Nonlinear Base Isolation Research Articles

Enhancing seismic resilience of structures through optimally designed nonlinear negative stiffness base isolators: Exact closed-form expressions

Enhancing seismic resilience of structures through optimally designed nonlinear negative stiffness base isolators: Exact closed-form expressions

The nonlinear negative stiffness inertial amplifier base isolators for dynamic systems

The nonlinear negative stiffness inertial amplifier base isolators (NNSIABI) for vibration reduction of dynamic systems are introduced in this paper. H 2 and H ∞ optimization methods are applied to derive the exact closed-form expressions for the optimal design parameters of novel isolators. For SDOF system, the dynamic response reduction capacity of H 2 and H ∞ optimized linear NSIABI are significantly 64.78% and 77.14% superior to the optimum traditional base isolators. In contrast, the dynamic response reduction capacities of H 2 and H ∞-optimized nonlinear NNSIABI are significantly 64.66% and 66.56% superior to the optimum traditional base isolators. For MDOF systems, the optimum linear NSIABI’s dynamic response reduction capacities are significantly 95.06% and 97.80%, superior to the optimum traditional base isolators. In addition, the optimum nonlinear NNSIABI are significantly 94.88% and 97.68%, superior to the traditional base isolators. All the results are mathematically corrected and applicable for practical applications.

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.

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).

Seismic Damage Assessment for Isolated Buildings with a Substructure Method

A seismic damage detection method for isolated buildings is proposed based on substructure identification with incomplete contaminated measurements. A concept of a pseudo substructure with virtual conditions is constructed for the proof of the proposed substructure identification method. This identification method is implemented in a two-stage procedure. The interface forces of the target substructure are identified in the first stage and the parameter of the target substructure is updated in the second stage, which can enable the parameter identification of substructures with unknown input. Two computational methods are also proposed to improve the two-stage identification algorithm. A sub-time zone identification method is utilized to reduce the computation effort and the simultaneous identification of the unknown force and initial structural responses is presented in the first-stage identification for a general case in practical engineering. Numerical studies of a shear frame with nonlinear base isolation subject to earthquake ground motion are investigated to validate the proposed seismic damage detection method. A fourteen-storey concrete shear wall building with a two-storey steel frame on top connected by isolation is studied experimentally with shaking table tests to further validate the proposed method. The shear wall structure is taken as the target substructure for damage assessment. The interface force and parameter of the concrete shear wall building are estimated with the proposed method. Results from both the numerical simulations and laboratory tests indicate that the proposed method can estimate seismic isolated structures and detect damage effectively based on only a few accelerometers. It is also demonstrated that the parameter identification results based on the structure response measurement during the earthquake are more accurate than the identification with post-earthquake structural response measurement.

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.

Nonlinear viscoelastic isolation for seismic vibration mitigation

The aim of this paper is to assess the effectiveness of nonlinear viscoelastic damping in controlling base-excited vibrations. Specifically, the focus is to investigate the robustness of the nonlinear base isolation performance in controlling the system response due to a wide set of possible excitation spectra. The dynamic model is derived to study a simple structure whose base isolation is provided via a Rubber-Layer Roller Bearing (RLRB) (rigid cylinders rolling on rigid plates with highly damping rubber coatings) equipped with a nonlinear cubic spring, thus presenting both nonlinear damping and stiffness. We found that, under periodic loading, due to the non-monotonic bell-shaped viscoelastic damping arising from the viscoelastic rolling contacts, different dynamic regimes occur mostly depending on whether the damping peak is overcome or not. Interestingly, in the former case, poorly damped self-excited vibrations may be triggered by the steep damping decrease.Moreover, in order to investigate the robustness of the isolation performance, we consider a set of real seismic excitations, showing that tuned nonlinear RLRB provide loads isolation in a wider range of excitation spectra, compared to generic linear isolators. This is peculiarly suited for applications (such as seismic and failure engineering) in which the specific excitation spectrum is unknown a priori, and blind design on statistical data has to be employed.

