Nonlinear Isolation System Research Articles

Feasibility of an inerter-based causal rate-independent damping model for the protection of seismically isolated structures

Rate-independent linear damping (RILD), also referred to as linear hysteretic damping, is a linear model of structural or material damping in which the energy dissipation per cycle is independent of the frequency. The resistive force of an ideal RILD model is in phase with the velocity to dissipate energy, while its amplitude is proportional to the displacement, which is suitable for the direct control of seismic response displacement when incorporated into a structure. The tuned Maxwell–Wiechert (TMW) model is a viable option for approximating the damping characteristics of RILD. However, the undesirable stiffness produced by the TMW model compromises the flexibility of the isolator, and thereby fails to deliver the benefits of RILD. To overcome this challenge, the addition of two inerter elements to the TMW model in series and parallel arrangements is proposed in this study to eliminate the undesirable storage stiffness. The parameters of the proposed model are determined using particle swarm optimization. Analyses of a 10-story building structure mounted on linear and nonlinear isolation systems demonstrated that the proposed model achieved lower interstory drifts and approximately 40% reduction in floor response accelerations, with similar isolator displacements compared with LVD when subjected to ground motions dominated by high-frequency components. Moreover, floor response acceleration mitigation was attained at the slight expense of isolator displacement, even when the proposed system was incorporated into nonlinear isolation systems and subjected to low-frequency ground motions.

Nonlinear Viscous Damping-Based Negative Stiffness Isolation System for Over-Track Complex Structures

ABSTRACT The over-track complex structures are driven by transit-oriented urban development, leading to the necessity for advanced seismic performance upgrades. An innovative solution is presented in this study, involving the negative-stiffness amplification system-enabled isolation system (NSAS-IS) with nonlinear viscous damping to establish a flexible isolation layer beneath over-track buildings. The multi-benefit-based design procedure and easy-to-use formula are developed. Its effectiveness and comparative superiority over conventional ones, particularly in mitigating negative effects of over-track buildings on lower podiums, is confirmed by case studies. NSAS-IS with an optimized nonlinear viscous damping exponent exhibits a significant reduction in isolation-layer displacement and robustness against earthquakes.

Stochastic Optimization of Electromagnetic Inertial Mass Dampers in Nonlinear Hybrid Base Isolation Systems Under Seismic Excitations

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure’s performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction.

Quasi-zero stiffness interval optimization design and dynamics analysis of a new bi-directional horizontal isolation system

The quasi-Zero Stiffness (QZS) isolation system is a typical nonlinear isolation system, which has high static stiffness characteristics to improve the bearing capacity and deformation resistance, and its low dynamic stiffness characteristics can reduce the inherent frequency of the system to realize a wider vibration isolation frequency band, so it has a more excellent low-frequency vibration isolation performance compared with the linear system. In this paper, a horizontal QZS isolator is constructed based on a pre-compressed oblique spring system, and two sets of the horizontal QZS isolators are mechanically assembled to work together to achieve a bi-directional horizontal QZS isolation system. Considering that the construction of two sets of horizontal vibration isolators is approximately the same, we focus on one of the isolators for the static analysis and derive the parameter conditions to be satisfied for achieving quasi-zero stiffness characteristics. We considered the effect of each adjustable parameter of the horizontal vibration isolator on the mechanical performance of the QZS system, and sought to optimize the QZS interval to improve the vibration isolation performance. A comparative study of the dynamical properties between the QZS system with ordinary and optimized parameters, as well as the equivalent linear system, is further carried out by means of nonlinear approximate analysis. Finally, the dynamic characteristics of the bi-directional horizontal QZS system and the equivalent linear system are compared by shaker tests on the prototype device, which proved the excellent vibration isolation performance of the proposed QZS isolation system.

