Frequent earthquakes worldwide have made seismic risk evaluation and mitigation a critical and essential aspect of structural engineering (Kazemi et al., 2024; Nandu et al., 2025). The two important considerations in vibration control are, finding the earthquake response of the structure and improving its resilience to earthquake (Jamshidiha and Yakhchalian, 2019). Various methods have been proposed to evaluate the structures for its seismic effects, including dynamic analysis techniques such as response spectrum analysis and time history analysis (Zentner et al., 2017). These approaches help engineers understand how structures respond to seismic forces under different conditions, thereby allowing them to assess the potential vulnerabilities of buildings and infrastructure. To enhance the resilience against earthquakes, engineers often incorporate vibration control devices into their designs. These devices, such as base isolators and dampers, play a crucial role in mitigating the effects of seismic activity by absorbing and dissipating energy from ground motion (Ma et al., 2021). Effective implementation of vibration control devices not only aids in the design phase but also enhances the retrofitting of existing structures, thereby improving their performance during seismic events (Wu et al., 2022). This integration minimizes risks of life and property, ensuring that buildings can withstand the forces generated by earthquakes while maintaining structural integrity (Chen et al., 2022).

The fundamental types of vibration control systems in structures include passive, active, semi-active, and hybrid systems (Elias and Matsagar, 2017; Çalım et al., 2023). These systems are designed to reduce structural vibrations by absorbing and dissipating vibrational energy from the primary structure through various mechanisms (Li et al., 2024). Each type employs different control strategies and technologies to enhance the structural stability and performance under dynamic loading conditions. Among these systems, passive vibration control systems have received considerable attention for controlling structural vibration (Elias and Matsagar, 2017; Long et al., 2023). This is because passive systems are simpler, cost-effective, require less maintenance compared to the other systems and they do not require an external energy source for activation (Elias and Matsagar, 2017; Jamshidiha and Yakhchalian, 2019; Song et al., 2023). In contrast, the other three systems often include controllable force devices, sensors, and controllers for activation during earthquakes (Elias and Matsagar, 2017; Islam and Jangid, 2021; Ma et al., 2021). Research has been conducted on different types of passive dampers over the years by incorporating various combinations of other passive dampers, including viscous dampers, tuned mass dampers, friction dampers, and many more, for structural response mitigation. This research has led to a better understanding of the effectiveness of passive dampers in reducing structural vibrations and improving the overall safety of buildings and other structures (Málaga-Chuquitaype et al., 2019; De Domenico et al., 2020; Rajana et al., 2023). In addition to component-based damping devices, base isolation has become a significant passive seismic protection strategy (Mazza et al., 2022; Mazza et al., 2024). Base-isolated systems effectively reduce the forces transmitted to the structure by decoupling the superstructure from ground motion. However, when exposed to near-fault pulse ground motions, base-isolated buildings can experience significant displacement demands despite their proven efficiency (Mazza and Labernarda, 2017; Mazza and Labernarda, 2021). While several previous studies have evaluated passive control systems using sets of natural ground motions with diverse characteristics, the specific effects of pulse-like motions remain insufficiently explored (Brando et al., 2015; De Matteis et al., 2018). Such vulnerabilities highlight the importance of investigating the behavior of passive vibration systems under pulse-type of ground motions.

The successful implementation of passive vibration control strategies has been consistently achieved using devices such as the tuned mass damper (TMD), which has been extensively proven to be an effective solution in various applications. The TMD system operates based on the principle of resonance, where the secondary mass is tuned to vibrate at frequencies close to the natural frequency of the primary structure (Li et al., 2023b; Rajana et al., 2023). When the primary structure vibrates at its natural frequency, the secondary mass also vibrates at its natural frequency, creating a force that counteracts the primary vibration. Tuned mass dampers are widely employed as passive dampers in tall structures, high-rise buildings, and bridges across the globe to manage sway and improve stability, especially in regions susceptible to dynamic vibrations. These systems are essential for addressing the resonance and stability challenges of such structures (Xu et al., 2022; Zhang et al., 2023b). Prominent examples of structures equipped with these dampers include the Statue of Unity in India, Taipei 101 in Taiwan, Akashi Kaikyo Bridge in Japan, and Sydney TV Tower in Australia (Larsen and Toubro Limited, 2025; Wang et al., 2019). Tuned mass dampers in the aforementioned structures have proven to be better structural vibration control systems because of their efficiency in vibration control, relatively simple design, and implementation.

