Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems

The tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass‐amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base‐isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc‐Wen hysteretic model, representative of friction pendulum and of lead‐rubber‐bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai‐Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy‐based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well‐known shortcomings of TMD‐like systems. This important feature makes the TMDI particularly suitable for nonlinear base‐isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.     

Optimum damping in linear isolation systems

Optimum isolation damping for minimum acceleration response of base-isolated structures subjected to stationary random excitation is investigated. Three linear models are considered to account for the energy dissipation mechanism of the isolation system: a Kelvin element, a linear hysteretic element and a standard solid linear element, commonly used viscoelastic models for isolation systems comprising natural rubber bearings and viscous dampers. The criterion selected for optimality is the minimization of the mean-square floor acceleration response. The effects of the frequency content of the excitation and superstructure properties on the optimum damping and on the mean-square acceleration response are addressed. The study basically shows that the attainable reduction in the floor acceleration largely depends on the energy dissipation mechanism assumed for the isolation system as well as on the frequency content of the ground acceleration process. Special care should be taken in accurately modelling the mechanical behaviour of the energy dissipation devices.     

Design of bilinear hysteretic isolation systems

This paper concerns the design of passive base isolation systems characterized by a bilinear hysteretic behaviour. The study refers to the case where the structure to be isolated (superstructure) vibrates according to the first mode. In this case the whole isolated structure can be modelled by a two‐degree‐of‐freedom system. The base isolation effectiveness has been evaluated for different characteristics of the device, namely mass, strength, elastic and plastic stiffness, by using mainly energetic quantities. The optimum values for the base device have been obtained by minimizing the input energy and the displacement of the superstructure. Conclusions are drawn for superstructures with a fundamental period of 0.5s, a damping ratio of 5% and for three different kinds of earthquake ground motions. The study showed that the seismic input greatly affects the behaviour of the isolated structure, and therefore the design ground motion must be carefully chosen, dependent on the characteristics of the site. A simple procedure that involves mainly linear dynamic analyses is proposed for the design of base devices used in conjunction with superstructures of any fundamental vibration period. The procedure produces good results in spite of its simplicity, and therefore it is suitable for practical use by design engineers. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.     

LQR control with frequency‐dependent scheduled gain for a semi‐active floor isolation system

Floor isolation is an alternative to base isolation for protecting a specific group of equipment installed on a single floor or room in a fixed‐base structure. The acceleration of the isolated floor should be mitigated to protect the equipment, and the displacement needs to be suppressed, especially under long‐period motions, to save more space for the floor to place equipment. To design floor isolation systems that reduce acceleration and displacement for both short‐period and long‐period motions, semi‐active control with a newly proposed method using the linear quadratic regulator (LQR) control with frequency‐dependent scheduled gain (LQRSG) is adopted. The LQRSG method is developed to account for the frequency characteristics of the input motion. It updates the control gain calculated by the LQR control based on the relationship between the control gain and dominant frequency of the input motion. The dominant frequency is detected in real time using a window method. To verify the effectiveness of the LQRSG method, a series of shake table tests is performed for a semi‐active floor isolation system with rolling pendulum isolators and a magnetic‐rheological damper. The test results show that the LQRSG method is significantly more effective than the LQR control over a range of short‐period and long‐period motions. Copyright © 2013 John Wiley & Sons, Ltd.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Hybrid isolation systems for equipment protection

This paper presents a formulation for earthquake resistant design of optimum hybrid isolation systems for sensitive equipment protection. The hybrid system under consideration consists of laminated rubber bearings, viscodampers and a set of actuators which, grounded on the main structural system, deliver forces on the basement of the isolated substructure mounted on the main structural system. An integrated design procedure for the passive and active components of the isolation system is developed aiming at acceleration reduction under random excitation. Linear models are used for the isolated structure, the main structural system and the isolation system. Fractional derivative Maxwell elements are used to model the mechanical behaviour of the viscodampers. The active component of the isolation system applies forces proportional to the absolute velocity of the isolated piece of equipment. Constraints in the deformation capacity of the isolators as well as constraints in the capacity of the actuators are considered for the design of an optimal hybrid isolation system. Simple numerical examples are developed herein to illustrate the design procedure. The superiority of hybrid systems over passive systems in reducing acceleration response is demonstrated.     

