing interface and resilient sliding isolation is carried out. Moreover, an optimum design procedure for the multiple‐slider bearing is proposed through the trade‐off between the maximum bearing displacement and the first story ductility demand ratio. The results of extensive numerical analysis verify the effectiveness of the multiple‐slider bearing in minimizing the damage from earthquake and protecting the soft first story from excessively large ductility demand. Copyright © 2012 John Wiley & Sons, Ltd.     

Component and shaking table tests for full‐scale multiple friction pendulum system

The use of base isolation in developed countries including the U.S. and Japan has already been recognized as a very effective method for upgrading the seismic resistance of structures. In this study, an advanced base‐isolation system called the multiple friction pendulum system (MFPS) is investigated to understand its performance on seismic mitigation through full‐scale component and shaking table tests. The component tests of the advanced Teflon composite coated on the sliding surface show that the friction coefficient of the lubricant material is a function of the sliding velocity in the range of 0.03–0.12. The experimental results also indicate that there were no signs of degradation of the sliding interface observed after 2000 cycles of sliding displacements. A full‐scale MFPS isolator under a vertically compressive load of 8830 KN (900 tf) and horizontally cyclic displacements was tested in order to assess the feasibility of the MFPS isolator for its practical use. After 248 cycles of horizontal displacement reversals, the behaviour of the base isolator was almost identical to its behaviour during the first few cycles. The experimental results of the shaking table tests of a full‐scale steel structure isolated with MFPS isolators show that the MFPS device can isolate seismic transmitted energy effectively under soft‐soil‐deposit site earthquakes with long predominant periods as well as strong ground motions with short predominant periods. These test results demonstrate that the MFPS isolator possesses excellent durability and outstanding earthquake‐proof capability. Furthermore, the numerical results show that the mathematical model proposed in this study can well predict the seismic responses of a structure isolated with MFPS isolators. Copyright © 2006 John Wiley & Sons, Ltd.     

Theory and experimental study for sliding isolators with variable curvature

Because a conventional isolation system with constant isolation frequency is usually a long‐period dynamic system, its seismic response is likely to be amplified in earthquakes with strong long‐period wave components, such as near‐fault ground motions. Seismic isolators with variable mechanical properties may provide a promising solution to alleviate this problem. To this end, in this work sliding isolators with variable curvature (SIVC) were studied experimentally. An SIVC isolator is similar to a friction pendulum system (FPS) isolator, except that its sliding surface has variable curvature rather being spherical. As a result, the SIVC's isolation stiffness that is proportional to the curvature becomes a function of the isolator displacement. By appropriately designing the geometry of the sliding surface, the SIVC is able to possess favorable hysteretic behavior. In order to prove the applicability of the SIVC concept, several prototype SIVC isolators, whose sliding surfaces are defined by a sixth‐order polynomial function, were fabricated and tested in this study. A cyclic element test on the prototype SIVC isolators and a shaking table test on an SIVC isolated steel frame were all conducted. The results of both tests have verified that the prototype SIVC isolators do indeed have the hysteretic property of variable stiffness as prescribed by the derived formulas in this study. Moreover, it is also demonstrated that the proposed SIVC is able to effectively reduce the isolator drift in a near‐fault earthquake with strong long‐period components, as compared with that of an FPS system with the same friction coefficient. Copyright © 2011 John Wiley & Sons, Ltd.     

Improved design of sliding mode control for civil structures with saturation problem

A systematic and improved design procedure for sliding mode control (SMC) of seismically excited civil structures with saturation problem is provided in this paper. In order to restrict the control force to a certain level, a procedure for determining the upper limits of the control forces for single or multiple control units is proposed based on the design response spectrum of external loads. Further, an efficient procedure using the LQR method for determining sliding surfaces appropriate for different controller types is provided through the parametric evaluation of the dynamic characteristics of sliding surfaces in terms of SMC controller performance. Finally, a systematic design procedure for SMC required to achieve a given performance level is provided and its effectiveness is verified by applying it to multi‐degree‐of‐freedom (MDOF) systems. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic isolation of buildings with sliding concave foundation (SCF)

In this paper, a new base isolation system, namely the sliding concave foundation (SCF), is introduced and the behaviour of the buildings using such a system is theoretically investigated. A building supported on the new system behaves like a compound pendulum during seismic excitation. The pendulum behaviour accompanied by the large radius of foundation curvature shifts the fundamental period of the system to a high value (e.g. more than 8sec), in a frequency range where none of the previously recorded earthquakes had considerable energy. This results in a large decrease in the structural responses. Since small friction forces are essential on the contact surfaces, PTFE sheets can be used as sliding surfaces. Although the pure frictional sliding systems have the same efficiency as the SCF, in reducing the responses of the superstructure, the main advantage of the new system is a significant decrease in sliding displacement. The performance of the SCF subjected to a number of harmonic and non‐harmonic base excitations is studied and its ability to reduce the structural responses is examined. Some numerical examples are solved for a single‐degree‐of‐freedom (SDOF) structure and the responses are compared with the responses of the same SDOF structure on a fixed base or a pure frictional sliding support system. The comparisons confirm the effectiveness of the new system. Copyright © 2002 John Wiley & Sons, Ltd.     

