Nonlinear Time History Analysis Research Articles

Seismic Response Prediction of Rigid Rocking Structures Using Explainable LightGBM Models

This study emphasizes the explainability of machine learning (ML) models in predicting the seismic response of rigid rocking structures, specifically using the LightGBM algorithm. By employing SHapley Additive exPlanations (SHAP), partial dependence plots (PDP), and accumulated local effects (ALE), a comprehensive feature importance analysis has been performed. This revealed that ground motion parameters, particularly peak ground acceleration (PGA), are critical for predicting small rotations, while structural parameters like slenderness and frequency are more significant for larger rotations. Utilizing an extensive dataset generated from nonlinear time history analyses, the trained LightGBM model demonstrated high accuracy in estimating the maximum rotation angle of rigid blocks under natural ground motions. The study also examined the sensitivity of model performance to lower bound thresholds of the target variable, revealing that reduced feature sets can maintain predictive performance effectively. These findings advance ML-based modeling of seismic rocking responses, providing interpretable and accurate models that enhance our understanding of rocking structures’ dynamic behavior, which is crucial for designing resilient structures and improving seismic risk assessments. Future research will focus on incorporating additional parameters and exploring advanced ML techniques to further refine these models.

Influence of Repeated Earthquake events on Structural Response of Multi‐storeyed RC buildings

Over the past decade, reinforced concrete (RC) multi-storeyed buildings have become more prevalent in urban environments. In addition, it has been well established in literature, that collapse of several RC buildings and resulting causalities, thereof are mainly attributed to the repeated nature of occurrence of earthquakes, more often leading to collapse. However, most existing design codes consider only a scenario earthquake characterized by the response spectrum specified by local codes of practice. This consideration do not address the repetitive nature of earthquakes, leading to inadequate estimation of design earthquake force. Hence, the present investigation focusses on proposing a probabilistic model to logically address the number of earthquake sequences to be considered at a chosen location. In addition, to ascertain attainment of collapse state of code designed 3D RC buildings, under a pattern of earthquake sequences (with simultaneous bi-directional ground motion data), a simple and computationally less intensive NLTHA (Nonlinear Time History Analysis) approach has been considered. Moreover, this approach captures the effect of sequential earthquakes and provides a quick rational decision on the structural behaviour, necessary for further analysis. Hence, eliminating the need to resort always for complex IDA (Incremental Dynamic Analysis) approaches to illustrate the structural behaviour. Moreover, the structural behaviour of RC buildings are represented in terms of base shear experienced and their corresponding response parameters (Horizontal displacement, Inter-story drift ratio (IDR), etc.,). The outcome of the results clearly contemplates the accumulation of damages in terms of response parameters, emphasizing the need for consideration of repeated earthquake sequences in seismic analysis.

Enhancement of the structural behavior of elevated water tanks using X-plate dampers

This study aims at utilizing of X-plate dampers to effectively address vibrations and minimize the possible structural harm to water tank facilities, and also at utilizing a finite element methodology to simulate and analyze the structural reactions. A non-linear time history analysis is employed to assess the effectiveness of X-plate dampers when subjected to different blast-induced ground motions. The efficiency of dampers was evaluated by conducting a comparative analysis of liquid storage structures with and without dampers using 50 m3 and 1500 m3 tanks in empty and full conditions. X – plate dampers are installed in a variety of bracing schemes, such as diagonal, X, V, Inverted V, and K bracing subjected to underground blast loads to improve the resilience of the selected elevated water tanks. The results showed the X-bracing pattern is the most effective configuration for X-plate dampers in mitigating blast loads in a 50 m3 elevated tank without water, resulting in a reduction of displacement, shear force, and bending moment by 43%, 15%, and 22%, in case of elevated tank with water reduced by 39% 25% and 33% respectively. In 1500 m3 elevated tank without water, the K-bracing is determined to be the most effective type of bracing, reducing the displacement, shear force, and bending moment by 50%, 70%, and 70%, in case of elevated tank with water reduced by 53%, 52%, and 54% respectively. The current study makes a significant contribution to the field of structural engineering by providing useful insights into raised water tank construction.