Seismic resilient design and negative stiffness-assisted nonlinear isolation system for adjacent non-coaxial buildings linked by corridors

Adjacent non-coaxial buildings have been widely built owing to complementary functions, while the non-coaxial layout could cause a great torsion effect and seismic-induced damage. This study proposes a negative stiffness-assisted hybrid isolation system and a corresponding earthquake-resilient design methodology to upgrade the multi-performances of the adjacent non-coaxial buildings and linking corridors. The hybrid isolation system includes synthetic employment of various isolators and negative-stiffness amplification systems comprised of nonlinear viscous dampers for adjacent structures, as well as tailored friction bearing for linking corridors. The mechanical property and model of the adjacent non-coaxial buildings are established, based on which a typical case is introduced. Next, the conception of the earthquake-resilient design method and procedure is elaborated, following which the functionality of each component in the hybrid system is investigated. The advantages of the developed hybrid isolation system and design methodology are illustrated by a systematic parametric analysis and time history analysis for the typical case. The results show that the torsional effect can be a dominant problem in non-coaxial adjacent buildings, which can be solved by the flexibly tailored negative stiffness effect produced by the negative stiffness-assisted isolation system. The collaboration within the proposed hybrid isolation system can produce improved isolating and enhanced nonlinear energy dissipation effects on adjacent buildings, simultaneously limiting the isolation displacement without weakening the isolating effect. The optimized friction sliding bearings effectively reduce the relative torsion concentrated on the linking corridors with a maintained function. The hybrid isolation system and earthquake-resilient design can be adopted as a high-efficiency solution to the non-coaxial linked historic buildings with insufficient seismic resistance.

Optimal Design and Dynamic Analysis of a New Quasi-Zero-Stiffness Isolation Device

Compared with the linear isolation system, the quasi-zero-stiffness (QZS) nonlinear isolation system has the characteristics of high static stiffness and low dynamic stiffness, which has better low-frequency vibration isolation performance. However, most of the existing QZS isolators only consider the quasi-zero-stiffness characteristic at the static equilibrium position achieved by the parallel connection of positive and negative stiffness structures. To optimize the isolation performance of the QZS system, a new isolation device based on the parallel connection of oblique springs and vertical springs was proposed. The device can not only achieve quasi-zero-stiffness at the static equilibrium position but also expand the interval of quasi-zero-stiffness through parameter optimization design to optimize the stiffness characteristics of the QZS system, thus effectively improving the vibration isolation performance. The QZS nonlinear systems with the optimal parameters were analyzed dynamically, and the nonlinear motion equations were approximately solved based on the fifth-order polynomials fitted by the restoring force curves. A prototype was further designed and fabricated to compare and analyze the vibration isolation performance of the QZS system and the equivalent linear system through a shaking table test.

Correction to “Dynamics characteristics of geometrically nonlinear isolation systems for seismic protection of equipment”

Correction to “Dynamics characteristics of geometrically nonlinear isolation systems for seismic protection of equipment”

Intermediate Isolation System with Nonlinear Lower Structure and Isolation System

This paper reports a study on the Intermediate Isolation System (IIS) applied to existing buildings. This kind of application is particularly suitable when a vertical addition is planned for buildings in seismic zones; in such a case, an isolation system can be placed at the base of the extension to prevent the increase, or, better, to reduce the seismic demand on the existing structure. In previous works, parametric response spectrum analyses have been carried out on lumped mass models by varying the period of the isolation system. As a result, a sort of IIS design spectrum has been derived and used for selecting design solutions for the vertical extension that minimize the overall seismic response. In this paper, the above design indications are assessed in the light of nonlinear time history analyses, accounting for the hysteretic response of the existing structure and the nonlinear behaviour of the isolation system. The IIS configurations are analysed and the results are discussed and compared in terms of peak response. In light of the obtained analysis results, the effectiveness and robustness of IIS applications for vertical extensions are discussed, and design implications are suggested.

Stochastic Optimization of a Nonlinear Base Isolation System with LRB and EIMD for Building Structures

Base-isolated structures achieve superior seismic performance but with the cost of large deformation of the base floor, which possibly causes superstructure collapse during severe earthquakes. Hence, it is of great interest to develop hybrid base isolation systems that can reduce the base deformation and simultaneously improve the superstructure’s performance. Recently, several hybrid base isolation systems using inerter-based dampers have emerged; however, the nonlinear performance of the isolators has rarely been considered in these studies. In this paper, we conduct a nonlinear stochastic optimization of a novel hybrid base isolation system with lead-rubber bearings (LRB) and electromagnetic inertial mass dampers (EIMD). Based on the Bouc–Wen hysteretic model of the LRB, we derive the semianalytical solutions of the response variances of a simplified base-isolated model subjected to stationary seismic excitations. Then, based on the semianalytical solutions, we propose a procedure for optimizing the EIMD aimed at minimizing the superstructure interstory drift. In addition, we investigate the effect of site conditions and postyielding to preyielding stiffness ratios of the LRB on the optimal EIMD parameters and corresponding seismic performance. It is found that the hybrid base isolation system achieves better performance at a soft site than at a firm site. Results of a hybrid base-isolated building under artificial and real earthquake excitations illustrate that the EIMD can reduce both the base deformation and superstructure response, which outperforms the hybrid base-isolated building with conventional viscous dampers (VD).