Performance of a nonlinear hybrid base isolation system under the ground motions

In order to reduce the displacement demand of the isolation layer under strong earthquakes, especially strong near fault pulse-like ground motions, the base isolation system-tuned mass damper inerter (BIS-TMDI) system is explored taking the nonlinear hysteretic characteristics of the isolation layer into inclusion. Likewise, different from traditional layout of the BIS-TMDI systems, the TMD is placed on the superstructure (such as first floor or third floor, etc.) rather than on the isolation layer and linked to the ground by an inerter. By resorting to the equivalent linearization method (ELM) and genetic algorithm (GA) optimization, the optimal design method of nonlinear BIS-TMDI system is established and then, the performance of the system is numerically investigated. Results demonstrate that the nonlinear BIS-TMDI system can significantly reduce the displacement demand of the isolation layer, and its control effectiveness and stroke performance are better than those of the nonlinear BIS-TMD system. The influences of the parameters of the superstructure, isolation layer, and earthquake ground motions on the vibration mitigation is further scrutinized. It follows that the robustness of nonlinear BIS-TMDI system is much better than that of nonlinear BIS-TMD system. Analyzing the nonlinear BIS-TMDI system subjected to the near-fault pulse-like ground motions, the superiority of the system in reducing the displacement of isolation layer, the responses of superstructure and the stroke performance of TMDI are further verified.

Adaptive control for smart-actuated base isolation structures regarding various reference-tracking strategies

An adaptive control framework considering servo-hydraulic dynamics is proposed for base isolation structures regarding various reference-tracking strategies. The reference-tracking-based adaptive controller is derived from a backstepping design methodology with Lyapunov stability analysis. Servo-hydraulic dynamics, including the control-structure interaction (CSI) and the actuator uncertainties, have significant effects on seismic control performance; accordingly, the critical issue of the control device dynamics-induced time-lag should be introduced in the control process. To drive a successful active control event, an inverse actuator model is integrated within the proposed controller. Such inverse dynamic models, with adaptive regulation characteristics, are expected to compensate the time-lag real-time. On the other hand, for a reference-tracking-based controller, control performance is determined by a reference model. Therefore, different reference generation strategies have been discussed in a comparative study by considering the effect of structure nonlinearity and substructure-interaction. To investigate the performance of the proposed controller in detail, the first example is a nonlinear single-degree-of-freedom (SDOF) system. Then, a multi-degree-of-freedom (MDOF) system with a nonlinear base isolation layer is employed in a comparative study with various reference-tracking strategies. Subsequently, the proposed control framework has been performed in a nonlinear base isolation benchmark problem; and, the control performance demonstrates the efficacy of the reference-tracking controller in a two-dimensional actuator control problem.

Uncertainties in dynamic response of buildings with non-linear base-isolators

Dynamic response of base-isolated buildings under uni-directional sinusoidal base excitation is numerically investigated considering uncertainties in the isolation and excitation parameters. The buildings are idealized as single degree of freedom (SDOF) system and multi-degrees of freedom (MDOF) system with one lateral degree of freedom at each floor level. The isolation system is modeled using two different mathematical models such as: (i) code-recommended equivalent linear elastic-viscous damping model and (ii) bi-linear hysteretic model. The uncertain parameters of the isolator considered are time period, damping ratio, and yield displacement. Moreover, the amplitude and frequency of the sinusoidal base excitation function are considered uncertain. The uncertainty propagation is investigated using generalized polynomial chaos (gPC) expansion technique. The unknown gPC expansion coefficients are obtained by non-intrusive sparse grid collocation scheme. Efficiency of the technique is compared with the sampling method of Monte Carlo (MC) simulation. The stochastic response quantities of interest considered are bearing displacement and top floor acceleration of the building. Effects of individual uncertain parameters on the building response are quantified using sensitivity analyses. Effect of various uncertainty levels of the input parameters on the dynamic response of the building is also investigated. The peak bearing displacement and top floor acceleration are more influenced by the amplitude and frequency of the sinusoidal base excitation function. The effective time period of the isolation system also produces a considerable influence. However, in the presence of similar uncertainty level in the time period, amplitude and frequency of the sinusoidal forcing function, the effect of uncertainties in the other parameters of the isolator (e.g., damping ratio and yield displacement) is comparatively less. Interestingly, the mean values of the response quantities are found to be higher than the deterministic values in several instances, indicating the need of conducting stochastic analysis. The gPC expansion technique presented here is found to be a computationally efficient yet accurate alternative to the MC simulation for numerically modeling the uncertainty propagation in the dynamic response analyses of the base-isolated buildings.

