Liquid storage tanks are critical components of energy and industrial infrastructure but have suffered severe damage in past earthquakes. Although base isolation has been proposed to control seismic response, theoretical and experimental studies reveal that isolated tanks may still experience excessive isolation displacement and amplified sloshing height. Inerter-based isolation system offers non-intrusive approaches to overcome these limitations, yet existing studies rely on white-noise-based design principle, and experimental validation for tanks is still absent. This study develops a stochastic design framework for an inerter-based combined isolation system (ICIS) considering various soil conditions. Semi-analytical solution is derived to characterize the seismic responses of ICIS-equipped tanks, and sensitivity analysis is conducted to identify the governing parameters. Then energy-oriented design strategy is developed and the multiple control effects of ICIS under different soil conditions and aspect ratios are verified in the case study. Finally, shaking table tests are performed to validate the effectiveness of the ICIS. The results demonstrate that ICIS can decrease base shear force, sloshing height, and isolation displacement, while maintaining robustness across different aspect ratios. Compared with conventional isolation system, ICIS achieves better anti-slosh effect and reduced isolation displacement. This work establishes a validated and scalable design paradigm for enhancing the seismic resilience of liquid storage tanks.

The nonlinear inerter that generates nonlinear inertial force has proven effective in enhancing structural vibration control, such as in nonlinear inerter-based vibration isolators. However, this technology has rarely been adopted in vibration absorbers, hindering the exploration of its potential benefits for vibration absorption. This study proposes a nonlinear inertia-enabled vibration absorber using a yoke-type inerter. The design and realization of the yoke-type inerter are briefly described, followed by the establishment and experimental validation of its mechanical model. A compact configuration of the yoke-type inerter-enabled nonlinear vibration absorber (YI-NVA) is then introduced. The transient responses of a single-degree-of-freedom oscillator equipped with the YI-NVA under impulsive loading are evaluated through numerical simulation. The absorbed and dissipated impulsive energy of the oscillator with YI-NVA is compared to that of an oscillator with linear inerter vibration absorber (LIVA) using an energy-based indicator. Analytical solutions for the steady-state responses of the oscillator with YI-NVA under harmonic excitation are derived using the complexification-averaging method and verified through the numerical integration. A comparative analysis of the oscillator with YI-NVA and that with LIVA is conducted for varying excitation amplitudes and absorber parameters. Under impulsive loading, the proposed YI-NVA absorbs and dissipates more impulsive energy from the primary oscillator than the LIVA across a wider range of the inertance-to-mass ratio. The oscillator with the YI-NVA also achieves a lower peak dynamic displacement amplitude, a broader control frequency band, and a lower stroke under harmonic excitation compared to the oscillator with LIVA across various absorber parameters. Overall, the proposed YI-NVA offers a more robust vibration absorption solution for enhanced vibration control than the classical LIVA.

The tuned mass inerter system (TMIS) has been proposed as a lightweight solution for tuned vibration control, contrasting with traditional tuned mass dampers (TMD). However, its effectiveness in lightweight vibration control lacks experimental validation. In this study, the mechanical model of TMIS was first outlined, followed by an explanation of its mechanism. Subsequently, a test design for TMIS was conducted using vertical vibration control as an example to validate its efficiency in lightweight vibration control. A ball-screw inerter was selected for this experiment. Initial tests were conducted on the chosen inerter element to obtain its apparent mass and mass amplification factor. Then, the TMIS was placed at the midpoint of a resonance-sensitive unidirectional slab. Dynamic experiments compared the conventional TMD with TMIS. The experimental findings reveal that the TMIS implementation results in a 77% reduction in structural mean square displacement responses and a 92% reduction in acceleration responses. The system achieved over 45% mass reduction compared to conventional TMDs while maintaining equivalent vibration attenuation performance and exhibiting a 40% broader suppression frequency bandwidth. A parametric robustness analysis shows that vibration control efficacy is maintained even with 45% deviations in mass ratio from optimal tuning parameters. Results substantiate TMIS's capacity to overcome limitations in traditional vibration control methodologies by specifically addressing high tuned mass requirements and low damping efficiencies through its lightweight design.