Study on the Effect of Burial Depth on Selection of Optimal Intensity Measures for Advanced Fragility Analysis of Horseshoe-Shaped Tunnels in Soft Soil

Seismic intensity measures (IMs) can directly affect the seismic risk assessment and the response characteristics of underground structures, especially when considering the key variable of burial depth. This means that the optimal seismic IMs must be selected to match the underground structure under different buried depth conditions. In the field of seismic engineering design, peak ground acceleration (PGA) is widely recognized as the optimal IM, especially in the seismic design code for aboveground structures. However, for the seismic evaluation of underground structures, the applicability and effectiveness still face certain doubts and discussions. In addition, the adverse effects of earthquakes on tunnels in soft soil are particularly prominent. This study aims to determine the optimal IMs applicable to different burial depths for horseshoe-shaped tunnels in soft soil using a nonlinear dynamic time history analysis method, and based on this, establish the seismic fragility curves that can accurately predict the probability of tunnel damage. The nonlinear finite element analysis model for the soil–tunnel interaction system was established. The effects of different burial depths on damage to horseshoe-shaped tunnels in soft soil were systematically studied. By adopting the incremental dynamic analysis (IDA) method and assessing the correlation, efficiency, practicality, and proficiency of the potential IMs, the optimal IMs were determined. The analysis indicates that PGA emerges as the optimal IM for shallow tunnels, whereas peak ground velocity (PGV) stands as the optimal IM for medium-depth tunnels. Furthermore, for deep tunnels, velocity spectral intensity (VSI) emerges as the optimal IM. Finally, the seismic fragility curves for horseshoe-shaped tunnels in soft soil were built. The proposed fragility curves can provide a quantitative tool for evaluating seismic disaster risk, and are of great significance for improving the overall seismic resistance and disaster resilience of society.

Multi-objective optimization of active control system using population guidance and modified reference-point-based NSGA-II

The optimization of the active control system is pivotal in achieving an acceptable performance level while minimizing control costs. The optimal location of actuators, efficient control force, and adequate vibration reduction are critical objectives in control system optimization. This study introduces a novel optimization algorithm, the Population-Guided and Modified Reference-Point Based Non-Dominated Sorting Genetic Algorithm-II (PMR-NSGA-II), tailored for actuator placement and tuning that incorporates input and output user preference. The analysis focuses on optimizing the vibration control of a 20-story steel frame building. The PMR-NSGA-II could reduce the computational expenses of three objectives optimization by guiding the initial population using prospective population prediction and orienting the search towards a reference point. The pre-calculated input energy distribution guides the determination of the prospective initial population. The reference point, along with the allowable drift and actuator capacity constraints, focuses the search process to efficiently obtain the Pareto fronts with less effort wasted to explore the less preferred areas in the search space. The non-dominated sorting and elitist operators are also employed to fasten the convergence. The structural analysis is conducted via non-linear time history analysis with seven ground motions considered. The PMR-NSGA-II exhibits significant computational efficiency in the active control system optimization. Results demonstrate that PMR-NSGA-II could provide the near-optimal solution closest to the reference point with a smaller population size and a faster convergence rate than the NSGA-II. The computational time per generation of the proposed PMR-NSGA-II is 1.36 to 2.43 times faster than NSGA-II for the seven ground motions analyzed. By applying PMR-NSGA-II, the number of individuals that need to be assessed to reach convergence is reduced by 50 % to 88 % compared to NSGA-II. Ultimately, the near-optimal configurations could significantly reduce the building responses and increase the performance level of the building based on FEMA 356 and ASCE 41 acceptance criteria.