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

SummaryThe 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.

Stochastic optimal design of novel nonlinear base isolation system for seismic-excited building structures

A novel nonlinear isolation system is numerically investigated by employing a stochastic response evaluation and experimentally studied with a small-scale preliminary prototype. The stochastic response of isolated building structures is first derived using a nonstationary random process and time-dependent equivalent linearization, regarding the nonlinear restoring force behavior of the proposed isolator. A parametric study is then performed to evaluate the potential influences of earthquake excitations properties and the optimum force ratio of the isolator that adopts the widely used Kanai–Tajimi model. According to the insights from the parametric study, the optimal design for nonlinear isolation is proposed based on a stochastic optimization procedure with the convergence of different performance objectives. The stochastically optimized isolation system is numerically studied by first comparing the present nonlinear isolator and conventional bearings. The present isolator is systematically illustrated to perform advantageously compared with conventional passive isolators in terms of base drift and structural acceleration through a relatively large group of 40 recorded seismic motions. To further investigate the efficiency of the nonlinear isolator, a benchmark building for smart base-isolation is adopted, and a comparison of the results indicates comparable performances between the proposed passive isolator and the classical active isolation system. Furthermore, an original design of the base isolation system simulating an energy dissipation mechanism is presented with favorable force-deformation behavior from experimental testing on small-scale prototypes.

A mixed explicit–implicit time integration approach for nonlinear analysis of base-isolated structures

The paper investigates the accuracy, the stability and the computational efficiency of a mixed explicit–implicit time integration approach proposed for predicting the nonlinear response of base-isolated structures subjected to earthquake excitation. Adopting the central difference method for evaluating the response of the nonlinear base isolation system and the Newmark’s constant average acceleration method for estimating the superstructure linear response, the proposed partitioned solution approach is used to analyze a 3D seismically isolated structure subjected to a bidirectional earthquake excitation. Both isolation systems adopting lead rubber and friction pendulum bearings are considered. Numerical results show that the computational time required by the proposed method, in spite of its conditional stability arising from the use of the central difference method in the explicit integration substep, is clearly reduced in comparison to the widely used implicit time integration method adopted in conjunction with the pseudo-force approach (i.e., pseudo-force method). As a matter of fact, the typical low stiffness of the isolation system leads to a critical time step larger than the one used to define the ground acceleration accurately and the proposed method preserves its computational efficiency even in the case of isolators with very high initial stiffness (i.e., friction pendulum bearings) for which the critical time step size could become smaller.

Probabilistic analysis for the response of nonlinear base isolation system under the ground excitation induced by high dam flood discharge

According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck- Kolmogorov (FPK) equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.

Exploring the effects of tuned mass dampers on the seismic performance of structures with nonlinear base isolation systems

Base isolation is a quite practical control strategy for enhancing the response of structural systems induced by strong ground motions. Due to the dynamic effects of base isolation systems, reduction in the interstory drifts of the superstructure is often achieved at the expense of high base displacement level, which may lead to instability of the structure or non-practical designs for the base isolators. To reduce the base displacement, several hybrid structural control strategies have been studied over the past decades. This study investigates a particular strategy that employs Tuned Mass Dampers (TMDs) for improving the performance of base-isolated structures and unlike previous studies, specifically focuses on the effectiveness of this hybrid control strategy in structures that are equipped with nonlinear base isolation systems. To consider the nonlinearities of base isolation systems, a Bouc-Wen model is selected and nonlinear dynamic OpenSees models are used to perform several time-history simulations in time and frequency domains. Through these numerical simulations, the effects of several parameters such as the fundamental period of the structure, dynamic properties of the TMD and isolation systems and properties of the input ground motion on the behaviour of TMD-structure-base isolation systems are examined. The results of this study provide a better insight into the performance of linear shear-story structures with nonlinear base isolators and show that there are many scenarios in which TMDs can still improve the performance of these systems.