However, the TMD system also has some limitations. It is only effective in reducing the amplitude of primary vibrations at specific frequencies, and it may not be effective in reducing the amplitude of vibrations at other frequencies. Another important design consideration in TMD is the mass ratio of the additional tuned mass to the primary structure mass (Kaveh et al., 2020). A higher mass ratio can provide greater energy transfer and more effective vibration reduction, but it also increases the cost, complexity of the system and additional weight in the design of structure (Lazar et al., 2016; Barkale and Jangid, 2022). To overcome these shortcomings, many concepts have been evolved for real-time control of structural vibration based on the actual vibration frequency (Weber et al., 2022). In recent years, there has been a growing interest in using the TMD system in conjunction with other passive damper systems to address the limitations of such systems. For example, the TMD system was used in conjunction with a seismic isolation system to provide additional protection against seismic activity. The TMD system was also used in conjunction with a tuned liquid damper system to provide additional protection against wind-induced vibrations. Research has shown that incorporating an inerter element into tuned mass dampers has become a notable area of focus, and it achieves a reduction in the additional weight that TMDs contribute to structures (Fabrizio et al., 2019; Xu et al., 2023; Akbari et al., 2024; Yue and Han, 2024).

The inerter is a two-node mechanical element, which was first introduced by Smith (2002). The proposed model improves the vibration control performance by using the relative acceleration between its two nodes. The primary function of the inerter element is to create a force directly proportional to the relative acceleration between its two terminals, with the proportionality factor referred to as ‘inertance (b)’ and expressed in kilograms (Smith, 2002; Faraj et al., 2019; Ma et al., 2021; Tiwari et al., 2021). It is capable of generating a substantial inertial mass effect with its small physical mass. It produces inertia because of its rotating mechanism, which makes it harder to resist motion while being lightweight. Research studies indicate that a system incorporating an inerter can replicate a dynamic effect equivalent to 60 to 200 times its physical mass, depending on the dimensions of its flywheel (Papageorgiou and Smith, 2005; Marian and Giaralis, 2014; Giaralis and Taflanidis, 2016). Over the years, many researchers have proposed various inerter configurations and studied their effects on structural vibration control. Inerter dampers are beneficial in buildings, automobiles, and mechanical systems where incorporating significant physical mass and large-size dampers would be unfeasible (Zhang and Cao, 2022). Inerter is effective because it mimics the impact of a heavy mass without actually increasing the physical weight. The inerter damper achieves the same effect as TMDs via rotational mechanics (Marian and Giaralis, 2014; Xu et al., 2019; Li et al., 2023a).

