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Frontiers in Built Environment ·

Volume 12 - 2026 | https://doi.org/10.3389/fbuil.2026.1966528

Seismic performance assessment of inerter-based damping systems for structural vibration control – a comprehensive review

  • Madhu Beerabbi Eshapurada1
  • K. S. K. Karthik Reddy1*corresponding author
  1. School of Civil Engineering, Vellore Institute of Technology (VIT), Vellore, Tamil Nadu, India
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Abstract

Devastating earthquakes across the globe have exposed the vulnerability of civil infrastructure, resulting in severe structural collapse, significant casualties, economic losses, and enduring societal impacts. These incidents emphasize the need for advanced seismic protection strategies capable of strengthening structural resilience and minimizing earthquake-induced damage. Among the various passive vibration control technologies currently available, inerter-based damping systems have gained considerable attention as a promising solution owing to their capacity to significantly amplify inertial effects while requiring minimal physical mass. Such systems offer greater tuning flexibility, improved space efficiency, and enhanced seismic response mitigation, ultimately contributing to more efficient structural control strategies. Although a wide range of analytical, numerical, and experimental investigations have demonstrated that well-optimized inerter-based dampers can effectively lower the seismic response of structures, research dedicated to performance-oriented evaluation remains limited. This review systematically examines the diverse inerter configurations adopted across different structural systems, along with studies addressing the seismic performance assessment of structures incorporating inerter-based dampers. It critically evaluates the range of performance metrics used to characterize these damping systems. The results indicate a progressive shift from conventional response-based approaches to more holistic performance-based assessment frameworks. However, the reviewed studies also identified important limitations, including sensitivity to ground motion characteristics, device configuration, and limited large-scale experimental validation. The review concludes by identifying existing research gaps and outlining future directions, providing a valuable resource for researchers engaged in the design and evaluation of advanced inerter-based damping systems.

Keywords

1 Introduction

Recent destructive earthquakes worldwide have highlighted the persistent threat posed by seismic hazards to human safety, infrastructure, and socioeconomic development. Major events such as the 2023 Turkey-Syria earthquakes, the 2024 Noto Peninsula earthquake in Japan, and the 2026 Venezuela earthquakes, together with the history of damaging earthquakes in India, have demonstrated the severe consequences of seismic events, including extensive structural damage, substantial loss of life, disruption of essential infrastructure, and significant economic losses (Suppasri et al., 2024; Wani et al., 2024). In India, seismic risk remains particularly significant due to the widespread presence of earthquake-prone regions, rapid urban development, and the vulnerability of existing infrastructure. The damage caused by earthquakes is influenced not only by the intensity of ground shaking but also by factors such as structural design, construction quality, material degradation, and compliance with building codes. As cities continue to expand and infrastructure systems become increasingly interconnected, the consequences of seismic failure can extend beyond the directly affected region impacting economic activities and essential services. Thus, ensuring adequate seismic performance remains a global engineering challenge that extends beyond high seismic regions. A thorough assessment of seismic performance allows engineers to analyse structural responses to varying magnitudes, estimate the likelihood of damage and collapse, evaluate resilience and functionality, and formulate effective strategies for seismic mitigation to enhance public safety, minimize economic losses, and encourage long-term sustainability (Goulet et al., 2007).

To attenuate the adverse impacts of earthquakes, numerous seismic protection strategies have been developed in recent decades. Standard practices primarily focus on enhancing the strength, stiffness, and ductility of structural systems through improved material properties, optimized structural configurations, and standardized earthquake-resistant design. Various seismic retrofitting techniques, including jacketing, bracing, isolation techniques and the use of fiber-reinforced polymer composites, have been widely used to enhance the performance of existing structures, along with aforementioned approaches (Güneyisi and Altay, 2008; Jangid, 2021; Jaimes et al., 2023; Kapasakalis et al., 2026b). Recently, structural vibration control technologies have gained significant recognition for their capability to dissipate or redistribute seismic energy. This property effectively alleviates structural responses without significantly increasing structural mass or stiffness. These technologies are typically classified into passive, active, semi-active, and hybrid control systems. Among these, passive vibration control devices including base isolation systems, Fluid Viscous Dampers (FVD), friction dampers, metallic yielding dampers, viscoelastic dampers, and Tuned Mass Dampers (TMD), have been widely adopted owing to their reliability, simplicity, and low maintenance requirements (Kiran and Naveenkumar, 2025; Lekeufack et al., 2026). Beyond these conventional methods and technologies, advanced approaches to seismic resilience, including Performance-Based Seismic Design (PBSD) and energy dissipation mechanisms, have gained increased attention due to their demonstrated effectiveness in enhancing structural performance and resilience (Hwang et al., 2007; Porter et al., 2007; Sharma et al., 2021; Pedone et al., 2023).

