Full-scale shaking table test and seismic fragility evaluation of all-bolted prefabricated steel frame structures with viscous dampers

Heuristic-based multi-objective optimization design for viscous dampers in RC frame structures considering soil-structure interaction

Over the past decade, extensive research has been conducted to investigate the properties and behavior of rubberized concrete as a sustainable green alternative to conventional concrete. This research involves replacing natural aggregates with rubber particles from discarded tires. Generally, these studies have shown an enhancement in ductility, energy dissipation, and the damping ratio of rubberized concrete. However, a significant reduction in mechanical properties, such as compressive and tensile strength, and modulus of elasticity, has been noted compared to standard concrete. Currently, the literature lacks a comprehensive numerical study that could provide structural engineers with a complete understanding of the seismic performance of rubberized concrete frames. Consequently, this study examines three low-rise RC frames subjected to sixty recorded ground motions (near-fault, pulse-like, and far-fault) using nonlinear response-history analysis, comparing rubberized concrete (RBC) with a control concrete (NC-C) and a similar-strength mix (NC-S). Across records, RBC exhibits lower base shear (mean reductions up to 11.6–13.8% versus NC-C and about 3–6% versus NC-S, depending on motion class), higher viscous damping energy (increases of 29–53%), and lower hysteretic energy (reductions of about 10–29%), while interstory drift ratios increase yet remain within ASCE 7 drift limits. Absolute floor accelerations reduce modestly (up to 11.8% in far-fault motions). The results indicate that substituting RBC can enhance damping efficiency and reduce seismic forces relative to both NC-C and NC-S under severe earthquakes at a drift trade-off.

This study systematically investigated the influence of slope effects on soil-pile interaction in integral abutment jointless bridges (IAJBs) under cyclic loading through pseudo-static cyclic tests. While existing studies on the soil-structure interaction in IAJBs had predominantly centered on level-ground conditions, the asymmetric constraint effects of sloped terrains remained inadequately investigated. To address this research limitation, three reinforced concrete piles-with varying ratios (b/d = 2.0, 0.0, -2.0) of the distance (b) from pile side relative to slope crest to the pile diameter (d)-were embedded in layered clay-sand slopes and subjected to cyclic displacements. Key results indicated that decreasing the ratio (b/d) from 2.0 to -2.0 increased the maximum damage depth by 25% and expanded the crack distribution range by 50%. The lateral load and soil reaction of the pile in the slope-facing direction decreased by 29.1% and 28.9%, respectively, while backslope values remained stable. Both the equivalent viscous damping and stiffness in the slope-facing direction degraded by 12-32%. These findings clarified the asymmetric soil-pile interaction mechanisms induced by slope effects and provided critical references for optimizing pile embedment depth and seismic design of IAJBs in sloped terrains.

Abstract Decaying pulsations have been simultaneously detected in the low-energy X-rays of solar/stellar flares, which are supposed to be associated with standing slow magnetoacoustic or kink-mode waves. The physical mechanism behind rapid decay remains unknown. We present the detection of quasiperiodic pulsations (QPPs) with rapid decay in high-energy emissions produced in two major flares on 2024 January 10 and May 14. Using empirical mode decomposition, decaying QPPs are identified in hard X-ray and microwave emissions during the flare-impulsive phase, suggesting a process of oscillatory magnetic reconnection. The quasi-periods and decay times are determined by a damped harmonic function, which are approximately 177 ± 8 s (249 ± 25 s) and 118 ± 4 s (124 ± 5 s), respectively. The restructured X-ray images reveal double footpoints connected by hot flare loops. Their phase speeds are estimated to be about 400 and 670 km s −1 , both below the local sound speed in high-temperature plasmas, indicating the presence of slow-mode waves in hot flare loops. We perform coronal diagnostics based on standing slow-mode waves and derive key physical parameters, including the polytropic index, the thermal ratio, viscous ratio and radiation ratio, which are consistent with previous results. Our observations support the conclusion that decaying QPPs are triggered by oscillatory magnetic reconnection that is modulated by standing slow magnetoacoustic waves, with their rapid decay attributable to a coeffect of viscous damping and localized magnetic reconnection rate.