In comparison with conventional TMDs, studies have proven that inerter-based damper systems have better resonance suppression and reduced peak displacements (Giaralis and Taflanidis, 2018; Jangid, 2024). Inerter-based devices have consistently outperformed classic TMDs in comparative studies. For instance (Pietrosanti et al., 2020), showed that, inerter dampers produce greater vibration suppression with lower mass ratios, making them ideal for structures in which adding significant physical mass is impractical or undesirable. In addition, in contrast to TMDs, which are primarily tuned to a single frequency, the mass magnification effect of the inerter allows the system to target multiple vibration modes (Li et al., 2023b). Research findings demonstrate that inerter dampers systems maintain their effectiveness across a variety of structural and excitation uncertainties, including variations in ground motion characteristics, structural properties, and modeling inaccuracies. The robustness of these systems makes them reliable and practical solutions for practical applications (Shi and Zhu, 2018; Zhang et al., 2023b). To alleviate seismic and wind vibrations, these inerter dampers are also being thoroughly studied in MDOF systems. The deployment of multiple tuned inerter dampers (TIDs) across various floors has shown greater improvement in structural performance by reducing peak displacements, inter-story drifts, and base shear forces (Wen et al., 2017; Giaralis and Taflanidis, 2018; Zhang et al., 2023a). Furthermore, extensive research has focused on optimizing the design and performance of inerter systems, particularly in terms of their placement and tuning parameters. Advanced optimization techniques, such as genetic algorithms and particle swarm optimization, and other techniques are employed to identify optimal configurations that maximize the vibration control efficiency (Li et al., 2023c; Elias and Djerouni, 2024). Inerter dampers are remarkably effective at minimizing structural responses under seismic excitation. For example, a study on a 12-story structure equipped with multiple TIDs reported up to 54% reduction in peak displacement and inter-story drift (Lara-Valencia et al., 2024).

Previous research on inerter dampers has primarily focused on optimizing their parameters to enhance their efficiency in structural vibration control (Marian and Giaralis, 2014; Giaralis and Taflanidis, 2018; Wu et al., 2022; Zhang et al., 2023b; Ma et al., 2024; Pandit et al., 2024). However, a comprehensive study of their performance has not been explored extensively. It is essential to understand the efficiency of inerter dampers under various seismic intensities for their effective application. Research into hybrid systems that combine inerters with other damping mechanisms continues to show potential for addressing a wider range of dynamic challenges, especially in areas at risk of significant earthquakes. Additionally, the risk assessment of inerter damper systems in seismic performance plays a critical role in the performance-based seismic design of resilient structures by evaluating how effectively inerter-based dampers reduce vulnerability to varying intensities. Thus, the present study provides a comprehensive vulnerability assessment of an SDOF system that incorporates an inerter element by employing incremental dynamic analysis and fragility curve development to evaluate its performance when subjected to ground motion records.

In this study, an incremental dynamic analysis procedure was used to assess the seismic performance of inerter dampers in an SDOF system to evaluate their behavior under increasing earthquake intensities. The IDA results are then used to generate fragility curves that quantify the likelihood of exceeding various damage states. This approach offers deeper insight into the effectiveness of inerter dampers in limiting damage, thereby aiding in the design of resilient structures and in making informed decision-making for seismic risk assessment. The seismic performance of the inerter-based system was assessed across low, medium, and high-rise structural representations addressing various fundamental periods and dynamic characteristics, in order to enhance the study’s practical relevance and scope. This expanded analysis enables a more comprehensive understanding of the fragility trends and control efficiency of the damper system across various building types.

This study’s main objective is to investigate the seismic fragility of a tuned mass inerter damper system subjected to pulse-like ground motions. To better understand the seismic vulnerability of the proposed system, the damage probability under various inertance ratios was compared. The fragility plots were developed by considering peak relative displacement as an engineering demand parameter, with peak ground acceleration (PGA) and spectral acceleration (Sa (T1, 5%)) as intensity measures. Fragility analysis is a powerful tool for understanding the behavior of structures subjected to ground motions with divergent characteristics (Sharma et al., 2021; Veggalam et al., 2021). The present research mainly examines how the effects of varying mass ratios affect the structural response, considering pulse-like ground motions. Record-to-record variability in pulse-like ground motions is considered to assess the resulting variability in nonlinear structural response across different excitation intensities. By capturing the nonlinear behavior and damage probabilities across different excitation intensities, this study quantifies the potential risk reduction of inerter damper systems and provides insights into their efficacy in structural resilience improvement.

The remaining framework of the paper is organized as follows. Section 2 describes the ground motion selection; classification of the Noto earthquake used in the current study and its characteristics. Section 3 explains the TMD modeling and its validation against the reference study. Section 4 deals with the incremental dynamic analysis for the inerter-based system, followed by the development of fragility curves for different damage states along with the HAZUS median fragility comparison. Discussion of results are presented in Section 5 and followed by conclusion in Section 6.