Experimental validation of semi‐active resetable actuators in a ⅕th scale test structure

The seismic performance of a test structure fitted with semi‐active resetable devices is experimentally investigated. Shaking table tests are conducted on a ?th scale four‐storey building using 27 earthquake records at different intensity scalings. Different resetable device control laws result in unique hysteretic responses from the devices and thus the structure. This device adaptability enables manipulation or sculpting of the overall hysteresis response of the structure to address specific structural cases and types. The response metrics are presented as maximum 3rd floor acceleration and displacement, and the total base shear. The devices reduce all the response metrics compared with the uncontrolled case and a fail‐safe surrogate. Cumulative probability functions allow comparison between different control laws and additionally allow tradeoffs in design to be rapidly assessed. Ease of changing the control law in real‐time during an earthquake record further improves the adaptability of the system to obtain the optimum device response for the input motion and structural type. The findings are an important step to realizing full‐scale structural control with customized semi‐active hysteretic behaviour using these novel resetable device designs. Copyright © 2008 John Wiley & Sons, Ltd.     

钢筋-沥青隔震层非线性震动特性研究

为了研究钢筋-沥青隔震层的材料与几何非线性震动特性,对钢筋-沥青隔震结构进行了振动台试验,分析了结构在不同加速度幅值输入时的隔震性能。同时,在钢材的应力-应变关系基础上,考虑构件竖向力的二次矩效应,提出了钢筋-沥青隔震层骨架曲线的计算方法,并结合双线型恢复力模型的滞回规则,建立了相应的恢复力模型。利用建立的恢复力模型,编制程序进行了弹塑性时程分析,并与试验结果作对比。结果表明:当钢筋-沥青隔震层的受力钢筋进入弹塑性阶段时,隔震层能够吸收大部分地震能量,显著降低上部结构的地震反应;弹塑性时程分析结果与试验结果吻合较好,由此建立的恢复力模型准确并且适用,可为钢筋-沥青隔震层的工程设计与非线性地震反应分析提供参考。     

Optimal energy‐based seismic design of non‐conventional Tuned Mass Damper (TMD) implemented via inter‐story isolation

Inter‐story isolation, an effective strategy for mitigating the seismic risk of both new and existing buildings, has gained more and more interest in recent years as alternative to base isolation, whenever the latter results to be impractical, technically difficult or uneconomic. As suggested by the name, the technique consists in inserting flexible isolators at floor levels other than the base along the height of a multi‐story building, thus realizing a non‐conventional Tuned Mass Damper (TMD). Consistent with this, an optimal design methodology is developed in the present paper with the objective of achieving the global protection of both the structural portions separated by the inter‐story isolation system, that is, the lower portion (below the isolation system) and the isolated upper portion (above the isolation system). The optimization procedure is formulated on the basis of an energy performance criterion that consists in maximizing the ratio between the energy dissipated in the isolation system and the input energy globally transferred to the entire structure. Numerical simulations, performed under natural accelerograms with different frequency content and considering increasing isolation levels along the height of a reference frame structure, are used to investigate the seismic performance of the optimized inter‐story isolation systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimized earthquake response of multi‐storey buildings with seismic isolation at various elevations

The response of multi‐storey structures can be controlled under earthquake actions by installing seismic isolators at various storey levels. By vertically distributing isolation devices at various elevations, the designer is provided with numerous options to appropriately adjust the seismic performance of a building. However, introducing seismic isolators at various storey levels is not a straightforward task, as it may lead to favourable or unfavourable structural behaviour depending on a large number of factors. As a consequence, a rather chaotic decision space of seismic isolation configurations arises, within which a favourable solution needs to be located. The search for favourable isolators' configurations is formulated in this work as a single‐objective optimization task. The aim of the optimization process is to minimize the maximum floor acceleration of the building under consideration, while constraints are specified to control the maximum interstorey drift, the maximum base displacement and the total seismic isolation cost. A genetic algorithm is implemented to perform this optimization task, which selectively introduces seismic isolators at various elevations, in order to identify the optimal configuration for the isolators satisfying the pre‐specified constraints. This way, optimized earthquake response of multi‐storey buildings can be obtained. The effectiveness of the proposed optimization procedure in the design of a seismically isolated structure is demonstrated in a numerical study using time‐history analyses of a typical six‐storey building. Copyright © 2012 John Wiley & Sons, Ltd.     