Seismic response prediction and fragility assessment of high-speed railway bridges using machine learning technology

Nowadays, reliable and accurate prediction of the seismic response of high-speed railway bridges and then rapid assessment of their seismic fragility is crucial for the risk assessment of regional high-speed railway bridges. However, the traditional seismic fragility assessment based on nonlinear time history analysis (NTHA) has a characteristic of high computational cost. Therefore, this study explores different machine learning (ML) methods to develop a reliable rapid seismic fragility assessment framework for high-speed railway bridges. Taking a typical high-speed railway continuous (HRC) bridge as a case, a large number of numerical model and ground motion pairs considering various structural and ground motion features are established. Then, the two types of models including six popular ML methods are investigated, in which Lasso regression, artificial neural network (ANN) and support vector machine (SVM) are single models, and random forest (RF), extreme gradient boosting (XGBoost) and light gradient boosting machine (Light GBM) are ensemble models. A database containing a large number of seismic responses of different components is established through the NTHA to develop prediction models, and the optimal hyperparameters of different ML models are determined by ten-fold cross-validation and grid search. The study results show that the ensemble model can reliably predict the seismic response of the HRC bridge compared with the single model, and the XGBoost model is recommended for seismic fragility assessment. On this basis, the optimal ML model obtained by the performance evaluation is applied to develop seismic fragility curves of the HRC bridge, which are compared with the fragility curves based on NTHA. The results indicate that the XGBoost model can effectively replace the traditional NTHA for rapid seismic fragility assessment of the HRC bridge, which can achieve a sufficient assessment level while saving calculation costs.

Development and application of out-of-plane deformable X-shaped brace for energy dissipation and thermal stress mitigation: An experimental and numerical study

Exoskeleton systems are increasingly employed in both new and existing buildings to enhance seismic performance. Addressing the critical challenges of energy dissipation and thermal stress mitigation in these systems, an out-of-plane deformable X-shaped energy dissipation brace (OPD-XEDB), integrating an out-of-plane X-shaped brace with a shear-type metallic damper, was proposed in this study. A seismic design methodology for OPD-XEDB was firstly developed, ensuring effective energy dissipation of the damper before any potential brace buckling. Following this methodology, two specimens, exhibiting distinct failure modes of damper shear fracture and brace buckling, were designed and subjected to quasi-static loadings to explore their energy dissipation mechanisms. Upon these experimental results, a numerical model incorporating buckling and pinching behaviors was proposed and calibrated, effectively capturing the hysteretic responses of the specimens. This model was then employed in a comprehensive numerical analysis, validating the effectiveness of design methodology and determining the optimal specifications for the OPD-XEDB in a prototype building. Ultimately, thermal analysis and nonlinear time history analysis were conducted on the prototype building. The thermal analysis proved the effectiveness of the OPD-XEDB's out-of-plane configuration in mitigating thermal stress by out-of-plane deformation, significantly mitigating thermal stress in braces and interconnected moment frames by 96.59-96.66%. The time history analysis revealed that the dampers in OPD-XEDBs dissipated 11.6-23.2% of total seismic energy, effectively preventing substantial buckling in the X-shaped braces. This energy dissipation mechanism led to a remarkable 79.7% reduction in steel consumption for post-earthquake retrofitting, thereby significantly enhancing the seismic resilience of the primary structure.

Rapid Emergency Response Resilience Assessment of Highway Bridge Networks under Moderate Earthquakes

Quick post-disaster emergency response of highway bridge networks (HBNs) is vital to alleviating the impact of disasters in affected areas. Nevertheless, achieving their emergency response resilience remains challenging due to the difficulty in accurately capturing the response capacity of HBNs and rapidly evaluating the damage states of regional bridges. This study delves into the emergency response, seismic resilience, and recovery scheduling of HBNs subjected to frequent yet mostly ignored moderate earthquakes. Firstly, the feasibility of intelligent methods is explored as a substitute for nonlinear time-history analysis of regional bridges. Subsequently, for realistic modeling of post-disaster HBNs, a decision tree model is developed to determine potential traffic restrictions imposed on damaged bridges. Moreover, their emergency response functionalities are thoroughly investigated, upon which a comprehensive multi-dimensional resilience metric vector is proposed. Finally, the proposed methodologies are applied to the Sioux Falls HBN as a case study, revealing a decreasing mean value and increasing deviation values in the long term. The results are expected to provide important theoretical and practical emergency response guidance.