Energy and Transmissibility in Nonlinear Viscous Base Isolators

Abstract High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.

Effects of soil–structure interaction on seismic base isolation

The effects of soil–structure interaction on the performance of a nonlinear seismic base isolation system for a simple elastic structure are examined. The steady-state response of the system to harmonic excitation is obtained by use of the equivalent linearization method. Simple analytical expressions for the deformation of the base isolation system and of the superstructure at resonance are obtained in terms of an effective replacement oscillator characterized by amplitude-dependent frequency, damping ratio, and excitation. Numerical results suggest that the seismic response of a structure resting on an inelastic base isolation system may be larger when the flexibility of the soil is considered than the corresponding response obtained by ignoring the effects of soil–structure interaction. It is shown that, in the undamped case and in the absence of soil–structure interaction effects, a critical harmonic excitation exists beyond which the steady-state resonant response of the isolators and structure become unbounded.

Discrete direct adaptive ELM controller for active vibration control of nonlinear base isolation buildings

Hybridization of base isolation and active control is a promising alternative to suppress the seismic vibrations in civil structures. The base-isolation system introduces hysteretic/frictional nonlinearity into the structure and hence there is a need to develop a nonlinear adaptive control approach to subdue the vibrations. In this paper, the authors propose discrete direct adaptive ELM controller for active control of nonlinear base isolated building, subjected to a set of near-fault earthquakes. A single hidden layer neural controller with random selection of input weights compensates the nonlinearity and provides desired vibration suppression. The neural controller is based on the extreme learning machine algorithm with random input weight selection and output weights are updated using Lyapunov like adaptation rule. The proposed discrete adaptive control law provides necessary stability and vibration suppression in nonlinear base isolated building. Simulation studies have been carried out using the full-scale three dimensional benchmark eight-storey building comprising hysteretic lead-rubber base-isolation. One earthquake record and perturbed model is used to train the controller offline. The offline trained controller is adapted online using the actual full-scale model for a wide range of near-fault earthquakes. The results clearly show that the proposed controller suppresses the vibration significantly without increasing superstructure responses. The comprehensive performance measures are compared with existing results reported in the literature.

Recent Advances on Vibration Control of Structures Under Dynamic Loading

In this paper, a review of recent journal articles on passive, active, semi-active, and hybrid vibration control of structures subjected to dynamic loading is presented. Passive systems reviewed include tuned mass damper (TMD), tuned liquid column damper (TLCD), tuned liquid column ball damper (TLCBD), circular TLCD (CTLCD), and pendulum TLCD (PTLCD). Active control systems include active tuned mass dampers (ATMD) and piezoelectric actuators. Semi-active systems include magnetorheological (MR) damper, negative stiffness devices (NSD), magneto-rheological damper TMD (MR-TMD), variable stiffness semi-active TMD (VS-STMD), variable damper STMD (VD-STMD), and recentering variable friction device (RVFD). Hybrid systems include active base isolation system and semi-active MR dampers with nonlinear base isolators. The current frontier of research is semi-active control of structures as well hybridization of various control systems. The problem is complex requiring integration of several different hardware and software technologies with structural design such as smart materials, adaptive dampers, actuators, sensors, and control and signal processing algorithms. This complexity also makes it an exciting area of research and development.

A new control algorithm to protect nonlinear base‐isolated structures against earthquakes

SUMMARYCurrently, nonlinear base isolation systems are widely used in the construction of earthquake resistant structures. However, they are found to be vulnerable in near‐fault regions as a result of long‐period pulses that may exist in near‐source ground motions. Various control strategies including passive, active and semi‐active control systems have been studied in order to handle this issue. In this study, a semi‐active control algorithm based on the different performance levels anticipated from an isolated building during different levels of ground shaking was developed. The proposed performance‐based algorithm is based on a modified version of the well‐known semi‐active skyhook control algorithm. A series of analyses were performed on the base‐isolated benchmark building, suggested by the American Society of Civil Engineers committee, subject to seven pairs of scaled ground‐motion records. The results proved that the new control algorithm is successful in improving structural and nonstructural performance of isolated buildings under near‐fault earthquakes. Copyright © 2012 John Wiley & Sons, Ltd.