Restoring capability of bilinear hysteretic seismic isolation systems

The restoring capability (or re‐centering capability) is identified by the current design codes as a fundamental feature of seismic isolation systems. In this paper, the restoring capability of bilinear hysteretic or frictional seismic isolation systems is investigated in some detail. Certain energy considerations are examined first in order to provide insight into and reveal governing parameters on individual aspects of the problem. The restoring capability is then investigated through an extensive parametric study of smooth bilinear single‐degree‐of‐freedom hysteretic systems, with parameters covering a range of typical seismic isolation systems, subjected to a large group of recorded earthquakes. The results of the parametric analyses are processed statistically and regression analysis relations are derived that show the dependence of the residual displacement after the earthquake and the cumulative build up of displacements after a series of successive earthquakes on the governing parameters. Based on the analysis results, the features of the bilinear system that ensure sufficient restoring capability are identified. Copyright © 2007 John Wiley & Sons, Ltd.     

Base isolation for near‐fault motions

Three analytical studies of base‐isolated structures are carried out. First, six pairs of near‐fault motions oriented in directions parallel and normal to the fault were considered, and the average of the response spectra of these earthquake records was obtained. This study shows that in addition to pulse‐type displacements, these motions contain significant energy at high frequencies and that the real and pseudo‐velocity spectra are quite different. The second analysis modelled the response of a model of an isolated structure with a flexible superstructure to study the effect of isolation damping on the performance of different isolation systems under near‐fault motion. The results show that there exists a value of isolation system damping for which the superstructure acceleration for a given structural system attains a minimum value under near‐fault motion. Therefore, although increasing the bearing damping beyond a certain value may decrease the bearing displacement, it may transmit higher accelerations into the superstructure. Finally, the behaviour of four isolation systems subjected to the normal component of each of the near‐fault motions were studied, showing that EDF type isolation systems may be the optimum choice for the design of isolated structures in near‐fault locations. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficiency of base isolation systems in structural seismic protection and energetic assessment

This paper concerns the seismic response of structures isolated at the base by means of High Damping Rubber Bearings (HDRB). The analysis is performed by using a stochastic approach, and a Gaussian zero mean filtered non‐stationary stochastic process is used in order to model the seismic acceleration acting at the base of the structure. More precisely, the generalized Kanai–Tajimi model is adopted to describe the non‐stationary amplitude and frequency characteristics of the seismic motion. The hysteretic differential Bouc–Wen model (BWM) is adopted in order to take into account the non‐linear constitutive behaviour both of the base isolation device and of the structure. Moreover, the stochastic linearization method in the time domain is adopted to estimate the statistical moments of the non‐linear system response in the state space. The non‐linear differential equation of the response covariance matrix is then solved by using an iterative procedure which updates the coefficients of the equivalent linear system at each step and searches for the solution of the response covariance matrix equation. After the system response variance is estimated, a sensitivity analysis is carried out. The final aim of the research is to assess the real capacity of base isolation devices in order to protect the structures from seismic actions, by avoiding a non‐linear response, with associated large plastic displacements and, therefore, by limiting related damage phenomena in structural and non‐structural elements. In order to attain this objective the stochastic response of a non‐linear n‐dof shear‐type base‐isolated building is analysed; the constitutive law both of the structure and of the base devices is described, as previously reported, by adopting the BWM and by using appropriate parameters for this model, able to suitably characterize an ordinary building and the base isolators considered in the study. The protection level offered to the structure by the base isolators is then assessed by evaluating the reduction both of the displacement response and the hysteretic dissipated energy. Copyright © 2003 John Wiley & Sons, Ltd.     

Reliability of U‐shaped steel dampers used in base‐isolated structures subjected to biaxial excitation

A reliable performance of anti‐seismic devices when the upper‐structure is subjected to strong biaxial seismic excitation is of vital importance to ensure the latter doesn't reach critical behavior. U‐shaped steel dampers are hysteretic devices used to dissipate the earthquake‐induced energy of base‐isolated structures. In the framework of performance‐based design, which is gaining more and more recognition, it is of particular importance to assess the performance of base‐isolated structures with such dampers under different intensity levels of bidirectional ground motion. To achieve this goal, an analytical model able to simulate the bidirectional displacement response of an isolation system is adopted. Incremental dynamic analysis (IDA) is used to obtain the relation between the earthquake‐induced bidirectional damage of U‐shaped steel dampers and different intensity levels of the considered records. The performance of the dampers is categorized into 5 levels delimited by 4 limit states for which fragility curves are derived. The results obtained using the bidirectional approach are quantitatively compared to those given by employing an in‐plane model (widely used in current design practices in Japan) with the purpose of assessing whether the latter provides unconservative estimates of the performance of the dampers. The main conclusion is that, for large seismic intensities, the safety margin against fracture of the dampers is significantly overestimated when an in‐plane model is adopted. Copyright © 2016 John Wiley & Sons, Ltd.     