Analysis and design of non-linear seismic isolation systems for building structures—An overview

In this paper, the development of non-linear building isolation systems is overviewed. The study summarizes commonly used linear building isolation systems in two categories, which are building base isolation systems and building inter-storey isolation systems. Typical isolators including Lead-Rubber Bearings Friction Pendulum Bearings inter-storey viscous damper and Tuned Mass Damper are reviewed. The analysis and design of linear building isolation systems are also reported. After that, non-linear building isolation systems are introduced from two aspects based on their dynamic characteristics. They are (i) non-linear stiffness isolators including Quasi-Zero Stiffness isolators and Non-linear Energy Sink and (ii) non-linear damping isolators including power-law viscous dampers and magnetorheological dampers. Practical implementations of these non-linear isolators are introduced. Finally, the analysis and design of non-linear building isolation systems are discussed. Traditional equivalent linearization approaches and advanced non-linear frequency design approaches are introduced. The promising applications of the non-linear frequency design approaches to building isolation systems are also demonstrated in this review paper.

Feasibility study of a practical causal rate-independent damping device for the improved performance of seismic isolated structures

When rate-independent linear damping (RILD) is incorporated into a base-isolated structure, it achieves a similar response displacement reduction effect with significantly lower floor response acceleration compared with linear viscous damping (LVD) with the same loss factor. To address the undesirable stiffness added to an isolation layer when we adopt a mechanical device comprising a few branches of a spring–dashpot link to realize RILD, this study proposes canceling the undesirable isolator stiffness by adding an inerter element and reducing the isolator stiffness. A heuristic optimization method was developed to design the proposed mechanical device to mimic the behavior of RILD. A parametric survey on the optimal designs of the device suggests that the three branches of the spring–dashpot link work best in terms of practicality and feasibility. Seismic control performance was assessed using a 10-story base-isolated building mounted on linear and nonlinear isolation systems. Analyses of linear systems revealed that the proposed device achieved lower inter-story drifts and approximately 40% reduction in floor response acceleration with a 4% increase in isolator displacement compared with the LVD when subjected to high-frequency ground motions. Analyses of the nonlinear systems showed that the displacement control performance of the proposed model was slightly compromised when subjected to ground motions dominated by low-frequency components, thereby identifying a further challenge in developing a causal RILD device for nonlinear structures.

The design of nonlinear damped building isolation systems by using mobility analysis

Additional power law nonlinear damping has shown advantages in seismic isolation of buildings. The design of nonlinear damped building isolation systems can be conducted in the frequency domain based on the output frequency response function (OFRF) of the building’s frequency output responses. But this often requires many runs of simulations of nonlinear building systems, which will spend a long time when the finite element (FE) model or differential equation model of the building system is complex. In this study, the issue will be resolved by an integrated mobility analysis and equivalent linearization approach. In this approach, the complex linear building system without additional nonlinear damping is represented by several data-driven autoregressive with exogenous input (ARX) models. Mobilities of the building system can be evaluated from these ARX models, so that a mobility-based frequency domain representation of the linear building system can be achieved. After that, an equivalent linearization approach is applied to simulate the building system with additional nonlinear damping. Finally, the OFRF-based design can be conducted based on the proposed mobility analysis and equivalent linearization approach. A 4-degree of freedom (DoF) building system is discussed to demonstrate the advantages of the proposed method. The results indicate that the new approach can significantly increase the efficiency of the design and be effectively applied to the design of complex nonlinear building isolation systems.