Regardless of their proven performance, each of these approaches has intrinsic limitations related to tuning requirements, added mass, installation constraints, or reduced performance when subjected to different excitation characteristics, which drives the ongoing pursuit of more efficient and adaptable vibration control solutions (Khasare et al., 2023; Sharma et al., 2025; Kapasakalis et al., 2026a; Mbasso et al., 2026). The increasing demand for resilient and cost-effective seismic protection in civil structures has driven the development of advanced damping systems. Recent advancements in seismic protection techniques, such as TMD and Inerter-Based Damper (IBD) systems, show promise in overcoming these drawbacks and improving overall structural resilience. In particular, inerter-based dampers are designed to improve the adaptability and efficiency of vibration control systems, thereby resulting in safer structures in earthquake-prone regions (Marian and Giaralis, 2014; Dadkhah et al., 2020; Khollari et al., 2026). The inerter damper was first conceptualized as two terminal mechanical elements that generate force proportional to relative acceleration, and it has emerged as a promising solution for seismic vibration control (Smith, 2002; Lazar et al., 2014). Their ability to amplify effective mass without significant physical weight addition offers unique advantages over traditional dampers, especially in applications where added mass is undesirable. Recent advances in nonlinear, semi-active, and smart-material-based inerter designs have further enhanced their adaptability and effectiveness in seismic events (Marian and Giaralis, 2014; Khasare et al., 2023).

Although inerter-based damping systems have attracted growing attention in earthquake engineering, very few studies have concentrated on detailed performance assessment of these systems. Most published work has focused on code-based, analytical modelling, numerical simulation, and parameter optimization. Although several experimental and shake-table studies have been reported, large-scale or full-scale experimental validation remains comparatively limited, especially for systematic performance comparisons under real earthquake ground motion records (Wagg, 2021; Su et al., 2022; Peng et al., 2025). Figure 1 presents the keyword co-occurrence overlay network for inerter-based damping systems based on 2021–2026 dataset. The colour gradient represents the average publication year of the selected keywords, resulting in a range of approximately 2021–2024. This research domain is characterized by the prominence of the keywords inerter and vibration control, which are strongly linked to tuned mass damper, parameter optimization, dynamic vibration absorber, base isolation, and passive vibration control. Earlier research, represented by blue and cyan frames, focused on seismic base isolation, optimization, and associated structural control applications. The green to yellow frames signifies a relatively recent shift toward multi-objective optimization, soil-structure interaction, shake table testing, and advanced optimization strategies. Despite the methodological progression, most of the existing literature focused on analytical modelling, parameter tuning, and design-oriented evaluation. Previous studies have provided significant insight into the behaviour of inerter-based systems under controlled conditions, but relatively limited studies have been carried out on their performance across a range of earthquake records and nonlinear conditions. This gap underscores the need for a more thorough performance-based seismic assessment of inerter-equipped structures. Konar and Ghosh (2024) reviewed tuned mass damper inerter (TMDI) systems, with emphasis on their development and seismic applications in multi-storey structures. In comparison, the present review covers a wider range of inerter-based damping systems and focuses on their installation configurations, seismic performance evaluation metrics, assessment methodologies, and response under different ground motion conditions. Accordingly, this review summarizes the existing research on the seismic performance of structures equipped with inerter-based dampers, with a particular focus on the performance evaluation metrics and methodologies employed in previous studies. Subsequently, Section 2 presents the fundamental concepts of inerter-based damping systems and their adopted strategies. Section 3 reviews various performance evaluation indices examined across different inerter configurations, and Section 4 details the methodologies used to assess the seismic performance of inerter-based dampers. Finally, Section 5 presents the concluding remarks, limitations, and outlines future directions regarding the evaluation of inerter-based systems.

Keywords co-occurrence overlay network for inerter-based damper study, showing the interconnections among major research themes. The connecting lines denote keyword co-occurrence relationships, while colour gradient represents the average publication year and highlights the evolution of research trends.
Figure 1. Keywords co-occurrence overlay network for inerter-based damper study, showing the interconnections among major research themes. The connecting lines denote keyword co-occurrence relationships, while colour gradient represents the average publication year and highlights the evolution of research trends.

2 Fundamentals of inerter-based damping systems

Understanding the fundamental concepts of inerter-based damping systems is essential for evaluating their application in seismic response control. This section briefly explains the working principle of the inerter and then outlines the typical installation and connection strategies adopted in structural applications. In addition, it summarizes the typical configurations reported in previous studies and their performance during earthquakes.

2.1 Principle of the inerter

The inerter concept was first introduced by (Smith, 2002), describing a mechanical element that functions as a spring’s dual network. This innovative device has since gained attention in various applications, particularly for vibration control in engineering structures and mechanical systems. In contrast to a conventional mass, whose one end remains permanently attached to a fixed reference, an inerter is a two-terminal mechanical component that joins two locations/masses within a structural system. It generates equal and opposite forces F(t) at its terminals in proportion to their relative acceleration as shown in Figure 2 (adapted from Wu et al., 2022).

Conceptual schematic of a simple two-terminal inerter illustrating its mechanical configuration and the corresponding force-acceleration relationship, where the equation indicates that the inerter force is proportional to the relative acceleration between its terminals through the inertance parameter.
Figure 2. Conceptual schematic of a simple two-terminal inerter illustrating its mechanical configuration and the corresponding force-acceleration relationship, where the equation indicates that the inerter force is proportional to the relative acceleration between its terminals through the inertance parameter.

Where ‘b’ denotes the inertance with kilogram (kg) as unit, and x ¨ 1 and x ¨ 2 represents the accelerations at the two terminals (Lazar et al., 2014; Marian and Giaralis, 2014). An important quality of the inerter is that it can generate a substantial apparent inertial effect without requiring an equivalent physical mass, making it a compelling option for vibration control applications where space and weight are constrained. The inerter has been effectively integrated into a range of engineering systems, such as automobiles, railway vehicle suspensions, and structural vibration control applications since it was first introduced. This adaptability of inerter continues to inspire innovative designs across a range of engineering disciplines, enabling the development of more advanced vibration mitigation solutions (Islam and Jangid, 2021; 2023; Liang et al., 2021). The following section discusses various inerter damper installation strategies in structural systems.