The classic linear inerter has proven effective in enhancing the performance of base-isolated structures, particularly in reducing isolation displacement. However, its constant inertance limits the ability to achieve adaptive structural control. This study introduces the crank inerter, which features variable inertance, to enhance the performance of base-isolated structures under multi-level earthquakes. The working mechanism of the crank inerter is briefly described, and a corresponding mechanical model is developed and validated through experimental testing. Analytical solutions for the single-degree-of freedom base isolator equipped with crank inerter are derived using the averaging method, providing insights into its dynamic characteristics. Parametric analyses are conducted on a base-isolated structure with crank inerter subjected to harmonic ground motions of varying amplitudes to evaluate its potential for enhancing seismic performance under multi-level earthquakes. Nonlinear time-history analyses are employed to examine the performance of the base-isolated structure with crank inerter under multi-level earthquakes. Comparisons are also made between the base-isolated structure with crank inerter and that with linear inerter. Under frequent earthquakes, the displacements of the isolation layer and superstructure in the base-isolated structure equipped with crank inerter are comparable to those observed in the base-isolated structure with linear inerter. Under moderate earthquakes, the base-isolated structure with crank inerter exhibits significantly lower displacements in both the isolation layer and the superstructure than the base-isolated structure with linear inerter. However, this reduction is accompanied by increased superstructure acceleration and inter-story displacement. As the earthquake intensity increases to the rare level, further reductions in the displacements of the isolation layer and superstructure are observed, while the acceleration and inter-story displacement of the superstructure are further amplified. Therefore, the trade-off between reduced isolation-layer displacement and increased superstructure acceleration should be carefully considered when applying crank inerters under multi-level earthquake conditions.

Digital modeling of vortex-induced vibration (VIV) in bridges is essential for analyzing the mechanism and implementing active control. To address the problems of insufficient accuracy and weak generalization ability of existing modeling methods of VIVs for large-span suspension bridges, this paper proposes a digital VIV modeling method based on the hybrid algorithm which integrates the wavelet transform (WT), convolutional neural network (CNN) and bidirectional long-short-term memory network (BiLSTM). The method achieves signal separation through WT, integrates the feature extraction ability of CNN and the time series modeling ability of BiLSTM, and thus effectively improves the model performance in vibration prediction tasks. Specifically, the approach involves first decomposing the captured acceleration data using WT to extract different frequency components. Then, wind velocity and wind direction are incorporated as external influencing factors, and digital modeling of each acceleration component is performed based on CNN-BiLSTM. Finally, multi-step acceleration prediction is realized through the superposition of component prediction results. Application of this method to a large-span suspension bridge shows that it exhibits excellent prediction performance in both the initial and stable stage of vortex-induced vibrations.

The tuned mass inerter system (TMIS), which has been proven efficient for the moving-load-induced vibration control of beams, has better vibration absorption effect and less tuned mass than the tuned mass damper (TMD). This study proposes a grounded tuned mass inerter system (G-TMIS), consisting of a tuned spring, a mass, and a grounded inerter-based subsystem, which achieves higher space utilization and better vibration absorption performance. The application and optimization of G-TMISs for vibration suppression of multi-span beam under moving load series are investigated. Comparative analyses demonstrate that G-TMISs exhibit superior vibration mitigation compared to TMISs with equal tuned mass while requiring less overall weight to achieve identical structural performance demands. Additionally, vertical deflection and acceleration responses of the beam along with mitigated resonance reduce due to designed G-TMISs.