Efficient neural network-aided seismic life-cycle cost optimization of steel moment frames

In this paper, a novel and efficient neural network-based methodology is proposed to achieve seismic total cost optimization of steel moment-resisting frames in a timely manner. The computational burden of an optimization process based on performing nonlinear time-history analysis is prohibitively high. To address this crucial issue, a new and efficient neural network model is proposed in this paper to accurately predict the nonlinear time history response of steel frames during the optimization process. In the proposed neural network model, an ensemble of parallel neural networks is used to provide excellent prediction accuracy. In addition, a new repairability constraint is proposed to check the seismic damage level of structures during the optimization process with the aid of the proposed neural network model. Moreover, an efficient metaheuristic algorithm is used to achieve the optimization task. Two numerical examples are illustrated to demonstrate the efficiency of the proposed methodology. The results show that the proposed neural network model outperforms the existing standard models in terms of prediction accuracy. Furthermore, it is shown that by using the proposed methodology, the optimal seismic total cost of steel frames increases by less than 2.5%, yet their seismic collapse capacity increases by at least 30%.

Accuracy and uncertainty of predicted maximum and residual displacements of RC bridge columns under earthquake excitations

Fundamental to the performance-based seismic design is the accuracy of predicted responses under earthquake excitations. This study evaluates the accuracy and uncertainty of predicted maximum and residual displacements of concrete bridge columns subjected to different types of ground motions. A series of nonlinear time-history analyses considering a wide range of element formulations and model parameter combinations was performed to reproduce measured responses from previous shake table tests. Variations in element formulation had little influence on the accuracy and uncertainty of predicted maximum displacements. The gradient inelastic force-based element, however, predicted bar tensile strain profiles across the plastic hinge with higher resolution, but at a higher computational cost than displacement-based and beam with hinges elements. Models with tangent stiffness-based Rayleigh damping produced the most accurate predictions of the maximum drift ratios with an RMSE of 0.011, indicating that the maximum displacement (or drift ratio) can be predicted with reasonable accuracy. Residual displacements, on the other hand, were predicted with unreasonable levels of error and uncertainty. A data-driven model was thus proposed to correct predicted residual displacement. Following correction, the RMSE of the predicted residual drift ratios was reduced by 43 % to 0.006.

Design and Nonlinear Dynamic Response of a Steel Stack

AbstractIndustrial stacks are built in order to reduce atmospheric pollution and release gases to the higher level of the atmosphere. Since they are high and slender structures, they are significantly affected by lateral forces, in particular, induced by winds and earthquakes. This paper aims to summarize the design principles for steel stacks given in the international standards, codes and specifications considering the evaluation of the results from the investigation on nonlinear dynamic response of a typical steel stack subjected to the earthquake. For this purpose, a typical self-supporting steel stack has been designed and its performance under earthquake and wind forces has been investigated in terms of the applied design principles, such as the displacement limit and the potential plastic deformations. The study is accomplished by using finite element models employing nonlinear time history and pushover analyses. The numerical results are presented particularly by considering the design principles used for the model. The results show that wind loads considered are more pronounced in the design of industrial steel stacks than earthquake especially in terms of limiting top displacement. The flue openings which reduce strength and lateral stiffness of the stack web is significantly effective in the lateral behavior of the stack. Moreover, the principles considered are found applicable for the design of such steel stacks. Based on the results from nonlinear time history analyses, no yielding and plastic deformation are detected along the stack.