2.2 Installation strategies of inerter-based damping system

The seismic performance of an inerter-based damping system is determined not only by its mechanical characteristics but also by its integration location within the structural framework, as these design decisions directly affect major performance metrics, such as inter-storey drift, floor acceleration, and energy dissipation (Wen et al., 2017; Pietrosanti et al., 2020; Xu et al., 2022). Different installation strategies modify the distribution of inertia, stiffness, and damping which affects the structural dynamic response and its overall seismic performance. Several studies have examined various placement strategies for inerter-based dampers and their impact on seismic performance. Figure 3 (i–iv) presents schematic illustrations of a few commonly adopted placement and connection configurations of inerter-based dampers in structural systems. These studies provide insights into how different installation strategies can optimize the effectiveness of these dampers. A multi-level configuration is shown in Figure 3 (iv), where one terminal of the inerter-damping system is connected to the top floor and the other terminal can be connected to the ground or various lower-storey levels. This arrangement represents potential connection configuration discussed in various studies. Table 1 provides typical configurations of inerter-based damping systems commonly adopted in structural applications along with their performance effect on structures. A comparative study by (Xu et al., 2022) showed that span-storey IBD installation provides superior vibration reduction by increasing drift amplification, thereby improving key performance indicators such as reduced modal response and lower control force. Xu et al. (2021) reported that Tuned Inerter Damper (TID) located at the maximum modal inter-storey drift position yields better vibration suppression, reducing modal response and structural acceleration. In another study on Tuned Mass Damper Inerter (TMDI), the findings indicated that the optimal vibration control performance occurs when the inerter is connected between the top-storey and the ground. This arrangement significantly lowers the inter-storey drift and response variability while enhancing seismic reliability relative to other configurations (Sun and Peng, 2025). Beyond the installation configuration, the effectiveness of inerter-based damping systems is sensitive to the selected inertance value. For example (Peng and Sun, 2024), observed that the optimal inertance-to-mass ratio tends to increase with increasing structural period. De Angelis et al. (2019) reported limited additional improvement in response reduction at higher inertance levels, particularly for highly damped structural systems, while (Saha, 2026) observed that the response reduction becomes relatively insensitive beyond an inertance ratio of approximately 0.30 for the selected damper configuration. These findings suggest that increasing inertance does not necessarily lead to a corresponding improvement in seismic response, and its effectiveness depends on the dynamic properties of the structure and damper configuration. A variety of structural performance metrics used to assess the effectiveness of inerter-based dampers are reviewed in the following section.

Representative placement and connection configurations of inerter-based damping systems reported in previous studies, illustrating different strategies for connecting inerter elements within structural systems: (i) base-isolated inerter connection; (ii) inerter connected between two adjacent structures; (iii) grounded inerter connection; and (iv) Top-floor inerter connected to different lower-storey levels and ground level (adapted from Jangid, 2024b; Kang et al., 2024a; Kang et al., 2024b).
Figure 3. Representative placement and connection configurations of inerter-based damping systems reported in previous studies, illustrating different strategies for connecting inerter elements within structural systems: (i) base-isolated inerter connection; (ii) inerter connected between two adjacent structures; (iii) grounded inerter connection; and (iv) Top-floor inerter connected to different lower-storey levels and ground level (adapted from Jangid, 2024b; Kang et al., 2024a; Kang et al., 2024b).

TABLE 1. Typical integration of inerter-based damper systems into structures and their seismic performance.

Installation strategiesInerter attachmentPrimary seismic functionReferences
Base-isolated structuresTMDI, TVMD, or other inerter-based dampers installed at isolation levelReduces isolation displacement and base shear; some configurations also enhance robustness and energy dissipation(Deastra et al., 2018; De Angelis et al., 2019; Islam and Jangid, 2023; Jangid, 2023)
Roof/Top floor mountedTMDI and other types attached on top floor or to an auxiliary massControls fundamental vibration mode, resulting in reduced roof displacement and floor acceleration(Marian and Giaralis, 2014; Konar and Ghosh, 2024)
GroundedOne terminal of the inerter is connected to the ground, while other is attached to the structureExploits structure-ground relative acceleration to generate inertial forces for effective seismic vibration control(Marian and Giaralis, 2014; De Angelis et al., 2019)
Inter-storeyInstalled between adjacent or non-adjacent storeysProvides improved control of higher vibration modes and inter-storey drift; cross-layer configurations further enhance control efficiency(Rajana et al., 2023; Zhang et al., 2023)
Adjacent building couplingInstalled between adjacent buildings or bridge segmentsMitigates pounding, reduces relative displacement, and enhances seismic robustness(Basili et al., 2018 ; 2019; Islam and Jangid, 2024a)
Bridge applicationsInstalled between the deck and pier or integrated with stay cablesReduces deck displacement and pier forces while suppressing cable vibrations(Xu et al., 2019; Liang et al., 2021; Li et al., 2023; Peng et al., 2025)
Clutched configurationConnected between structural components through a clutch mechanismImproves control efficiency by engaging only when required under dynamic excitation(Málaga-Chuquitaype et al., 2019; Jangid, 2021; Barkale and Jangid, 2022)

3 Performance evaluation metrics

To assess the effectiveness of inerter-based damping systems, appropriate response parameters are required to capture various aspects of structural behaviour under seismic excitation. These parameters provide a basis for quantifying the reduction in structural demand and evaluating the overall effectiveness of the control system. Consequently, various performance indices are examined using displacement-, force and acceleration-, energy-, and performance-based criteria, reflecting different aspects of seismic response and structural performance.

