Adjustable vertical vibration isolator with a variable ellipse curve mechanism

This paper presents a passive vertical quasi‐zero‐stiffness vibration isolator intended for relatively small objects. The present isolator has features of compactness, long stroke, and adjustability to various load capabilities. To realize these features, we use constant‐force springs, which sustain constant load regardless of their elongation, and propose a variable ellipse curve mechanism that is inspired by the principle of ellipsographs. The variable ellipse curve mechanism can convert the restoring force of the horizontally placed constant‐force springs to the vertical restoring force of the vibration isolator. At the same time as converting the direction, the vertical restoring force can be adjusted by changing the ratio of the semi‐minor axis to the semi‐major one of the ellipse. In this study, a prototype of a class of quasi‐zero‐stiffness vibration isolator with the proposed variable ellipse curve mechanism is created. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the prototype can reduce the response acceleration within the same specified tolerance even when the mass of the vibration isolated object is changed. Copyright © 2017 John Wiley & Sons, Ltd.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of a guideway seismic isolator with magnetic springs for precision machinery

This paper proposes the use of the nonlinear restoring force in an isolation system to improve the performance of a seismic isolator. Nonlinear magnetic springs applied to guideway sliding isolators (GSI) that protect precision machinery against seismic motion were studied. The magnetic springs use a non‐contact magnetic repulsion force to achieve a nonlinear property. A numerical simulation model of the GSI system using step‐by‐step integration in the time domain was developed. A full‐scale shaking table test was performed to verify the accuracy of the numerical model. Simulation and experimental results show that the GSI system with magnetic springs has good performance when subjected to floor vibrations during earthquakes. A parametric analysis of the magnetic springs in the GSI system under seismic motion was theoretically investigated. It was found that sufficient magnetic forces can diminish the system relative displacements. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

An isolation system for limited seismic gaps in near‐fault zones

The ability of a recently proposed seismic isolation system, with inherent self‐stopping mechanism, to mitigate or even eliminate seismic pounding of adjacent structures is investigated under severe near‐fault earthquakes. The isolation system is referred to as roll‐in‐cage (RNC) isolator. It is a rolling‐based isolator that provides in one unit the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, hysteretic energy dissipation, and resistance to minor vibration loads. In addition, the RNC isolator is distinguished by a self‐stopping (buffer) mechanism to limit the bearing displacement under excitations stronger than a design earthquake or at limited seismic gaps, and a linear gravity‐based self‐recentering mechanism to prevent permanent bearing displacement without causing vertical fluctuation of the isolated structure. A previously developed multifeature SAP2000 model of the RNC isolator is improved in this paper to account for the inherent buffer mechanism's damping. Then, the effectiveness of the isolator's buffer mechanism in limiting peak bearing displacements is studied together with its possibly arising negative influence on the isolation efficiency. After that, the study investigates how to alleviate or even eliminate those possibly arising drawbacks, due to the developed RNC isolator's inner pounding as a result of its buffer activation, to achieve efficient seismic isolation with no direct structure‐to‐structure pounding, considering limited seismic gaps with adjacent structures and near‐fault earthquakes. The results show that the RNC isolator could be an efficient solution for aseismic design in near‐fault zones considering limited seismic gaps. Earthquake Engineering and Structural Dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of a kinematic self‐centring seismic isolator

This investigation deals with the analytical formulation and experimental validation of a prestressed reinforced concrete seismic isolator with kinematic constraints at both ends. The kinematic isolator was proposed initially as a low‐cost solution for seismic protection of low‐income people housing usually placed at the periphery of big cities where regular to bad soil conditions are common. So, the isolator is also a pile foundation with a central prestressed cable and two rolling steel surfaces at the top and bottom ends. By varying the shapes of the end rolling surfaces, different force–deformation constitutive relationships for the isolator may be obtained. Energy dissipation is introduced by yielding of passive reinforcement at the rolling interphase. Apart from stating the large‐deformation formulation of the element, several relevant aspects of the behaviour of these devices are studied herein, such as the increase in the tension of the central prestressed cable, responsible for the self‐centring action of the isolator, the floor uplift that results from the geometry of the isolator, and the vertical stability of the system. Experimental and theoretical results obtained for a group of 9 testing specimens show an excellent agreement in the force–deformation constitutive relationship. Although not the intent of this article, the device proposed may be extended directly as a coupling beam element for shear wall systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Cyclic behavior and failure mechanism of self‐centering energy dissipation braces with pre‐pressed combination disc springs