Ground motions of magnitude 7.6 (M_w) were selected from Japan’s Noto earthquake that occurred in January 2024 (National Research Institute for Earth Science and Disaster Resilience, 2019). The records were obtained from Japan’s K-NET strong-motion seismograph network (National Research Institute for Earth Science and Disaster Resilience, 2019). To prepare the data for analysis, a high-pass Butterworth filter of 4th order was applied to the velocity time histories to remove the low-frequency noise content and baseline drift. A cutoff frequency of 0.1 Hz was adopted, which was selected to suppress long-period components while preserving the relevant dynamic response of the signal. The Butterworth filter was selected due to its smooth passband response, which helps preserve the original signal shape (Xue et al., 2020). Consequently, this filtering process was necessary to ensure the accuracy of the results. These velocity pulses were extracted using an open-source platform that employed Baker’s pulse classification method (Shahi and Baker, 2014; Papazafeiropoulos and Plevris, 2018; Karthik Reddy et al., 2021; Wani et al., 2024; Kumar et al., 2025). A total of 22 pulse ground motion records were extracted as pulse-like ground motions. Among these, 13 records were from the north-south components and 9 records were from the East-West components. In this classification, the largest velocity pulse was extracted from each record using wavelet transform method. The 4^th-order Daubechies wavelet was used as the mother wavelet in this process. Due to the limited availability of pulse-like ground motions in the east-west direction, this study considers only north south components for subsequent analysis.

Extracted pulse with corresponding station codes are shown in Figure 1, while characteristics of pulse motions are listed in Table 1.

Incremental Dynamic Analysis is a key approach in performance-based seismic analysis technique used to evaluate seismic performance across a broad range of earthquake intensities (Vamvatsikos and Allin Cornell, 2002; Tidke and Adhikary, 2021). In this method, a set of ground motion records is progressively scaled to multiple intensity levels, and the non-linear structural response is computed for each scaled ground motion. This generates a series of peak response points corresponding to different intensity measures, allowing the construction of IDA curves. While IDA is a robust method, its results can be influenced by the selection and scaling of ground motions, which may introduce variability in demand and collapse predictions. Additionally, the approach requires significant computational effort due to the large number of nonlinear time history analysis (Vamvatsikos and Allin Cornell, 2002). In this study, each pulse-like ground motion record was scaled from 0 to 2 at an increment of 0.1 m/s², ensuring a comprehensive assessment of structural response across a range of seismic intensities. The selection of intensity measures and engineering demand parameters plays an important role in analyzing the seismic performance of structures. In particular, intensity measure selection is very critical because IMs are strongly correlated with earthquake risks and the resulting structural response. There are about 25–30 IMs are proposed in many studies based on their correlation, efficiency, practicality, and proficiency (Jamshidiha and Yakhchalian, 2019; Irslan Khalid et al., 2023; Sun et al., 2023). Peak ground acceleration (PGA) and spectral acceleration at the fundamental time period of the structure (Sa T1, 5%) were considered in this study because these IMs are versatile, effective, and strongly correlated with the structural response (Aghani and Farahmand-Tabar, 2024). The response of the proposed system was then evaluated using the peak relative displacement as the engineering demand parameter.

Fragility curves were subsequently developed from the IDA results to quantify the probability of exceeding specific damage thresholds at a given level of seismic intensity (Bakalis and Vamvatsikos, 2018). As mentioned in previous studies, 10–20 ground motion records are sufficient to estimate seismic demand in structures through incremental dynamic analysis (Bakalis and Vamvatsikos, 2018; Luo et al., 2018; Sharma et al., 2021). In this study, pulse-like ground motions of thirteen records in the NS direction were considered (as mentioned in the Section 2) to develop the fragility curves. The fragility function P () given in Equation 3 is the probability of exceeding a damage state in any structure for a given ground motion intensity measure (IM). This is typically modeled as a lognormal cumulative distribution function φ () (Zentner et al., 2017; Tidke and Adhikary, 2021). P E D P ≥ E D P T h | I M = φ ln I M − ln θ σ (3)