3.1 Overview

To assess the effectiveness of inerter-based damping systems during seismic events, researchers have employed a range of structural performance metrics that capture different aspects of earthquake response. These performance indices act as quantitative tools for evaluating the ability of inerter-based dampers to minimize structural deformation, control acceleration and force demands, dissipate seismic energy input, and improve overall structural performance (Kang et al., 2024b; Jha et al., 2025). These indices are essential for comprehending the efficacy of damper systems in real-world seismic scenarios, providing insights for design enhancements and risk assessment in the field of structural engineering. These performance parameters not only quantify the damping efficiency but also guide engineers in optimizing the design of resilient structures subjected to seismic loading. Furthermore, the integration of these indices into a performance-based design framework allows for a more informed selection of damping systems, enhancing the overall resilience of structures against seismic forces. Multiple response parameters, such as displacement, inter-storey drift, base shear, and energy dissipation, are classified as shown in Figure 4, which are essential for characterizing the seismic behaviour of controlled structures (Patsialis et al., 2023; Liao et al., 2024; Saha, 2026). These indices offer a comprehensive framework for comparing the seismic performance of structures with various IBD systems and assessing their effectiveness against conventional passive control devices. A summary and critical comparison of studies investigating the seismic performance of various inerter-based damping systems are presented in Table 2, including the adopted ground motion selection, key findings, and reported limitations.

Classification of performance assessment metrics used for the seismic evaluation of inerter-based damping systems, grouped according to different assessment criteria.
Figure 4. Classification of performance assessment metrics used for the seismic evaluation of inerter-based damping systems, grouped according to different assessment criteria.

TABLE 2. Summary and critical comparison of studies on the seismic performance assessment of various inerter-based damping systems.

Structure studiedDamper typeKey findingsGround motion selectionLimitations/Critical observationsReference study
Base-isolated SDOF systemGrounded TMDI4 ground motions including near-fault and far-field recordsStudy assumes linear idealized model and performance is sensitive to near-fault pulse characteristics(De Angelis et al., 2019)
Ten-storey base-excited shear buildingSingle- and double- inerter TMDI25 Far-field earthquake recordsLimited to linear structural response and far-field ground motions(Kaveh et al., 2020)
SDOFThree configurations of Inerter-based TMD3 representative ground motions including Imperial Valley earthquakeSDOF-based formulation; validation limited to three recorded ground motions(Zuo et al., 2021)
Nine-storey benchmark steel frame buildingIVA (TMDI and TID)Seven ground motion records, with a mean Peak Ground Acceleration (PGA) of 0.39 gRelative IVA efficiency decreases with increasing structural nonlinearity and seismic intensity(Patsialis et al., 2023)
Five-storey shear buildingTHIVDTHIVD device exhibits control efficiency in the range ofRecorded near-fault pulse, near-fault non-pulse, and far-field ground motion recordsOptimal device number and optimal placement are not investigated(Saha, 2026)
3-story steel frame structureSeparated fluid inerter integrated with base-isolationNear-field and far-field seismic waves were applied at varying PGA amplitudes: 0.05 g, 0.1 g, and 0.2 gLimited experimental conditions; device response is notably sensitive to key geometric parameters(Liao et al., 2024)
Six-story reinforced concrete frame buildingISCD44 FEMA P695 far-field ground motion records scaled for different hazard levels and IDAIdeal inerter is assumed and experimental validation is not considered(Kong et al., 2025)
Benchmark base-isolated structureFRIDPrimarily numerical assessment with simplified device(Zhu et al., 2024)
MSCSS - steel building comprising four mega structures and several substructuresInter-story TVMDI and outrigger-based TVMDIReliability analysis is computationally intensive, and applicability to high-dimensional reliability problems was not investigated(Abdulhadi et al., 2024)
Two-story shear frame (low-rise reinforced-concrete building)TMID (Low-Cost Passive Inerter System)Multidirectional and multi-support effects experienced by real buildings were not assessed(Mbasso et al., 2026)
10-, 15-, and 20-storey buildingsTMDIPerformance strongly dependent on pulse characteristics and adverse response may occur for highly impulsive motions(Djerouni et al., 2022)
Representative post-tensioned rocking walled timber structures: 3-,6-, and 9-storey buildingsBall-screw and gear inerters, with and without clutchesNon-clutched inerters can amplify ground-storey shear; limited applicability of the proposed strategy in high-rise buildings(Thiers-Moggia and Málaga-Chuquitaype, 2021)
Base-isolated structure and five-story shear frame structureTMDI with varying device placement and inerter connection configurationsHigher mode effects in tall/complex structures are not explicitly considered(Sun and Peng, 2025)