This study was conducted based on hybrid damping control theory, and an equivalent damping ratio calculation method was proposed. Additionally, a response calculation method for the elastoplastic stage of the hybrid control system was developed. Furthermore, a cooperative working mechanism between viscous dampers and metal composite dampers was introduced. A time–history analysis was employed to verify the system’s effectiveness in optimizing the multi-dimensional seismic performance of frame structures. Using actual engineering as the research background, an elastoplastic analysis of the hybrid control system was conducted. The analysis results show that the first three natural periods of vibration were shortened by 6.1% (in the X direction), 5.9% (in the Y direction), and 21.0% (torsion), effectively enhancing the overall stiffness of the structure. Under seismic action, the inter-story displacement decreased by 37.1% to 0.166 m in the X direction and by 48.3% to 0.080 m in the Y direction; the base shear forces were reduced by 58.8% (in the X direction) and 41.7% (in the Y direction). Regarding damage control, the number of plastic hinges was significantly reduced, and they appeared only on the most unfavorable floors; the axial compressive stress peaks in the frame columns were strictly controlled below 0.65 fc, and the inter-story displacement angles (<1/50) met the standards of GB50011-2010 for key protection structures. The hybrid system demonstrated multi-dimensional synergistic effects, whereby the viscous dampers primarily controlled the acceleration responses in the X direction, while the metal composite dampers dominated energy dissipation in Y displacement. The difference in seismic reduction efficiency between the two main axes was less than 11%, and a 21% improvement in the torsional period was achieved simultaneously.

In this paper, we address the regularity of weak solutions to a crane model subject to nonlinear boundary feedback and distributed viscous damping, considered up to sets of measure zero. Based on the weak formulation of the system, the Faedo-Galerkin method is applied to prove existence and uniqueness of solutions. The use of suitable intermediate spaces then allows us to enhance regularity results and establish additional differentiability properties, offering a more precise characterization of the system's dynamics and a solid foundation for subsequent numerical analysis.

Signed graphs encode cooperative and antagonistic interactions in dynamical systems. In this paper we will study how explicit damping transforms unstable linearized dynamics into stable behavior, mapping the system Jacobian to a signed weighted matrix to diagnose destabilizing pathways and guide damping or edge reweighting. Beyond graphical intuition, stability is certified by a Lyapunov/spectral test on the symmetric part S with diagonal damping D, namely D −S ≻ 0 (equivalently, λmax(S) < mini di). Using the inverted pendulum as a benchmark, we derive a cleaned state-space model, show undamped instability, and demonstrate how viscous damping enforces the certificate. We provide a concise numerical verification (eigenvalue checkand time-response illustration). The results clarify when signed graphs aid design and placement of damping, while the Lyapunov/spectral certificate supplies the formal guarantee of stability through a computable criterion.

This study develops empirical equations relating viscous damping ratios (ξ) and damper coefficients (c) in steel structures for seismic design applications. The objective is to establish predictive formulas that enable conversion between equivalent viscous damping ratios and physical damper characteristics through dynamic analysis. This research employs a two-phase analytical methodology on steel building frameworks. Initially, inherent viscous damping ratios are incrementally varied from 3% to 40% to establish baseline response characteristics. Subsequently, supplemental damping devices are integrated with damper coefficients (c) adjusted according to manufacturer specifications. Linear time-history analyses are conducted for both configurations to determine equivalent damping relationships, with a particular focus on Interstory Drift Ratios (IDR) and Peak Floor Accelerations (PFA) as key seismic demand parameters. By comparing response quantities between inherent and supplemental damping scenarios, empirical relationships linking physical damper coefficients with equivalent viscous damping ratios are formulated. The resulting equations provide practicing engineers with a practical tool for estimating damper specifications based on target damping levels in steel structures. The formulations are derived from linear time-history analysis of steel frame configurations and are applicable within the scope of linear elastic response and viscous damper behavior consistent with typical design conditions.

Improved toggle-brace viscous damper for vibration mitigation of wind turbine blade

Analysis of the Impact of Vertical Geometric Irregularity on the Seismic Stability of Buildings with Viscous Wall Dampers and Viscous Fluid Dissipaters