A new type of bracing system composed of friction energy dissipation devices for energy dissipation, pre‐pressed combination disc springs for self‐centering and tube members as guiding elements is developed and experimentally studied in this paper. The mechanics of this system are explained, the equations governing its hysteretic responses are outlined and large‐scale validation tests of two braces with different types of disc springs are conducted under the condition of low cyclic reversed loading. The experimental results demonstrate that the proposed bracing system exhibits a stable and repeatable flag‐shaped hysteretic response with an excellent self‐centering capability and effective energy dissipation throughout the loading protocol. Furthermore, the maximum bearing force and stiffness are predicted well by the equations governing its mechanical behavior. Fatigue and destructive test results demonstrate that the proposed bracing system can maintain stable energy dissipation and self‐centering capabilities under large deformation cyclic loading even when the tube members exceed the elastic limit and that a larger bearing capacity is achieved by the system that has disc springs without a bearing surface. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of horizontal stiffness of fibre‐reinforced elastomeric isolators

Unbonded fibre‐reinforced elastomeric isolator (U‐FREI) is relatively new seismic base isolator in which fibre layers are used as reinforcement to replace steel shims as are normally used in conventional isolators. Further, the top and bottom end steel connector plates of conventional isolators are also removed. In general, the horizontal response of U‐FREI is nonlinear because of reduction in contact area due to rollover deformation and reduction in shear modulus of isolator under large deformation. Thus, evaluation of horizontal stiffness of U‐FREI is a challenging problem. Most previous studies were focused on the investigation of horizontal response of scaled models of U‐FREIs with low shape factors. A few analytical approaches were suggested for predicting the horizontal response of U‐FREI; but their results were not in good agreement with experimental observations. In the present study, the horizontal responses of prototype U‐FREIs are evaluated under a constant vertical pressure and cyclic loading using both experiments and finite element analysis. Prototype U‐FREIs with different shear moduli and with different shape factors are considered. Finite element simulations of corresponding bonded FREIs are also performed under the same loadings as in U‐FREIs. A rational analytical approach including the influence of rollover deformation and simultaneous reduction in shear modulus is proposed as a basic analytical tool for predicting the horizontal stiffness of FREIs (both bonded and unbonded). It is in reasonably good agreement with the results obtained from experiments and numerical analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

超弹性-复摩擦摆隔震支座的性能试验与数值模拟

利用复摩擦支座（Double friction pendulum bearing,DFPB）和形状记忆合金（Shape Memory alloy,SMA）拉索,提出了一种超弹性-复摩擦支座（Superelastic-double friction pendulum bearing,SDFPB）。该新型滑动隔震支座在水平方向可适应多水准地震激励,且在竖向拥有抵抗拉拔的功能。阐述了SDFPB的构造特点和工作原理。通过性能试验考察了这一隔震装置的力学特性。建立了SDFPB的恢复力模型,利用其模拟了试验条件下的滞回响应。研究结果表明:SDFPB的耗能能力优良,且具有较好的多级抗震自适应能力;模拟值与试验值吻合较好,验证了上述力学模型的正确性。     

Performance‐based earthquake engineering assessment of a self‐centering,post‐tensioned concrete bridge system

Highway bridges in highly seismic regions can sustain considerable residual displacements in their columns following large earthquakes. These residual displacements are an important measure of post‐earthquake functionality, and often determine whether or not a bridge remains usable following an earthquake. In this study, a self‐centering system is considered that makes use of unbonded, post‐tensioned steel tendons to provide a restoring force to bridge columns to mitigate the problem of residual displacements. To evaluate the proposed system, a code‐conforming, case‐study bridge structure is analyzed both with conventional reinforced concrete columns and with self‐centering, post‐tensioned columns using a formalized performance‐based earthquake engineering (PBEE) framework. The PBEE analysis allows for a quantitative comparison of the relative performance of the two systems in terms of engineering parameters such as peak drift ratio as well as more readily understood metrics such as expected repair costs and downtime. The self‐centering column system is found to undergo similar peak displacements to the conventional system, but sustains lower residual displacements under large earthquakes, resulting in similar expected repair costs but significantly lower expected downtimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