Here, EDP is engineering demand parameter, EDP_Th is the threshold value of EDP associated with the specific damage limit state, and IM is the intensity measure parameter, which is PGA and Sa (T1, 5%) considered in this study. θ is the median of the fragility function (the IM level with a 50% probability of collapse) and σ is the standard deviation of lnIM (also referred to as the dispersion of IM) (Baker and Eeri, 2015). The combination of IDA and fragility analysis provides a comprehensive understanding of structural performance, enabling probabilistic seismic risk assessment of TMDI systems.

Evaluating the seismic performance of structural systems can be efficiently conducted through fragility analysis, providing a probabilistic approach to determine the likelihood of surpassing predetermined performance thresholds under seismic forces. The performance of an inerter-based tuned mass damper system was assessed using Japan ground motion records from Noto earthquake of magnitude 7.6 (M_w). Investigations have been conducted into the incorporation of an inerter device that generates an inertia force proportional to relative acceleration to assess its impact on enhancing seismic performance. Incremental Dynamic Analysis (IDA), a non-linear analysis method, was used. In the IDA analysis, the structural system was subjected to scaled versions of ground motion records to capture its nonlinear dynamic properties.

IDA curves provide a crucial tool for engineers for assessing the performance of a system under seismic loading. By analyzing the relationship between engineering demand parameters and intensity measures, these curves enable the identification of specific damage states and track the corresponding system responses. This information is then used to construct fragility curves, which offer a probabilistic representation of the system’s likelihood of reaching or exceeding various damage states as a function of seismic intensity.

Fragility curves were derived using lognormal distribution fitting based on the IDA results to represent the variability in structural response associated with record-to-record difference in pulse-like ground motions. It is recognized that seismic performance may also be influenced by various source of uncertainty, including source-to-source variability, uncertainties in structural properties, and uncertainties related to damper properties. These sources of uncertainty are not explicitly considered in the present study and are considered as a part of future scope of work. Previous investigations have shown that uncertainties in damper parameters generally have negligible influence on overall seismic response compared to ground motion variability; therefore, they are often excluded from fragility-based assessments (Vamvatsikos and Cornell, 2004; Masi et al., 2021; Cocco et al., 2024). The consideration of PGA and Sa (T1, 5%) as intensity measures and peak relative displacement as an engineering demand parameter, as discussed in section 4, provides a comprehensive understanding of the structural response under seismic loading. The response spectra for ground motions considered is provided in Figure 4. Employing Sa (T1, 5%) as the spectral acceleration at the fundamental period, this parameter serves as a reliable intensity measure (IM) for fragility plotting. By employing Sa (T1, 5%) in this manner, a direct correlation can be established between the structural response and the dominant characteristics of the ground motion. This approach significantly enhances the reliability and physical significance of the fragility curves, thereby ensuring that they accurately reflect the structural vulnerabilities in the context of pulse-like ground motion events.

In the present investigation, a tuned mass damper inerter (TMDI) system was modeled to evaluate its efficacy in improving its structural performance subjected to pulse-like ground motions excitations. The study encompassed low, medium, and high-rise structures to assess how the performance of the TMDI system varies with building height. Initially, a non-linear time history analysis IDA was conducted to calculate the collapse capacities of the system across a range of mass ratios. Utilizing the resultant peak relative displacement responses, a performance-based seismic assessment was executed through fragility analysis. The probability of exceedance for four different damage states was computed and fitted using cumulative distribution function. Ultimately, for evaluation and comparison the median fragility values derived from the analysis were juxtaposed with fragility metrics defined by HAZUS. Based on the findings, the following conclusions are drawn:

Comparisons of fragility curves show that TMDI systems outperform conventional TMDs when the mass ratio is reduced from 1.0 to 0.6, particularly in low and mid-rise structures, owing to the enhanced inertial effect provided by the inerter damper.