Inerter-based dampers, especially the tuned viscous mass damper (TVMD), have been demonstrated as highly effective and promising approaches for vibration control due to their enhanced damping and flexible tuning capabilities. However, the damping enhancement effect is accompanied by excessive damping force under high-frequency excitations, leading to significant force transmission and reduced acceleration control efficiency. To address this issue, a butterfly-shaped damping (BSD) device integrated with an inerter has been proposed, designed to produce a control force opposite to the structural restoring force. The inerter, employing a ball-screw mechanism as a core component of the BSD, is initially tested to validate its feasibility and effectiveness. Subsequently, the configuration, mechanical model, and governing equations of the BSD-integrated TVMD (BTVMD) and the BTVMD-equipped structure are developed. Frequency sweep and parametrical investigations are conducted to assess the vibration control performance and enhanced energy dissipation of the BTVMD relative to the conventional TVMD. Consequently, a nonlinear damping enhancement-oriented design strategy is proposed to maximize energy dissipation while meeting control targets, with practical design curves and fitted formulae provided for various structural periods and site conditions. Results confirm the superior tuning, acceleration suppression, and energy dissipation of the BTVMD, attributed to BSD-induced negative stiffness. The proposed design strategy and formulae apply to real seismic scenarios, demonstrating the potential of nonlinear BTVMDs for protecting acceleration-sensitive nonstructural components.

A coupled wall can be transformed into a structural control device by the introduction of damped coupling and rocking mechanisms. To further enhance the structural control efficiency, inerter systems are proposed as the damped coupling devices in the rocking coupled wall. The theoretical model which can represent the key mechanism of the multi-pier rocking coupled wall with inerter systems is presented. The expression for the mechanical energy of each component is derived and then the corresponding equations of motion for the rocking coupled wall with inerter systems are established according to Lagrange’s equation. Closed-form expressions of stochastic seismic responses of the rocking coupled wall with inerter systems are derived subsequently. The demand-oriented design philosophy and the damping enhancement maximization principle of the inerter system are adopted as guidance to design the key parameters of the rocking coupled wall with inerter systems. A series of concise closed-form design formulae are derived to achieve the desired damping ratio and maximize the damping enhancement of inerter systems. Finally, the proposed mechanical model and formulae are validated by the design and analysis of a ten-story rocking coupled wall under seismic excitations. It is shown that the results of dynamic time-history analyses are in good agreement with the results of the theoretical formulae.

The classic inerter element that generates an inertia force proportional to its relative acceleration has demonstrated effective vibration suppression. However, this technology, characterized by constant inertance, lacks the capability for adaptive control. This study introduces a yoke-type mechanism designed to implement a nonlinear inerter device with adaptive control potential, referred to as the yoke-type inerter. A mechanical model of the proposed nonlinear inerter is developed to illustrate its nonlinear inertial behavior and variable inertance. A prototype yoke-type inerter is fabricated, and dynamic testing is conducted to validate the mechanical model. Analytical solutions for an isolator equipped with the yoke-type inerter are derived to explore its adaptive control potential. A base-isolated structure incorporating the yoke-type inerter is proposed to enhance performance under multiple earthquake levels. The nonlinear inertial behavior of the yoke-type inerter is demonstrated through the mechanical model. Experimental results closely align with theoretical predictions, confirming the effectiveness of the proposed model. Under frequent earthquakes, the isolation displacement of the base-isolated structure with the yoke-type inerter is nearly equivalent to that of the structure using the linear counterpart. However, a marked improvement in isolation displacement reduction is observed for the structure with the yoke-type inerter under rare earthquakes. Thus, the proposed yoke-type inerter can be considered a viable candidate for nonlinear inertance and has the potential to adaptively enhance the seismic performance of base-isolated structures during multi-level earthquakes.

Lateral-torsional coupling effect leads to poor seismic performance in eccentric structures, while traditional methods have their own limitations. This paper proposes an inerter-based solution to improve the seismic performance and develops the corresponding optimal design method. Comparative analysis under different control strategies is conducted to evaluate the vibration-suppressing effect of the inerter system by finite element simulation. The results show that inerter system can significantly reduce the seismic response, especially the torsional response, and exhibits greater efficiency than viscous damper with the same damping coefficient. Thus, the proposed inerter-based solution can effectively control the vibration of eccentric structures.