Computational study of self‐centering buckling‐restrained braced frame seismic performance

Recent research developed and experimentally validated a self‐centering buckling‐restrained brace (SC‐BRB) that employs a restoring mechanism created using concentric tubes held flush with pretensioned shape memory alloy rods, in conjunction with a buckling‐restrained brace (BRB) that dissipates seismic energy. The present computational study investigated how the SC‐BRB can be implemented in real buildings to improve seismic performance. First, a computational brace model was developed and calibrated against experimental data, including the definition of a new cyclic material model for superelastic NiTi shape memory alloy. A parametric study were then conducted to explore the design space for SC‐BRBs. Finally, a set of prototype buildings was designed and computationally subjected to a suite of ground motions. The effect of the lateral resistance of gravity framing on self‐centering was also examined. From the component study, the SC‐BRB was found to dissipate sufficient energy even with large self‐centering ratios (as large as 4) based on criteria found in the literature for limiting peak drifts. From the prototype building study, a SC‐BRB self‐centering ratio of 0.5 was capable of reliably limiting residual drifts to negligible values, which is consistent with a dynamic form of self‐centering discussed in the literature. Because large self‐centering ratios can create significant overstrength, the most efficient SC‐BRB frame designs had a self‐centering ratio in the range of 0.5–1.5. Ambient building resistance (e.g., gravity framing) was found to reduce peak drifts, but had a negligible effect on residual drifts. Copyright © 2014 John Wiley & Sons, Ltd.     

Physical model for dynamic analysis of structures with FPS isolators

This article presents a physical model for frictional pendulum isolators (FPS) that is ready to be implemented in most commercial software. The model is capable of accounting for effects such as large deformations, sticking, and uplift and impact by sensing the normal loads in the isolators through a gap element. Sticking has been incorporated into the model by extending the Park–Wen hysteretic model to the case of large deformations. The proposed model has been tested against a theoretically ‘exact’ formulation leading to essentially identical results. To facilitate its use, the physical FPS model has been cast into a typical non‐linear structural element format, i.e. with deformation as input and restoring force as output. Examples of a building and a bridge have been chosen to show the potential of the element and to provide further insight into the earthquake response of structures with FPS isolators; in particular, in aspects such as the orientation in placement of the isolator, sticking, P? Δ, and other large deformation effects. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamics of resilient-friction base isolator (R-FBI)

The Resilient-Friction Base Isolator (R-FBI) is composed of a set of flat rings which can slide on each other with a central rubber core and/or peripheral rubber cores. In this base isolator the interfacial friction force acts in parallel with the elastic force in the rubber. It combines the beneficial effect of friction damping with that of the resiliency of rubber. The rubber cores distribute the sliding displacement and velocity along the height of the R-FBI. They do not carry any vertical loads and are not vulcanized to the sliding rings. The system's analytical model and the computer experimental results for both horizontal and vertical components of recorded ground motions and various levels of friction and damping are presented. These results clearly demonstrate the R-FBI's potential as an effective aseismic base isolator.     

Piecewise‐continuous velocity inversion

We suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion.     

Design,simulation, and large‐scale testing of an innovative vibration mitigation device employing essentially nonlinear elastomeric springs