3.2 Displacement-based metrics

Displacement-based metrics are the most widely used measures for assessing the seismic performance of structures that employ inerter-based damping systems. By capturing the structural lateral movement and deformation during and after an earthquake event, these metrics offer a direct basis for quantifying structural damage, serviceability, and the ability to recover after an earthquake. The displacement-based measures most commonly used to investigate inerter-based dampers include peak (or roof) displacement, inter-storey drift (or drift ratio), residual drift, and base-isolation displacement (Kaveh et al., 2020; Lara-Valencia et al., 2020; Javidialesaadi and Wierschem, 2021). Together, these indices offer a comprehensive assessment of the ability of inerter damping systems in reducing structural deformation and enhancing seismic performance. De Angelis et al., (2019) studied displacement as primary performance measures to assess the grounded inerter in the base-isolated structure. Their result demonstrated that by incorporating a grounded inerter effectively reduced the lateral displacement by enhancing the apparent inertia of the TMD. (Kaveh et al. (2020) evaluated the performance of TMDI considering roof displacement, roof acceleration, and kinetic energy as performance indicators under 25 far-fault earthquake records. Inter-storey drift is a widely adopted displacement-based metric for evaluating the effectiveness of various inerter-based damping configurations, including TMDIs (Sun and Peng, 2025), Force-Restricted Inerter-Dampers (FRID) (Zhu et al., 2024), and Inerter Vibration Absorbers (IVA) (Patsialis et al., 2023). It characterizes the relative lateral displacement between two adjacent floors and is widely recognized as one of the most reliable indicators of both structural and non-structural damage during earthquakes. The reported findings consistently show significant reductions in drift compared to uncontrolled structures, confirming that the incorporation of an inerter effectively mitigates seismic-induced deformation (Sun and Peng, 2025; Saha, 2026).

3.3 Force and acceleration-based metrics

Force and acceleration-based metrics are generally used to assess the dynamic response of structures fitted with inerter dampers under earthquake excitation. Acceleration-based indices outline the structural dynamic behaviour and are mainly applied to evaluate vibration reduction and the protection of occupants and non-structural components. Whereas, force-based indices measure the forces produced in structural members and damper devices, providing insights into the mechanical demands imposed by the control system. Base shear, floor acceleration, damper force, peak and Root Mean Square (RMS) acceleration are some of the forces and acceleration-based metrics considered in the inerter damper systems study under various ground motion records (Kaveh et al., 2020; Liao et al., 2024; Mbasso et al., 2026). To evaluate the performance of IVA (Patsialis et al., 2023), have employed two performance metrics: J1 based on acceleration and drift-sensitive Engineering Demand Parameters (EDP), and J2, which quantifies the control force demand.

3.4 Energy-based metrics

Energy-based metrics analyse the seismic behaviour of inerter-based damping systems by measuring how effectively they absorb, dissipate, or redistribute earthquake-induced energy throughout the structural system. These metrics will give insight into the underlying vibration control mechanism by assessing how seismic input energy is handled by the structure during dynamic excitation. Commonly examined metrics in the inerter damper study include input energy, energy dissipation ratio, and hysteretic energy. These measures are especially useful for understanding how inerter-based devices help to limit energy transfer into the primary structure and thereby strengthen overall seismic resilience. Several studies have utilized energy-based indicators to evaluate the energy efficacy of inerter-based dampers. Kaveh et al. (2020) relied on total kinetic energy to study the performance of TMDI as one of its response parameters. Absorbed energy has been considered to characterize the energy transfer mechanism of an inerter damper, while the energy dissipation index has been introduced to quantify the energy dissipation capability of a grounded inerter. De Angelis et al. (2019); Mbasso et al. (2026) reported that the proposed low-cost passive inerter system achieves higher energy dissipation efficiency than a conventional TMD.

3.5 Performance-based metrics

Performance-based metrics offer a comprehensive approach for assessing the seismic performance of inerter-based damping systems by connecting structural behaviour to predefined performance objectives, rather than concentrating solely on minimizing peak responses. One of the earliest studies that explicitly applied a performance-based framework to inerter-based dampers was carried out by (Radu et al., 2019). In this work, the authors presented a fully probabilistic approach for the seismic design of TID using maximum structural displacement as engineering demand parameters. The proposed framework assessed seismic performance using the probability distribution of the EDP and tuned the damper by minimizing the probability of exceeding the specified critical displacement. Thiers-Moggia and Málaga-Chuquitaype (2021) employed a probabilistic, performance-based approach based on fragility functions, using peak inter-storey drift and peak floor acceleration as the primary performance metrics. Their results showed that inerters significantly enhanced structural performance by reducing drift demands and lowering peak floor acceleration. A recent study employed peak relative displacement as the EDP to assess the seismic performance and vulnerability of the TMDI system through fragility curve analysis (Beerabbi Eshapurada and Reddy, 2026).

3.6 Comparative assessment of seismic performance

The studies summarized in Table 2 demonstrate considerable variability in the effectiveness of inerter-based damping systems. This variability may be attributed to differences in structural properties, ground motion characteristics and selection, device configuration and placement, modelling assumptions, and the response metrics adopted. Accordingly, the reported percentages of response reduction should not be regarded as directly comparable measures of performance across studies. In particular, ground motion characteristics can significantly influence the performance of IBDs. De Angelis et al. (2019) reported reduced effectiveness for near-fault motions dominated by early-arriving low-frequency pulses, whereas (Djerouni et al., 2022) demonstrated that highly impulsive motions may result in limited or even adverse responses. Similarly (Liao et al., 2024), reported a 19.30% increase in top-floor acceleration under one near-field excitation condition, despite observing reductions under other ground motions and intensity levels. These contrasting observations indicate that the effectiveness of inerter-based systems is strongly dependent on the characteristics of the seismic excitation.