Sloped multi‐roller isolation devices for seismic protection of equipment and facilities

The rolling motion of mutually orthogonal rollers respectively sandwiched between two bearing plates in which one or both have V‐shaped sloping surfaces makes the sloped rolling‐type isolation device have an excellent in‐plane seismic isolation performance. In this study, the sloped rolling type isolation device in which a single roller moves between two V‐shaped sloping surfaces along each principle horizontal direction is refined by incorporating multi‐roller, built‐in damping, and pounding prevention mechanisms. The associated dynamic behavior is further clarified, and a simplified twin‐flag hysteretic model, which can be easily applied in most commercial computational tools is then proposed. Seismic simulation tests on the refined isolation devices (i.e. the sloped multi‐roller isolation devices) with different design parameters such as sloping angles of bearing plates and built‐in damping capabilities, together with a raised floor system by employing the sloped multi‐roller isolation devices, were conducted. Not only is the efficiency of the sloped multi‐roller isolation devices in seismically protecting the important objects, but also the practicability and accuracy of the proposed simplified numerical model in predicting the seismic responses of the sloped multi‐roller isolation devices is experimentally verified. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic response of light internal equipment in base-isolated structures

The seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system. The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base-isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment-structure interaction need not be considered and multiple support response analysis is rendered unnecessary. Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead-rubber hysteretic bearings, having a force-displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead-rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment. The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.     

Seismic base‐isolation by use of a telescoping stepping mechanism

A new base‐isolation mechanism corresponding to a variance of the stepping A‐shaped frame is proposed and its seismic performance is investigated numerically for strong ground accelerations with peak values in the range from 0.5 to 1g. In its simplest two‐dimensional form, the system consists of a frame with two telescoping legs pinned at the apex at a sharp angle. The legs are attached to the foundation through a spring and a damper acting in parallel. Both the springs and viscous dampers have bilinear characteristics that make them very stiff in compression but very soft in tension. As the structure rocks sideways, the length of the loaded leg remains essentially constant while the length of the unloaded leg increases. When the ground acceleration changes direction, the process is reversed. The resulting system has three main characteristics: (i) as the structure steps on a rigid leg, the maximum acceleration that can be transmitted to the superstructure is limited to a value which is approximately independent of the amplitude of the ground motion; (ii) there is a systematic lifting of the superstructure with kinetic energy being systematically transformed into potential energy during the strong phase of the ground motion; and (iii) the system is slowly self‐centering at the end of the earthquake. The seismic performance of the system is evaluated for a tall bridge pier and for a smaller frame that could be used in a multi‐story building. The results obtained for the 1940 El Centro ground motion scaled to 1g and for the near‐field Rinaldi ground motion recorded during the Northridge earthquake show that substantial reductions of the absolute acceleration can be obtained with reasonable relative displacements of the superstructure and small strokes in the isolation devices. Copyright © 2004 John Wiley & Sons, Ltd.     

Direct estimation of seismic response in reduced-degree-of-freedom isolation and energy dissipation systems

A methodology for the development of design tools for direct estimation of peak inelastic response in reduced-degree-of-freedom (RDOF) isolation and energy dissipation systems is presented. The suggested procedure is an extension of an earlier method addressing purely hysteretic isolation systems. Herein, the dynamic equation of motion is first normalised to reduce the number of design parameters that significantly affect the response. The sensitivity of normalised response quantities to the amplitude of the ground motion is then investigated through extensive parametric nonlinear dynamic analyses of isolated single-degree-of-freedom (SDOF) systems with linear viscous damping using code-based target spectra. Regression analysis is subsequently employed to develop generalised design equations (GDEs) suitable for design. Further investigations are made to address nonlinear viscous damping and the effect of the transverse component of seismic action in two-degree-of freedom (2DOF) systems under bidirectional excitation, making the procedure applicable to common bridge isolation schemes. GDEs constitute an alternative to equivalent linearisation approaches commonly adopted by codes, informing the selection among alternative isolation and energy dissipations schemes without requiring iterative analysis. The approach is incorporated in the Deformation-Based Design methodology for seismically isolated bridges in a forthcoming paper.