Traditional tuned mass dampers (TMDs) have been effectively adopted in engineering structures owing to their reliable vibration control performance. Previous studies demonstrate that the apparent mass amplification effect of inerter devices can significantly reduce the required mass of TMDs while maintaining their vibration control effectiveness. However, this approach lacks an explicit experimental validation. Moreover, existing studies neglect the relationship between the physical implementation mechanisms of inerters and their lightweight control effects. To address these gaps, this study proposes a pendulum tuned mass inerter system (PTMIS), which incorporates an inerter with high apparent mass amplification into a conventional pendulum TMD. This achieves a lighter design without compromising the vibration control efficacy of the tuned-type device. A coupled dynamic model integrating the PTMIS with a single-degree-of-freedom primary system is developed to analyze the influence of the inerter's apparent mass amplification factor on lightweight vibration control performance. A demand-oriented optimization framework is also introduced. The results indicate that inerter devices with low apparent mass amplification factors in the PTMIS do not sufficiently enable the lightweight control effect. Experimental results demonstrate that under comparable control objectives, PTMIS requires 39 % less tuned mass than a traditional TMD. A case study in a wind turbine application demonstrates that the PTMISs achieve comparable control efficacy to conventional TMDs while reducing the tuned mass by 10-26 % and the mass block displacement amplitude by an average of 17.3 %. This work validates the engineering feasibility of the PTMIS and provides an efficient lightweight vibration control solution for weight-sensitive structures by employing a socalled "replacing mass with inertia" paradigm.

Wind-induced vibration of offshore wind turbine tower would have adverse influences on the its power generation efficiency. Tuned Liquid Damper (TLD) has been demonstrated an effective device for vibration control of offshore wind turbine tower. However, shallow water theory necessitates maintaining a low ratio of liquid depth to tank length to ensure maximal engagement of the liquid mass in oscillations, resulting in a contradiction between the high-demand liquid mass and insufficient installation space. In this case, a tuned liquid inerter system (TLIS), characterized by its lightweight tuning effect, is proposed to realize vibration control of offshore wind turbine tower, The theoretical basis of the offshore wind turbine tower with TLIS is firstly introduced, including governing equation of motion and mechanical models. Parametrical analysis is subsequently conducted to explore the variations in structural performances against the design parameters of TLIS. Verified by a finite element model of offshore wind turbine tower, the control superiority of the TLIS subjected to the wind load is illustrated through a comparison case with TLD. The results demonstrate that the inerter element can significantly reduce the tuned liquid within the TLIS applied to the offshore wind turbine tower, simultaneously meet the same control efficiency as TLD. The proposed TLIS is conducive to achieve lightweight control with high-efficiency, which is suitable for energy infrastructures with limited installation space, providing an alternative wind-induced vibration control approach for the offshore wind turbine tower.

Previous studies have shown that inserting an inerter whose force-acceleration relationship is linear into the isolation layer of a base-isolated structure can effectively improve its seismic performance. A nonlinear strategy has the potential to provide a better control effect than its linear counterpart. This study proposed a yoke-type nonlinear inerter device by employing the Scotch yoke mechanism. The mechanical model of the proposed nonlinear inerter is built to illustrate the nonlinear inertial behavior using the Euler-Lagrange method. Then, The yoke-type inerter is incorporated into the isolation layer of a base-isolated structure to improve seismic performance. The relative displacement of isolation layer and responses of the superstructures are checked under different seismic events. The nonlinear inertial behavior of the yoke-type inerter is indicated by the proposed mechanical model. The relative displacement of the isolation layer and responses of the superstructures for the base-isolated structure with yoke-type inerter is smaller than that of the base-isolated structure with a linear inerter whose inertance is the same as the linearized yoke-type inerter, especially for the rare earthquake. It is said that the proposed yoke-type inerter can be seen as a candidate of the nonlinear inerter and can be used to improve the seismic performances of base-isolated structures.