Design standardisation and seismic protection of SMRs through modular metafoundations

This paper investigates the seismic protection of the Nuward™ small modular reactor (SMR) building, focusing on design loading and beyond design basis earthquake (bDBE) conditions. The study aims to achieve two primary objectives: i) to enhance seismic mitigation of a SMR building under bDBE conditions, through the use of the innovative modular single-layer (SLM) and multi-layer (MLM) metafoundations (MFs); ii) to effectively standardise and harmonise SMR building designs in locations prone to beyond design basis conditions. To accomplish these goals and demonstrate the protective capabilities of the MFs, the study employs non-linear time-history analyses (NLTHAs) for both DBE and bDBE conditions. Along these lines, a reduced-order model was developed from a refined finite element (FE) model of the SMR building using the Craig-Bampton mode synthesis technique. Then, finite locally resonant modular MFs were designed and analysed using NLTHAs. Specifically, physics-based ground motion models (GMMs) were used to generate and select seismic triplets that mimicked DBE and bDBE scenarios for NLTHAs. Successively to achieve improved seismic performance, the optimization of the MFs was pursued by targeting the optimal number of columns, resonator parameters, and unit cell dimensions. Additionally, the deployment of inerters was considered, to significantly reduce the size of the MFs and enable their application in multiple layers for ultra-low frequency attenuation. The overall findings suggest that modular MFs meet seismic protection requirements, and positively contribute to the standardization process of SMR buildings, even in areas characterized by beyond-design seismic conditions.

The cumulative plastic deformation demand for buckling restrained braces imposed by the strong motions in the 2023 Turkey earthquake sequence

The Turkey earthquake sequence on February 6, 2023, was featured by the closely located earthquake doublet of Mw7.8 and Mw7.5. The consequent strong ground motions are supposed to be able to impose high demands on the ultra-low-cycle fatigue performance of metallic dampers in buildings, including the widely used buckling restrained braces. This study evaluates the cumulative plastic deformation (CPD) demands on buckling-restrained braces (BRBs) in multi-story buildings imposed by the strong ground motions in the 2023 Turkey earthquake doublet. Thirty-two records of the highest peak ground accelerations were selected from the strong motion database. Among them, eight captured the ground motions during both the events, and the rest only captured the shaking of either of the events. The CPD demands on the BRBs in reinforced concrete frames with various fundamental periods, brace-to-frame stiffness ratios, and BRB ductility ratio are calculated by nonlinear time history analyses, and are summarized in the form of enveloped spectra of CPD ratios at constant ductility. The results show that the CPD demands on BRBs increase with smaller brace-to-frame stiffness ratios and larger BRB ductility ratio. The enveloped CPD demands are several hundreds of times the nominal yield deformation of the BRB, which are much higher than the CPD demands for the calibration tests of BRBs stipulated by AISC 341 in the US.

Strong ground motion characteristics observed in the February 6, 2023 MW7.7 Türkiye earthquake

Türkiye is located in a seismically active region, where the Anatolian, African, and Arabian tectonic plates converge. High seismic hazards cause the region to be struck repeatedly by major earthquakes. On February 06, 2023, a devastating MW7.7 earthquake struck Türkiye at 01:17 am local time (01:17 UTC). In this regard, near and far-field ground motion data within the distance of 120 km are compiled and later characterized to identify the key ground motion intensity measures. Additionally, the vertical components of ground motions were examined to capture the complete three-dimensional nature of the seismic event. Moreover, the effect of Pulse-Like (PL) and Non-Pulse-Like (NPL) ground motion on a representative RC frame structure built as per the Türkiye code was investigated. The results indicate that PL behavior was observed in both horizontal and vertical components of ground motions and PL behavior were noted both near the epicenter and at higher distances from the epicenter. Moreover, the ratio of the peak vertical acceleration to peak horizontal acceleration at certain stations was found to be close to 1. Finally, the non-linear time history analysis of the representative reinforced concrete frame structure for ground motions recorded at stations located equidistant from the epicenter, indicated that PL ground motions led to more significant damage compared to NPL ground motions.