The reported performance is also influenced by structural behaviour, device configuration, and modelling assumptions. Patsialis et al. (2023) reported a reduction in relative IVA efficiency with increasing structural nonlinearity and seismic intensity, while (Thiers-Moggia and Málaga-Chuquitaype, 2021) observed amplification of ground storey shear for non-clutched inerter configurations. Moreover, the reviewed studies range from linear and SDOF formulations with idealized inerters to nonlinear models and experimentally validated systems, which further contributes to differences in the reported performance. These findings demonstrate that improvement in one response measure does not necessarily imply consistent improvement in all structural responses. Hence, the observed variability highlights the need for more consistent evaluation approaches. Future studies should employ clearly defined performance indicators, well-documented modelling assumptions, ground motion selection, and scaling procedures to facilitate the inerter implementation. A more unified framework for seismic performance assessment would improve the reliability and support for the practical implementation of inerter-based damping systems.

4 Performance assessment methodologies

Assessing the seismic performance of structures equipped with inerter-based systems requires appropriate methodologies capable of capturing structural response, damage, and associated seismic risk. Accordingly, this section discusses the commonly adopted analysis methods, the Performance-Based Earthquake Engineering (PBEE) framework, and fragility-based assessment using different damage states to provide a comprehensive basis for evaluating the performance of inerter-equipped structures under seismic loading.

4.1 Analysis methods

Although the performance metrics define the criteria used to evaluate the performance of inerter dampers, it is equally important to understand the methodologies employed to quantify these indices. The methodological framework used to evaluate the performance of inerter-based dampers has evolved considerably since (Smith, 2002) first presented the inerter as a two-terminal mechanical element. In its early applications, performance evaluation mainly focused on frequency-domain analyses, closed-form optimization, and variance-minimization methods applied to simplified Single-Degree-of-Freedom (SDOF) systems excited by stationary white noise or by harmonic base excitation. These analytical strategies offered important understanding of the dynamic behaviour of inerter components while enabling the derivation of optimal tuning parameters under idealized assumptions. As research progressed, the focus shifted toward more advanced analytical and numerical methods. The adoption of H2 and H ∞ optimization frameworks led to the formulation of explicit design formulae and robust performance criteria for inerter-based systems. Subsequently, Nonlinear Time History Analysis (NTHA), statistical linearization, and experimental shake table testing were broadly implemented to assess device performance under realistic excitations while accounting for structural nonlinearities (Deastra et al., 2023; Konar and Ghosh, 2024; Cheng et al., 2025). Among the methodologies adopted for seismic performance assessment, Performance-Based Earthquake Engineering (PBEE) has emerged as a comprehensive framework for evaluating structural performance under earthquake excitation (Porter, 2005).

4.2 Performance-based earthquake engineering (PBEE)

PBEE has gained significant attention in recent years as an effective framework for assessing the seismic performance of structures. Conventional seismic evaluation of structures has largely emphasized force-based design approaches, in which structural adequacy is assessed using code-prescribed strength and stiffness requirements (Cao et al., 2023). Nevertheless, these methods offer only a limited understanding of expected damage and its consequences post-earthquake. PBEE was developed as an integrated probabilistic methodology that connects seismic hazard with structural response, enabling a more realistic and decision-oriented evaluation approach. Unlike conventional analyses, PBEE systematically estimates key performance measures such as repair costs, downtime, functionality, and associated risk, thereby providing well-informed decisions in the design, assessment, and retrofit of structures (Sharma et al., 2025). This shift towards more holistic evaluation of seismic performance is crucial for improving the design and practical application of inerter-based damping systems in real-world scenarios.

Early research on inerter-based dampers primarily concentrated on tuning the parameters for better structural vibration control. However (Lekeufack et al., 2026), emphasized the need for a broader engineering design approach, illustrating the importance of integrating various performance objectives. This evolution led to the embedding of performance assessment of inerter dampers within the PBEE framework. Further advancements were made by (Giaralis and Taflanidis, 2016), who introduced a reliability-based probabilistic design framework that enhanced TMDI by explicitly accounting for structural uncertainties, stochastic seismic excitation, and the probabilities of exceeding predefined EDPs. Further, recent research has applied reliability-based optimization to device configuration and placement of IDVAs by using fragility analysis (Miguel et al., 2025). Additionally, the development of fragility curves for structures incorporating TMDI under pulse ground motions has helped capture seismic vulnerability more completely across various damage states (Beerabbi Eshapurada and Reddy, 2026). Figure 5 illustrates a generalized PBEE workflow for evaluating structures incorporating inerter-based dampers. Adapted from the conventional PBEE framework, it outlines the step-by-step procedure for defining performance objectives, selecting ground motion records and damper characteristics, optimizing design parameters, and assessing structural performance via nonlinear analysis. The process is iteratively repeated until the desired performance objectives are achieved.

Flowchart of the performance-based seismic design framework of structures equipped with inerter-based damping system, illustrating the sequential steps from structural definition to final performance assessment (Porter, 2005).
Figure 5. Flowchart of the performance-based seismic design framework of structures equipped with inerter-based damping system, illustrating the sequential steps from structural definition to final performance assessment (Porter, 2005).