This study addresses the seismic performance improvement of complex and irregular indoor substations in high-intensity areas by integrating computer algorithm optimization with new damper technology. With the rapid development of urban construction, unconventional buildings with complex shapes are becoming more common. Indoor substations exhibit significant planar and vertical irregularities due to equipment installation needs. The spatial misalignment between the mass center and stiffness center exacerbates the planar-torsional coupling effect under seismic loads, making traditional seismic design methods inadequate for high-intensity area seismic codes. This research aims to address the issues of insufficient parameter allocation accuracy and hardware performance limitations in existing energy dissipation and vibration reduction technologies when applied to irregular structures through innovative algorithm optimization and damper design. Methodologically, an improved Kasai method is proposed to construct a dynamic allocation strategy for multi-degree-of-freedom system damping parameters. A single-degree-of-freedom equivalent subsystem and multi-degree-of-freedom parameter coupling optimization model are established. A damper configuration algorithm considering the non-uniform distribution of inter-story drift ratios is developed. By introducing a dynamic allocation coefficient, the critical layer non-uniform configuration of damping parameters is achieved. An optimization model for stiffness-damping coupling regulators is established to ensure that the convergence condition of the algorithm is met with ∥Rd–R′d∥<5%. The 3D finite element model is constructed using SAUSAGE software, and time-history analysis is conducted using five natural waves and two artificial waves for validation. Additionally, a new viscous damper with improved damping holes is designed, and frequency-dependent, low-speed friction, and fatigue performance tests are conducted using a 3530 kN electro-hydraulic servo system. The results show that the improved algorithm reduces the number of dampers by 15% compared to traditional designs. Under moderate seismic conditions, the maximum vibration damping efficiency in the X/Y-directions reaches 37.18% and 21.09%, respectively, with inter-story drift ratio precisely controlled within the 1/400 limit. The new Type B damper shows an 8% reduction in measurement error compared to the traditional Type A damper under a 9.425 mm/s condition. After 30 fatigue cycles, the damping force decay rate is only 7.8%, and the energy dissipation efficiency increases by 23%. The study confirms that the improved Kasai method effectively overcomes the precision issues in the parameter allocation of traditional equivalent linearization models for multi-degree-of-freedom systems. When combined with the new damper, it can reduce the flat torsion coupling vibration effect by more than 40%. This achievement breaks through the design bottleneck of seismic resistance for complex structures in high-intensity areas. By innovating in both algorithm and hardware, it establishes a new paradigm for intelligent vibration damping system design, providing a solution that is both cost-effective and reliable for critical infrastructure. It also promotes the transition of energy dissipation and vibration damping technology towards model-driven methods, offering significant engineering value and social benefits in enhancing the earthquake resilience of urban infrastructure.

The Lekszycki method for damage detection in structures with viscous damping

Abstract Vibration mitigation remains a critical challenge in mechanical and structural systems under resonant and broadband excitation. While conventional tuned mass dampers (TMDs) are widely used, their effectiveness is constrained by substantial mass requirements and narrow operational bandwidths. This study introduces two inertial amplification mechanism (IAM)-based absorbers designed to overcome these limitations, the tuned inertial amplified mass damper (TIAMD) and the tuned inertial amplified viscous mass damper (TIAVMD). The TIAMD integrates an IAM into a Voigt-type TMD, while the TIAVMD embeds the IAM within a grounded viscous-TMD configuration. Mathematical models of both systems, coupled with a single-degree-of-freedom primary system, are derived using Lagrange’s equations and solved using an adaptive step-size Runge–Kutta method. Numerical optimization using pattern search algorithms identifies optimal frequency and damping ratios to minimize peak steady-state response under harmonic excitation. The influence of key design parameters including Mass ratio, Mass distribution ratio, and IAM angle on dynamic performance is investigated, and comprehensive design charts for optimal tuning are presented. Results demonstrate that both configurations significantly outperform conventional TMDs, with the TIAVMD achieving 40.4% greater vibration suppression, 75.5% wider bandwidth, and 68.2% lower absorber displacement. The TIAMD shows comparable improvements, including 31.2% enhanced attenuation and 58% bandwidth expansion. These IAM-based absorbers offer superior vibration control without mass penalties, providing efficient and compact solutions for diverse engineering applications.

Coupling beam systems have appeared widely in various engineering fields, where several additional beams are generally set near coupling beam systems, which may be designed as a vibration control mechanism by introducing some unique connecting relations. This study introduces nonlinear connecting relations to connect an additional beam and a two-layer beam system, where the additional beam equipped with connecting nonlinear stiffness is defined as an internal beam-type CNES. The Lagrange method is chosen to calculate the nonlinear vibrating system’s numerical responses, which can correctly calculate the nonlinear vibrating system’s numerical responses. Introducing the internal beam-type CNES is beneficial for broadband attenuation of the vibration of the vibrating system’s main structures. The internal beam-type CNES’s representative working states are divided into linear and nonlinear broadband vibration attenuating states. The appearance of representative nonlinear responses can be judged as a sign of the internal beam-type CNES working in the nonlinear broadband vibration attenuating state. Increasing the nonlinear stiffness of the internal beam-type CNES can motivate representative nonlinear responses of the vibrating system, while increasing its viscous damping can eliminate representative nonlinear responses. A delicate parameter selection of the nonlinear stiffness of the beam-type CNES helps enhance the vibration attenuation of the two-layer beam. Importantly, the internal beam-type CNES reveals the attractive vibration-attenuation potential in controlling the vibration of coupling beam systems. The proposed internal beam-type CNES provides a feasible way to use unimportant additional beams near main beam structures to control their vibration. It is beneficial for effectively utilizing existing engineering structures to carry out the vibration-attenuation design.