层间滑移隔震结构地震作用有限元分析

将二硫化钼作为摩擦材料设计出一种带限位器的滑移隔震支座。根据多层框架结构变形的特点,给出适用于滑移框架隔震结构的计算模型,推导出层间滑移隔震结构的运动方程。运用SAP2000有限元软件建立一层间滑移框架隔震结构的有限元模型,对比分析El Centro地震波下摩擦系数和隔震层位置不同时隔震结构的地震反应。结果表明,上部结构的动力反应随摩擦系数的增加而不断增大,滑移隔震结构的减震效果逐渐减弱,但隔震层的滑移量却在不断减小;摩擦系数的选取应综合考虑减震效果和隔震层滑移量两个因素。随着隔震层的增高,结构的加速度反应和层间位移反应整体上呈增大趋势,隔震效果不断减弱,且隔震层的加速度值下部层比上部层要大得多,一层隔震和三层隔震时的变形主要集中于隔震层,而五层隔震时结构层间位移并未出现突变,说明隔震层设置在较高位置处对结构体系的影响较小。     

DYNAMIC RESPONSE OF EQUIPMENT IN STRUCTURES WITH SLIDING SUPPORT

The dynamic behaviour of a single degree-of-freedom (DOF) equipment mounted on a sliding primary structures subjected to harmonic and earthquake ground motions is studied numerically. To deal with the discontinuity nature of sliding structural systems, in this work the fictitious spring model is adopted. With the problem formulated in a state space form, an incremental numerical scheme capable of dealing with multi-DOF sliding structural systems is proposed for solving the time history responses. Numerical examples excited by harmonic and real earthquake ground motions are considered in order to study the following three effects: (1)the variation of the frictional coefficient of the sliding support, (2)subharmonic resonance and (3)effect of tuning (i.e. when the frequency of the equipment is coincident with or close to the fundamental frequency of the primary structure) on the mounted equipment. The dynamic characteristics of the mounted equipment are highlighted in the analysis of the numerical examples. © 1997 by John Wiley & Sons, Ltd.     

Seismic fragility of structures isolated by single concave sliding devices for different soil conditions

This study deals with the seismic fragility of elastic structural systems equipped with single concave sliding (friction pendulum system (FPS)) isolators considering different soil conditions. The behavior of these systems is analyzed by employing a two-degree-of-freedom model, whereas the FPS response is described by means of a velocity-dependent model. The uncertainty in the seismic inputs is taken into account by considering artificial seismic excitations modelled as timemodulated filtered Gaussian white noise random processes of different intensity within the power spectral density method. In particular, the filter parameters, which control the frequency content of the random excitations, are calibrated to describe stiff, medium and soft soil conditions. The sliding friction coefficient at large velocity is also considered as a random variable modelled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities of exceeding different limit states related to both the reinforced concrete (RC) superstructure and isolation level, defining the seismic fragility curves within an extensive parametric study carried out for different structural system properties and soil conditions. The abovementioned seismic fragility curves are useful to evaluate the seismic reliability of base-isolated elastic systems equipped with FPS and located in any site for any soil condition.     

Shaking table tests of a reinforced concrete bridge pier with a low-cost sliding pendulum system

After the occurrence of various destructive earthquakes in Japan, extensive efforts have been made to improve the seismic performance of bridges. Although improvements to the ductile capacities of reinforced concrete (RC) bridge piers have been developed over the past few decades, seismic resilience has not been adequately ensured. Simple ductile structures are not robust and exhibit a certain level of damage under extremely strong earthquakes, leading to large residual displacements and higher repair costs, which incur in societies with less-effective disaster response and recovery measures. To ensure the seismic resilience of bridges, it is necessary to continue developing the seismic design methodology of RC bridges by exploring new concepts while avoiding the use of expensive materials. Therefore, to maximize the postevent operability, a novel RC bridge pier with a low-cost sliding pendulum system is proposed. The seismic force is reduced as the upper component moves along a concave sliding surface atop the lower component of the RC bridge pier. No replaceable seismic devices are included to lengthen the natural period; only conventional concrete and steel are used to achieve low-cost design solutions. The seismic performance was evaluated through unidirectional shaking table tests. The experimental results demonstrated a reduction in the shear force transmitted to the substructure, and the residual displacement decreased by establishing an adequate radius of the sliding surface. Finally, a nonlinear dynamic analysis was performed to estimate the seismic response of the proposed RC bridge pier.