Comparative Analysis of Concentrically Braced Frames with FeSMA and Steel BRBs Under Long-Duration Earthquakes

ABSTRACT Owing to high fatigue life, the iron-based shape memory alloy (FeSMA) buckling-restrained braces (BRBs) are emerging as a promising candidate against long-duration earthquakes. However, the corresponding analysis cannot be found. Current emphasis is paid on unveiling the seismic response differences between concentrically braced frames (CBFs) with FeSMA and steel BRBs when they are attacked by long-duration earthquakes. To directly assess the effect of earthquake duration, this paper selects a total of 90 pairs of short- and long-duration earthquake records, which are record-to-record spectrally equivalent over a wide range of fundamental periods, for nonlinear time history analysis. A benchmark six-story CBF is selected for demonstration purposes. In the numerical simulation process, the fatigue-induced damage is particularly considered. A preliminary examination is first conducted in the case study, in which a representative pair of short- and long-duration records is selected. In what followed, the statistical results from the ground motion suites are analyzed. This work not only highlights the higher failure risk of steel BRBs than FeSMA BRBs under long-duration earthquakes associated with maximum considered earthquake hazard level, but also confirms the advantages of FeSMA BRBs over steel BRBs in controlling residual deformations.

Seismic evaluation and retrofit of a typical reinforced concrete hospital building in Indonesia with DCFP isolation system

In this paper, a study on seismic evaluation and retrofit of a typical reinforced concrete (RC) hospital building in Indonesia is presented. Seismic evaluation is performed against basic structural performance objectives outlined in the current code for structural seismic evaluation. The target building is a typical 5-story RC building designed by the 1970s Indonesia seismic and building codes, which imposed lower seismic demand and were not as strict as the current codes in the requirements for strength and ductility. The first part of the paper describes a seismic evaluation procedure against specific target performance levels. Nonlinear time history analysis (NLTHA) is conducted and structural performances were evaluated against structural responses (base shear force and inter-story drift ratio) and acceptance of seismic performance level for local (element rotational limit) and global (roof drift ratio) performance criteria under 225, 975, and 2475-year return period earthquake scenarios. Results reveal that seismic performances of some structural elements are unsatisfactory and under the acceptable performance level, especially for 2475-year return period (BSE-2 N/MCER) earthquake scenario. Seismic retrofit is thus recommended and the use of double-concave friction pendulum (DCFP) base-isolation system as a retrofit strategy is explored. The seismic performance of DCFP-retrofitted building is examined by NLTHA, where effectiveness of DCFP base-isolation system in improving seismic performance is confirmed by comparing structural responses, local and global structural performance of the existing building and the DCFP-retrofitted building under 2475-year return period earthquake scenario. Results of NLTHA demonstrate that local structural performance level has improved from Collapse Prevention to Immediate Occupancy level, whereas the global structural performance has improved from Limited Safety level to Operational level.

Seismic retrofit of framed structures using a steel frame with springs and friction dampers

In this research, a seismic retrofit device was proposed and its performance was tested under cyclic loading. The developed damper is composed of a steel frame with friction hinges and springs at corners to provide stiffness and restoring force. Theoretical formulas for its mechanical behavior and its analytical model were developed and verified by comparing them with the results of an experimental test. To further evaluate the applicability of this retrofit system, it was applied to the seismic retrofit of a case study structure designed without considering seismic load. The structure was retrofitted to satisfy a given performance objective and its seismic behavior was compared using nonlinear time history analysis before and after retrofit. The seismic performance of the structure was assessed in terms of maximum interstory drift ratio, residual displacement, and energy dissipation. It was observed that the installed retrofit frames could properly dissipate the seismic energy and reduce both inter-story drifts and residual displacements of the case study structure.