This study proposes an innovative passive vibration mitigation device employing essentially nonlinear elastomeric springs as its most critical component. Essential nonlinearity denotes the absence (or near absence) of a linear component in the stiffness characteristics of these elastomeric springs. These devices were implemented and tested on a large‐scale nine‐story model building structure. The main focus of these devices is to mitigate structural response under impulse‐like and seismic loading when the structure remains elastic. During the design process of the device, numerical simulations, optimizations, and parametric studies of the structure‐device system were performed to obtain stiffness parameters for the devices so that they can maximize the apparent damping of the fundamental mode of the structure. Pyramidal elastomeric springs were employed to physically realize the optimized essentially nonlinear spring components. Component‐level finite element analyses and experiments were conducted to design the nonlinear springs. Finally, shake table tests using impulse‐like and seismic excitation with different loading levels were performed to experimentally evaluate the performance of the device. Experimental results demonstrate that the properly designed devices can mitigate structural vibration responses, including floor acceleration, displacement, and column strain in an effective, rapid, and robust fashion. Comparison between numerical and experimental results verified the computational model of the nonlinear system and provided a comprehensive verification for the proposed device. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of lead core heating on the seismic performance of bridges isolated with LRB in near‐fault zones

In this paper, the effect of lead core heating and associated strength deterioration on the seismic response of bridges isolated with lead rubber bearings (LRB) is investigated as a function of the characteristics of the isolator and near fault ground motions with forward rupture directivity effect. Furthermore, the ability of bounding analyses to provide a design envelope for maximum isolator force and maximum isolator displacement is verified. For this purpose, a series of nonlinear dynamic analyses are conducted for LRB isolated bridges where both deteriorating and non‐deteriorating force‐deformation relationship of LRB were employed. The analyses are performed for both simulated and recorded ground motions. It is found that while the temperature rise in the lead core generally increases with increasing magnitude and number of near fault ground motion velocity pulses, it decreases with larger distances from the fault. It is also found that bounding analysis method provides conservative (envelope) estimates of maximum isolator displacement and maximum isolator force for design purposes that fulfill its intended purpose. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental and numerical study on hysteretic performance of SMA spring-friction bearings

This paper presents an experimental and numerical study to investigate the hysteretic performance of a new type of isolator consisting of shape memory alloy springs and friction bearing called an SMA spring-friction bearing (SFB). The SFB is a sliding-type isolator with SMA devices used for the seismic protection of engineering structures. The principle of operation of the isolation bearing is introduced. In order to explore the possibility of applying SMA elements in passive seismic control devices, large diameter superelastic tension/compression NiTi SMA helical springs used in the SFB isolator were developed. Mechanical experiments of the SMA helical spring were carried out to understand its superelastic characteristics. After that, a series of quasi-static tests on a single SFB isolator prototype were conducted to measure its force-displacement relationships for different loading conditions and study the corresponding variation law of its mechanical performance. The experimental results demonstrate that the SFB exhibits full hysteretic curves, excellent energy dissipation capacity, and moderate recentering ability. Finally, a theoretical model capable of emulating the hysteretic behavior of the SMA-based isolator was then established and implemented in MATLAB software. The comparison of the numerical results with the experimental results shows the efficacy of the proposed model for simulating the response of the SFB.     

Lead core heating in lead rubber bearings subjected to bidirectional ground motion excitations in various soil types

This paper investigates the response of lead rubber bearings (LRBs) under bidirectional earthquake excitations when lead core heating effect is of concern. For this purpose, a series of nonlinear response history analyses were conducted with a bilinear force‐deformation relation for LRBs. In the considered bilinear representation, the strength of LRBs deteriorates because of lead core heating under cyclic motions. Response of LRBs was studied in terms of maximum isolator displacements (MIDs) and maximum lead core temperature as a function of isolator characteristics (characteristic strength to weight ratio, Q/W, and post‐yield isolation period, T). Nonlinear response history analyses were performed using two sets of ground motions clustered according to their soil classifications. To quantify the interacted effects of coupled analysis and lead core heating on MID, unidirectional analyses were also performed. Furthermore, the efficacy of equivalent lateral force procedure in estimating the MID of LRBs was also tested for the cases in which temperature‐dependent behavior of LRBs was considered. The results demonstrate that the temperature rises in the lead core of LRBs in bidirectional analyses are approximately 50% higher than that of unidirectional ones. It decreases with increasing Q/W ratio and T. It is also revealed that equivalent lateral force procedure gives close estimations for MID with some overestimation even for temperature‐dependent behavior of LRBs. Copyright © 2013 John Wiley & Sons, Ltd.