Overall, the analysis of inerter-based damping systems using the PBEE approach remains relatively limited compared with other evaluation approaches. There is limited research that has addressed probabilistic performance objectives, robustness to uncertainties, and multi-objective optimization within the PBEE framework. Therefore, future research is expected to extend in the direction of fragility-based assessment, resilience quantification, life-cycle performance evaluation, repair loss estimation, and functional recovery, thereby supporting a more comprehensive understanding of the seismic performance of inerter-based damping systems across multiple hazard levels (Lekeufack et al., 2026).

4.3 Fragility assessment and damage states

Early studies on inerter-based damping systems primarily evaluated seismic performance using a deterministic approach. More recently, research has shifted towards probabilistic and reliability-based assessment methods to explicitly account for seismic excitation and structural response uncertainties. Among these approaches, fragility analysis has emerged as a key component of the performance-based earthquake engineering (PBEE) framework, offering a probabilistic measure of the likelihood that a structure will surpass a predefined damage state under various levels of earthquake intensity (Sharma et al., 2025). Fragility curves outline the probability of damage occurring beyond a certain threshold, as determined by specific seismic intensity indices, such as Peak Ground Acceleration (PGA) and Spectral acceleration at the fundamental period (Sa (T1, 5%)) (Baker, 2015). These curves are widely used to quantify seismic vulnerability, compare alternative structural control strategies, and support resilience-based seismic decision-making. The seismic fragility function is typically assumed to follow a lognormal cumulative distribution and is expressed as given in Equation 1, where φ denotes the standard normal cumulative distribution function (Baker, 2015; Beerabbi Eshapurada and Reddy, 2026).

P E D P ≥ E D P T h | I M = φ ln I M − ln θ σ (1)

Here, θ is the median of the fragility function representing the intensity measure corresponding to a 50% likelihood of surpassing the specified damage state, and σ is the logarithmic standard deviation, reflecting the uncertainty associated with the fragility function (Baker, 2015; Giaralis and Taflanidis, 2018). Fragility curves are typically developed using Incremental Dynamic Analysis (IDA), where nonlinear structural responses under scaled ground motions are evaluated against predefined damage state thresholds. Damage state classification and threshold values are commonly adopted from the HAZUS manual, FEMA P-58, and ASCE 41 standards depending on the structural performance level. Figure 6 displays four representative seismic fragility curves that depict the probability of exceeding structural damage states, accompanied by illustrative building damage (Federal Emergency Management Agency, 2000; Ohtori et al., 2004; Cremen and Baker, 2019; Federal Emergency Management Agency, 2020).

Representative seismic fragility curves showing the probability of exceeding damage states as a function of earthquake intensity measure, together with a schematic representation of the corresponding structural damage (adapted from Rajkumari et al., 2022).
Figure 6. Representative seismic fragility curves showing the probability of exceeding damage states as a function of earthquake intensity measure, together with a schematic representation of the corresponding structural damage (adapted from Rajkumari et al., 2022).

One of the early studies by (Giaralis and Taflanidis, 2018) developed a reliability-based design framework for TMDI, by optimizing device parameters to minimize the probability of exceedance. This work provided a foundation for reliability-oriented design in inerter-based vibration control. By using a stochastic reduced-order model. Radu et al. (2019) proposed a PBEE framework for TID, enabling efficient optimization of nonlinear structures under seismic excitation. Another study on IVA (TID and TMDI) by (Patsialis et al., 2023) expanded the probabilistic performance-based method to hysteretic multi-storey steel buildings. Their study found that when structural yielding occurs, designs that rely only on linear models tend to overestimate device performance. This highlights the need for nonlinear response-history analysis for reliable performance assessment and device optimization. More recently, fragility analysis has been employed to evaluate the seismic performance of structures with inerter-based dampers subjected to pulse-like ground motions. Such assessment is particularly important for quantifying damage and collapse risk since pulse ground motions can cause large displacement demands and significantly alter the effectiveness of vibration control devices (He et al., 2024; Madhu and Karthik Reddy, 2025; Beerabbi Eshapurada and Reddy, 2026).

5 Conclusion and future perspectives

The findings synthesized from the reviewed literature provide useful insights into the current capabilities and challenges associated with inerter-based damping systems for seismic applications. The major conclusions are summarized together with practical implementation issues and existing limitations, followed by future research directions aimed at improving their performance, reliability, and broader structural application.

5.1 Concluding remarks

The systematic review of the performance evaluation of inerter-based damper systems has been carried out across a range of performance metrics and assessment methodologies for different structural connections. A few concluding remarks are listed as follows.

  • The assessment of inerter-based damping systems has evolved from conventional deterministic and frequency-domain methods to more advanced performance-based and reliability-based approaches.
  • Inerter-based damping systems have reported reductions of 20%–85% in peak displacement and inter-storey drift, 18%–45% in floor/roof acceleration, and up to 32% in base shear. The variation in displacement and drift reduction is mainly influenced by the relationship between the structural natural period and ground motion characteristics, along with damper placement and structural nonlinearity. Acceleration reduction is additionally affected by ground motion frequency and pulse characteristics, seismic intensity, and higher mode effects.
  • Effective inertance required for seismic response control depends on the structural period, damping characteristics, and damper configuration, while further increase in inertance beyond a certain level may provide only limited additional response reduction.
  • The installation location and connection configuration strongly influence the effectiveness of inerter-based damping systems. Grounded or lower-storey connections can enhance control efficiency by providing a favourable acceleration reference and increasing the relative acceleration across the inerter terminals. Roof-mounted inerter systems can be effective for fundamental mode dominated structures. Therefore, optimal placement depends on the structural modal characteristics, device configuration, and targeted response.
  • Fragility analysis has proven to be a highly effective probabilistic method for evaluating the performance of damper systems, as it quantifies the likelihood of exceeding damage states under varying seismic intensities. Performance assessment of inerter-damper systems using fragility analysis provides a deeper understanding of how their performance is affected by varying earthquake intensities.