Seismic performance of BRBF with SMA core using incremental dynamic analysis

ABSTRACT In this paper, a new model for Buckling Restrained Braced Frames (BRBF) is proposed that Shape Memory Alloy (SMA) is used for the yielding core instead of steel. The seismic behaviour of a framed structure with chevron type buckling restrained braces is investigated and their seismic performance factors, such as permanent displacements, inter story drifts and response modification factors are evaluated. Nonlinear time history analysis and Incremental Dynamic Analysis (IDA) of two models subjected to 11 ground motion records is performed using OpenSees software. In order to evaluate the efficiency of the proposed model, it is compared to a BRB model with a steel core that the length of yielding core is 1 m for each model. Comparing the proposed bracing systems with conventional BRBFs indicates that buckling restrained braced frames equipped with SMA are better in terms of permanent roof displacement and maximum inter-story drift. However, the response modification factor of BRB models with steel core is higher.

Feasibility of using superelastic shape memory alloy in plastic hinge regions of steel bridge columns for seismic applications

AbstractThis paper contributes to the further development of seismic resilient infrastructure by introducing a novel prototype bridge which integrates tubular steel piers with superelastic shape memory alloy (SMA). The proposed bridge pier is composed of a circular steel tube which is bonded to a superelastic SMA tube in regions of high stress. The pier is distinguished by its ability to minimize residual drifts following inelastic deformations induced by cyclic loading. Three‐dimensional continuum finite element (FE) models are utilized to examine its lateral behavior. Experimental data is used to demonstrate the effectiveness of the continuum FE procedure in replicating the cyclic response and capturing both global and localized behaviors. A novel composite material model is proposed to represent the degradation of strength and accumulation of irreversible strains in the cyclic response of superelastic SMAs. An iterative procedure for the calibration of this material is presented. Investigations, employing the calibrated FE procedure, focus on the quasi‐static cyclic response of steel piers with superelastic SMA in the plastic hinge zone, aiming to identify the optimal length of the SMA tube for achieving a self‐centering response with reduced residual deformation. The study is then further expanded to examine the seismic response of a bridge structure incorporating such piers. Development of the FE model for the prototype bridge includes the modelling of the piers using continuum elements, while the superstructure, bearing units, abutment walls, and backfill material are modelled using discrete elements. Nonlinear time history analyses are undertaken to investigate the effects of column wall thickness and materials used in the plastic hinge zones of the piers. Dynamic FE study results indicate that bridges employing such piers are capable of returning to their original position, provided the SMA tube is of adequate length.

Seismic response of structures with friction pendulum inerter system (FPIS) under near-fault earthquakes

Near-fault ground motions with high acceleration peaks and long-period velocity pulses pose a serious threat to the reliability of engineering structures. To reduce the displacement of isolation layer and improve the seismic performance of superstructure under the near-fault ground motions, a composite isolation system, which is composed of friction pendulum system (FPS) and inerter system, namely FPIS, was used in this paper. Based on D’Alembert’s principle, the nonlinear motion equations of a base-isolated structure with FPIS were established. The damping effect of two different mechanical layouts of FPIS subsystems, i.e, series-parallel inerter system-I-FPS(SPIS-I-FPS) or series-parallel inerter system-II-FPS(SPIS-II-FPS), were investigated in this study. The strong nonlinearity of FPIS was considered, and the inerter system parameters were designed based on the principle of maximum damping enhancement. The fourth-order Runge-Kutta approach was used to solve the dynamic response of a multi-degree-of-freedom system under seismic excitations. The effectiveness of FPIS was verified by comparing the isolation layer displacement and the acceleration of superstructure calculated by MATLAB with the friction pendulum system and viscous damper (FPS-VD). The nonlinear time history analysis results indicate that within a certain additional damping range, the SPIS-I-FPS subsystem performs effectively than SPIS-II-FPS in reducing the superstructure acceleration and isolation layer displacement. To increase the energy dissipation efficiency of structures, it is recommended to increase the design parameters of the inerter system and control the friction coefficient of FPS within the range of 0.05∼0.10.