Seismic response of isolated structures with an improved model of the UFREI

An improved formulation of the horizontal shear behavior of the unbonded fiber-reinforced elastomeric isolators (UFREI), which predicts both the pre-rollover and the post-rollover behavior considering the effect of the vertical load, is proposed. A simplified and computationally inexpensive formulation of the horizontal shear behavior of the UFREI has also been proposed afterward. Further, these formulations are verified using experimental results and compared with the results obtained using the other earlier methods in the recent literature. The horizontal shear behavior predicted by both of the proposed formulations is observed to fit the experimental results very well. The shear behavior predicted by these formulations is observed to be more accurate than the corresponding predicted by the other formulations from the recent literature. A parametric study characterizing the effect of the vertical pressure and the initial elastomeric shear modulus on the horizontal shear behavior of isolators is also carried out. The proposed formulations are further used to model the behavior of the UFREI employed to isolate the benchmark structure considered in the study.Supplementary damping devices are further installed alongside the nonlinear UFREI isolation system to mitigate the excessive displacement demand on isolators under near-fault ground motions. The isolated benchmark structure is thus coupled with a Magneto-rheological Damper (MRD) with an improved control algorithm for nonlinear isolation systems in three configurations, i.e., semi-active, passive-on, and passive-off. A comparative study of these configurations shows that MRD in passive-on mode provides the minimum isolators displacement response, but an overall improved structural response is achieved with MRD in the semi-active mode of operation.

Comparison of meta-heuristic approaches for the optimization of non-linear base-isolation systems considering the influence of superstructure flexibility

The main aim of this study is to investigate the meta-heuristic approaches called Harmony Search (HS), Grey Wolf Optimizer (GWO), Teaching-Learning Based Optimization (TLBO), and Jaya Algorithm (JA) in the optimization process of non-linear base isolation systems under near-fault earthquakes considering the effect of the superstructure flexibility. The optimization processes were performed by achieving the objective function set as minimizing the peak top floor acceleration to peak ground acceleration ratio with and without base displacement limits. The context of the optimization process, the analytical model of the superstructure, and the number of isolators are considered as the design constants. The mechanical parameters of the non-linear isolation systems, such as the isolation system period, the total characteristic strength ratio, and the yield displacement, are determined as the independent design variables. According to the results obtained in this study, GWO, JA, and TLBO algorithms can be more suitable for solving such design problems among the considered algorithms. Although the objective function values are amplified with the increase in the superstructure flexibility, these values remain around 1.0, even for the most stringent base displacement limit. It can be expressed as a successful seismic performance, especially considering such strong near-fault ground motions, which are the most challenging types for seismically isolated buildings.

Performance analysis of a geometrically nonlinear isolation system subjected to high levels of excitation

This study develops a modified harmonic balance method (HBM) and uses it to analyze the vibration isolation performance of a geometrically nonlinear isolation system subjected to high levels of excitation. The modified 5th-order Taylor series expansion (TSE) is applied to simplify the geometrically nonlinear stiffness (GNS) and geometrically nonlinear damping (GND). Using a modified elliptic harmonic balance method (EHBM), we can calculate the approximate free vibration frequencies consistent with the exact solutions. After illustrating the limitation of the high-order solution assumed by Jacobi elliptic functions, a modified HBM is proposed to solve the damped cubic-quintic Duffing (CQD) equation with high-level external excitation. The stability analysis is obtained, and the characteristics of unstable regions are shown according to different values of the damping coefficient. The results show that GNS and GND profoundly affect the high-order harmonic components of amplitude-frequency response and force transmissibility. The characteristics of low frequency and resonance regimes with or without quasi-zero stiffness (QZS) are different as the amplitude of excitation increases. The modified TSE and HBM are desirable and straightforward for the detailed study of the characteristics of the GNS and GND vibration isolation system.

Teaching-Learning Based Optimization of Nonlinear Isolation Systems under Far Fault Earthquakes

Seismic isolation systems exposed to far-fault earthquakes can reduce floor accelerations and story drift ratios to acceptable levels. However, they exhibit different structural performances in each earthquake due to different excitation frequency contents. By optimizing the isolation system parameters, their performance may be maintained at the best level under different far-fault earthquakes. In this study, the optimization of the parameters of the nonlinear isolation system of a 5-story benchmark building is performed by Teaching-Learning Based Optimization (TLBO) algorithm to minimize peak floor accelerations under historical far-fault earthquakes with and without exceeding a specified base displacement limit. According to the results of the analyses, it can be said that TLBO algorithm is a robust algorithm with low standard deviations for determining optimum nonlinear isolation system parameters.