5.2 Practical implementation and limitations

Despite the reported effectiveness of inerter-based damping systems for seismic response control, their wider structural application has several practical limitations. The key challenges identified from the literature review are summarized below.

  • Physical inerters may deviate from the ideal behaviour assumed in analytical and numerical models due to mechanical non-idealities such as friction, bearing losses, and transmission inefficiencies.
  • Large inertial forces can impose significant demands on supporting members and structural connections.
  • The finite device stroke, installation space, and geometric requirements may limit the practical applicability of certain inerter configurations.
  • Long-term durability issues, including wear, lubrication requirements, fatigue, and degradation of moving components, remain insufficiently investigated and require further experimental validation.

5.3 Future research perspectives

Over the last 2 decades, extensive research has been carried out and is still progressing on various inerter-based dampers due to their unique ability to produce large inertial force via mass amplification effect. This distinctive feature has made these devices as a promising alternative to conventional passive vibration control systems. Considering the existing literature and research gaps the following key future directions are recommended for developing and practical implementation of inerter dampers in various structures for vibration mitigation.

  • Performance-based, resilience-focused evaluation: Future research could be directed toward comprehensive PBSD framework that integrate engineering demand parameters to intensity measures, probabilistic fragility, repair cost, downtime and resilience measures. This will support a more comprehensive evaluation of the seismic effectiveness of inerter damping systems.
  • Seismic performance assessment under realistic conditions: Extensive investigations are needed to assess the inerter performance under complex earthquake scenarios, including near-fault pulse-like ground motions and multi-hazard loading conditions. By incorporating these evaluation approaches, researchers can better understand how inerter-based systems respond across wide range of seismic characteristics, which will improve the design and implementation strategies.
  • Artificial intelligence (AI) and data-driven approaches: Integrating artificial intelligence and machine learning offers significant opportunities for finding the optimized parameters, optimal design and operation of damping systems. AI-assisted PBSD framework, probabilistic fragility forecasting, and machine learning-based surrogate models enable more effective design optimization and seismic decision-making.
  • Life-cycle optimization and experimental validation: Future research should prioritize optimizing life-cycle performance by including initial construction costs, maintenance demands, anticipated seismic losses, repair expense, downtime, and environmental impacts within multi-objective optimization frameworks. Additionally, large-scale shake-table experiments, and full-scale field study are necessary to verify analytical models and to support their practical adaptation for inerter-based systems.
  • Integration of digital twin: Digital twin frameworks provide a promising approach for real-time monitoring and for improving performance of inerter-based damping systems by creating a virtual replica that continuously reflects the physical structural response. This capability can support adaptive parameter tuning, damage detection, and life-cycle performance assessment of inerter devices subjected to varying seismic demands.

Correction note

This article has been corrected with minor changes. These changes do not impact the scientific content of the article.

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Glossary

θ Median of fragility function σ Logarithmic standard deviation μ Mass Ratio β Inertance Ratio ξ Damping Ratio AI Artificial Intelligence CP Collapse Prevention EDP Engineering Demand Parameter EDP **Th** Engineering Demand Parameter Threshold FRID Force-Restricted Inerter Damper FVD Fluid Viscous Damper IBD Inerter-Based Damping/Damper IDA Incremental Dynamic Analysis IDVA Inerter-based Dynamic Vibration Absorber IM Intensity Measure IO Immediate Occupancy ISCD Inerter-enhanced Self Centring Damper IVA Inerter-based Vibration Absorber LS Life Safety MSCSS Mega Sub-controlled Structure System M **w** Moment Magnitude NTHA Nonlinear Time History Analysis PBEE Performance-Based Earthquake Engineering PBSD Performance-Based Seismic Design PGA Peak Ground Acceleration Sa (T **1** , 5%) Spectral acceleration at the fundamental period SDOF Single-Degree-of-Freedom TID Tuned Inerter Damper THIVD Tuned Hysteretic Inerter Viscous Damper TMD Tuned Mass Damper TMDI Tuned Mass Damper Inerter TMID Tuned Mass Inerter Damper TVMDI Inerter-enhanced Tuned Viscous Mass Dampers VMD Viscous Mass Damper

Footnotes

Edited by: Ehsan Noroozinejad Farsangi, Western Sydney University, Australia

Reviewed by: Evangelos J. Sapountzakis, National Technical University of Athens, Greece

Wenke Li, Harbin Engineering University, China

Statements

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Seed Grant Scheme of Vellore Institute of Technology (VIT), Vellore, India (Grant No. SG20230141).

Author contributions

ME: Conceptualization, Writing – original draft. KR: Supervision, Writing – review and editing.

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Citation

Eshapurada, M. B. & Reddy, K. S. K. K. (2026). Seismic performance assessment of inerter-based damping systems for structural vibration control – a comprehensive review. Frontiers in Built Environment, Volume 12. https://doi.org/
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12 - 2026

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Copyright © 2026 Eshapurada and Reddy.

License: https://creativecommons.org/licenses/by/4.0/

*Correspondence: K. S. K. Karthik Reddy

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