Yoke-type inerters demonstrate adaptive apparent mass properties and dynamic negative stiffness characteristics; however, prior research has yet to establish an engineering-applicable mechanical constitutive model, thereby constraining their implementation in structural vibration control applications. This study proposes a multi-body dynamics-derived constitutive model that considers backlash-induced collision effects in yoke-type inerters, accompanied by experimental validation. Building upon established theoretical frameworks, a constitutive model is first formulated to incorporate inertial forces, Coulomb friction, and backlash nonlinearities. Subsequently, experiments are conducted on a prototype yoke-type inerter. To rigorously characterize the device’s nonlinear behaviors arising from backlash and collision, a multi-body dynamics simulation is implemented, which facilitates the development of an enhanced constitutive model integrating collision. The enhanced model is then employed to quantitatively assess the influence of the backlash and collision on vibration isolator response. Experimental findings confirm the yoke-type inerter’s the adaptive apparent mass effect and dynamic negative stiffness characteristics, suggesting its potential as a viable mechanism for advanced vibration mitigation systems. Comparative analysis reveals that simulation results obtained through the proposed multi-body dynamics model demonstrate strong concordance with experimental trends, thereby verifying both model validity and predictive accuracy. Parametric studies further establish that backlash-induced collision effects exert influence on isolator dynamic responses. The developed modeling framework provides critical theoretical foundations for optimized design of yoke-type inerter-enhanced structures, advancing practical applications in high-performance vibration suppression engineering.

Base-isolation method performs well in controlling superstructure responses but is limited in maintaining stability with special earthquake like long-period earthquakes or extreme rare earthquakes. This study proposes an inerter-based hybrid isolation system which can improve the robustness of isolation structure, utilizing traditional linear natural rubber bearing (LNR), elastic slide bearing (ESB) and viscous damper combined with acceleration-dependent inerter. A two-stage optimal design method is also proposed by leveraging the synergistic effect of the inerter and stiffness of isolation layer. The proposed system can effectively reduce the crucial responses and increase the robustness of isolation structure. This paper firstly builds the inerter-based hybrid isolation structure. Then, the key parameters are classified into two parts based on period-correlation. And the two-stage optimal method is introduced utilizing parameters. An actual engineering structure is used to investigate the feasibility of the inerter-based hybrid isolation system and the optimal method under rare and extreme rare earthquakes. A U-shape high-strength-and-toughness-steel (HSTS) is employed to bear part of stiffness in the isolation layer which brings negative and nonlinear stiffness. Further, displacement and acceleration depended indicators is introduced to evaluate the robustness of structure. The results show that by employing the inerter, the displacement and acceleration responses both decrease compare to the traditional isolation structure without inerter while keeps the isolation layer displacement in the same level. The inerter-based hybrid isolation system can also increase the robustness under extreme rare earthquake. It provides a new reference for combining different types of mechanics components to improve the performance of isolation method, enhancing the safety, stability, and comfort of structures.

Inerter-based isolation systems are effective in providing seismic protection for storage tanks. However, the vibration control-oriented mechanism of inerter-based seismic isolation systems on the seismic response of liquid storage tanks remains unclear, with designs limited to rigid base assumptions. Moreover, the objective existence of the soil-structure interaction (SSI) is overlooked. This study contributes to a discovered advantage of the inerter-based isolation system, including the reduction of input energy and precise control of specific or multiple modes of sloshing heights. Furthermore, an advantageous feature-oriented optimal design for storage tanks with an inerter-based isolation system and with the incorporation of soil conditions is proposed in this study. Initially, an analytical model is developed, considering a storage tank with multi-mode sloshing responses and representing SSIs with frequency-dependent stiffness and damping coefficients. Stochastic response analysis is performed, leading to a novel formulation of multi-mode control and an empirical power equation that quantifies the input energy reduction effect. An advantageous feature-oriented optimal design framework, in which the SSI effect, tank geometric parameters, and inerter-based isolation system parameters are implemented, is established through comprehensive parametric analysis. The results demonstrate that the inerter-based isolation system can be intentionally designed to mitigate specific modes of sloshing height, with the inerter effectively reducing the input power of the entire tank. This study emphasizes the importance of incorporating the SSI effect in the seismic analysis and optimal design of inerter-based tanks. Particularly, the inerter-based isolation system designed assuming a rigid base cannot perform as expected due to the SSI effect, significantly resulting in larger seismic responses and energy dissipation burdens. The developed optimal design method guarantees a target base shear force and sloshing height regarding the considered soil condition.