Mathematical model and results for seismicresponses of a nonlinear isolation system

The friction and viscous damping actions always cause nonlinear responses of a seismic isolation system under earthquakes. Their influence on the seismic responses needs investigation in detail. In order to analyze the effects of nonlinear phenomenon on the seismic isolation system, a mathematical model was built for such a nonlinear isolation system, and the nonlinear responses were calculated and analyzed. The numerical results indicate that an appropriate combination of spring, Coulomb friction and viscous damper is able to achieve an optimal seismic performance. The stiffness and natural period of system are significantly influenced by the friction action. Both the friction action and the viscous damping action can dissipate earthquake energy, and the optimal value of one depends on the value of the other in the seismic isolation system. All of the values of spring, Coulomb friction and viscous damper should be accurately evaluated before the design of seismic isolation system.

Analytical and experimental study on sloped sliding‐type bearings

Seismic isolation design has been publicly accepted as one of the most effective strategies to reduce seismic threat to (or seismic demand for) the to-be-protected targets including building structures, infrastructure, and equipment. Recently, many studies have aimed to develop nonlinear seismic isolation systems, of which the sloped sliding-type bearing can exhibit the nonlinear behavior by mechanically designing a simple slope for sliding motion. Therefore, this bearing does not have a fixed isolation frequency. In addition, it features that the seismic isolation performance is realized through the sliding mechanism, the inherent self-centering capability is provided through the slope design, and the excellent and stable energy dissipation capability is contributed by the sliding friction. In this study, the equation of motion of the bearing is deduced first. Sensitivity analysis is then performed, and the results demonstrate that the maximum horizontal acceleration transmitted to the isolated superstructure is only dependent on two important design parameters-sliding friction coefficients and sloping angles. In other words, the acceleration control performance of the bearing is irrelevant to different characteristics of external disturbance. Finally, shaking table tests were conducted to verify the effectiveness of the bearing and the accuracy of the numerical prediction.

Evaluation of optimal FVDs for inter-storey isolation systems based on surrogate performance models

Inter-storey seismic isolation is increasingly gaining attention. One of the main related issues is the need to limit the relative displacement between substructure and superstructure, while maintaining a good seismic performance of the superstructure. As shown in some studies, fluid viscous dampers (FVDs) mounted in isolation systems are effective in reducing isolator deflection but can be harmful by amplifying inter-storey drifts and floor accelerations. Additionally, the effectiveness of FVDs for inter-storey applications was investigated only recently, and specific approaches for their optimisation and performance evaluation are missing. Therefore, this paper proposes a method for the optimal multi-objective design of FVDs, based on the definition of appropriate surrogate response models, which allows for rationally comparing the FVD effects for a wide range of dampers and structures. In particular, the optimal FVD parameters are provided in a dimensionless form, so that they can be predicted by design equations of general validity within the range of the structures analysed. This method is applied to a stock of regular structures with various vibration periods of superstructure, isolation and substructure, examining a linear and a non-linear isolation system and a set of natural records, in order to comprehensively assess the effects of FVDs and their non-linearity on the seismic performance of these structures. Finally, prediction models of optimal FVD parameters are provided based on the results obtained and are applied to three case studies as an example.

Dynamics characteristics of geometrically nonlinear isolation systems for seismic protection of equipment

AbstractEarthquakes pose risks to sensitive equipment and may result in dramatic economic loss. A widely used control strategy is to install an isolation system underneath equipment; however, excessive isolation displacements may be induced during severe earthquakes. Viscous dampers are recommended to be placed along with the isolation layer and to reduce displacements. Indeed, this combination is designed for a certain earthquake level and may be less effective in other earthquake levels. In this study, an isolation system with viscous dampers, which is installed perpendicular to the motion direction at the equilibrium position, is proposed to enhance seismic performance of important equipment through this geometrically nonlinear configuration. This configuration provides a better reduction in absolute accelerations during small‐to‐moderate earthquakes, while isolation displacements can be effectively mitigated during severe earthquakes. To understand the dynamic characteristics of this system, a series of investigations are carried out. The features of the effective control force are explored by the effective damping, and the phase plane analysis is conducted to understand the isolation system behavior. Then, the averaging method is employed to obtain the frequency–amplitude relationship of the proposed system, and the results inform the frequency domain behavior. The geometrically nonlinear damping is experimentally explored. Control effectiveness of the proposed system is also evaluated under seismic excitation and compared with the conventional isolation system (i.e., viscous dampers installed parallel to the isolation motion direction). As a result, the viscous damper with geometric nonlinearity can be more adaptive to different earthquake levels and thereby improves seismic isolation performance.