An innovative cable-bracing inerter system (CBIS) has been proposed and shown to be effective in mitigating the structural response under dynamic excitation. The CBIS comprises an inerter element, an eddy current damping element, and a pair of tension-only cables that can transfer the story drift to rotating flywheels. To further investigate the characteristics of the CBIS, a system identification approach based on an adaptive extended Kalman filter (AEKF) and a recursive least-squares (RLS) algorithm is proposed. Depending on the CBIS model's availability, the proposed approach uses two strategies: the AEKF identifies the parameters of the structure and the CBIS when the model is specific; alternatively, when the model is unspecific, the KF combined with an RLS algorithm identifies the restoring force generated by the CBIS as an unknown fictitious input. In addition, the AEKF incorporates a time-variant fading factor to track the target adaptively. The proposed approach is validated through free vibration and shaking table tests, demonstrating the accuracy in identifying structural parameters and restoring force provided by the CBIS. The identification process involves two stages: initially, the AEKF identifies the parameters of the bare structure without the CBIS, followed by a dual strategy using either AEKF or KF-RLS for identifying the parameters of the CBIS or its restoring force, respectively. The findings also verify the feasibility and validity of the mechanical model and operating principle of the CBIS, thereby contributing to the advancement and application of the CBIS in future studies.

Negative stiffness-incorporated dampers have been widely accepted as effective vibration mitigation systems for flexible structural stiffness adjustment and enhanced energy dissipation. However, current investigations and optimal designs of negative stiffness-incorporated structures are limited to the linear elastic assumption of primary structures, potentially causing stability issues and unsatisfactory control performance. In this case, this study derives the stability criterion for negative stiffness amplifying damper (NSAD)-incorporated nonlinear structures and establishes stability-oriented design as well as modification formulae. The theoretical foundation of NSADs and nonlinear primary structures are initially introduced, based on which the stability criterion is derived according to the Routh–Hurwitz stability criterion. Following the existing design of linear elastic assumption, an endurance time acceleration series is generated subsequently to examine the proposed stability criterion for NSAD-equipped nonlinear structures. Consequently, the stability-oriented design method and corresponding modification formulae are proposed for near-field and far-field earthquakes, of which the effectiveness is validated through design cases. The results underscore the importance of considering structural nonlinearity for ensuring stability and designing NSAD-equipped nonlinear structures, demonstrating the feasibility of using the proposed correction factors to guarantee the stability of NSAD-equipped nonlinear structures subjected to multi-type earthquakes with various intensities. Additionally, the established design framework successively provides a high-efficiency energy dissipation device for seismic control of nonlinear structures, simultaneously generating easy-to-use design formulae for NSADs by combining the linear structure-based design and modification factors, facilitating direct design of nonlinear structures.

The resilient transit-oriented model stimulates the necessity of seismic performance enhancement or retrofitting of over-track complexes with concrete-encased steel slender supporting columns. This study proposes a novel low-damping-ratio-based vibration control approach and easy-to-use design for over-track complexes by flexibly installing the negative stiffness amplification system (NSAS) at the multistory of the over-track building and lower podium. Moreover, a multilocation-oriented design strategy and fitted formulae are developed for the NSAS-damped complex with enhanced energy-dissipation efficiency and an adjustable structural modal shape. By utilizing the negative stiffness device, dashpot, and tuning spring, the NSAS is theoretically constructed, and a simplified model of the NSAS-damped over-track complex is established. Stochastic response analysis and parametric investigation are performed to quantify the benefit of the NSAS-damped story over the conventional control method. Then, easy-to-use design formulae are provided in the initial design and parameter modification stages to realize the simultaneous control of the upper and lower structures. Based on a typical over-track complex with concrete-encased steel slender supporting columns, design cases are analyzed for the NSAS and conventional viscous dampers to verify the applicability of the proposed NSAS and design. The results indicate that the target-story located NSASs contribute a higher-efficiency approach to realize the significant performance improvement or retrofit of the over-track complexes without perturbing the daily function. Particularly, NSASs tailored for distinct stories in the over-track complex effectively satisfy the modification demand for structural modal shape and enhanced energy dissipation efficiency, which cannot be realized by conventional viscous dampers or the existing design of NSASs in normal buildings. In addition, the NSAS-damped story demonstrates a released stiffness abruptness and robust seismic performances against various earthquakes.