In this study, the torsional vibration behavior of viscoelastic nanorods under elastic boundary conditions is analyzed using nonlocal strain gradient theory. The governing equations are derived and solved using Fourier series and Stokes transforms to obtain a semi-analytical solution. The influence of damping on size-dependent torsional response is examined, with significant effects observed in highly damped systems. Moreover, to overcome the computational cost of the analytical method, a Gaussian Process Regression (GPR) model is proposed as a surrogate for predicting torsional frequencies. The GPR model demonstrates strong predictive capability across varying material and geometric parameters, offering a practical and efficient alternative. To assess the model’s robustness, white noise was introduced at 5%, 10%, and 15% levels; the GPR maintained R 2 values above 0.96, indicating high accuracy under uncertainty. A Shapley Additive Explanations (SHAP) analysis was also conducted to interpret the model, revealing that viscous damping is the most influential parameter affecting frequency. Overall, the GPR model offers an accurate, noise-resilient, and interpretable approach for analyzing the dynamic behavior of viscoelastic nanorods.

ABSTRACTThis paper presents a gradient‐based optimization framework for the preliminary seismic design of alternative isolation systems and fluid viscous dampers in vertically irregular 2D shear frames. The proposed method simultaneously optimizes the number, locations, and properties of isolation layers together with viscous damper coefficients, allowing base isolation to naturally emerge as an optimal configuration when appropriate. This is done while adopting an equivalent linear model of the isolators. The methodology integrates the mixed Lagrangian formulation as analysis, adjoint sensitivity, the solid isotropic material with penalization (SIMP) approach, and penalty functions to minimize realistic costs while satisfying drift constraints (at both isolation levels and regular stories) and absolute floor acceleration limits, while also achieving binary (active/inactive) topology decisions for isolation placement. A numerical example using a suite of ground motions demonstrates the method's efficiency, achieving convergence in 330 iterations and a final design cost 4.7% lower than particle swarm optimization (PSO) while requiring three orders of magnitude fewer function evaluations. Results confirm that multi‐floor isolation can achieve target seismic performance at significantly lower cost than conventional base isolation. Additionally, a comparison with nonlinear time‐history analysis was performed, which highlighted the differences between linear and nonlinear responses and emphasized the importance of such analysis in the design verification stage to accurately capture the true seismic behavior. These findings underscore the method's computational efficiency, cost‐effectiveness, and applicability to complex irregular buildings.

ABSTRACT This study proposes a novel method to enhance energy dissipation in building structures by partitioning three-dimensional building’s skeleton into four parts, two short-period (stiff) and two long-period (soft), interconnecting by linear viscous dampers. First, a set of 3-, 5-, and 10-story regular steel buildings were designed using the conventional design code. Then, each building’s skeleton was divided into four architecturally equal parts of the same mass, but different stiffness values, and optimal damping coefficient values were found by trial and error, to minimize the seismic responses, obtained by nonlinear time history analyses (NLTHA). To conduct NLTHA, three-component records of eleven site-compatible earthquakes were selected, and the seismic responses, including Inter-story drift, roof absolute acceleration, base shear forces, and dampers’ force-displacement hysteresis, were obtained. The results demonstrated, on average, a decrease of 43% in drift values, and 41% in base shear forces was achieved using optimal dampers. Roof absolute acceleration was reduced by 47% and 66% for stiff and soft substructures, respectively. Finally, a comparison of the created plastic hinges, in the two groups of structures revealed that their performance in the four-part vertically isolated structures remains at the IO level, while in the single-part structures, they mostly exceed the LS level.

Shaft deflection degrades roller alignment and intensifies stress concentration/edge effects at roller-ends and raceway edges, ultimately compromising service performance of tapered roller bearings (TRBs). Therefore, a dynamic model was developed for a TRB subjected to a deflected shaft in which Johnson’s load–deformation relationship was applied to reflect non-uniform cross-sectional structures of the tapered rollers and raceways, viscous damping was integrated into the roller/cage interaction, and friction actions at the raceways and flange areas were treated separately. Then, moment load and angular misalignment of the tapered roller were analyzed under various shaft deflection and operating conditions. Results indicate that tilt angle remains orders of magnitude smaller than skew angle. Shaft deflection amplifies both skew and tilt, and the influence level is proportional to the bearing size. Centrifugal effect primarily affects skew motion, whereas gyroscopic effect mainly influences tilt motion. Axial forces exert greater influence on roller skew than tilt. The flange typically constrains roller skew, whereas both raceways may induce bidirectional tilt/skew motion.

ABSTRACTThis paper proposes a combined outrigger and multilayer amplified viscous damped substructure system (COMAVDSS). First, a simplified analysis model for the COMAVDSS was established, and the mechanical models of the single‐layer amplified viscous damper (SAVD) and multilayer amplified viscous damper (MAVD) were derived. Subsequently, the theoretical predictions were compared with the experimental results to validate the mechanical model. Finally, to evaluate the vibration control capability of COMAVDSS, a high‐rise structure was numerically simulated. The deviation between the test and theoretical values of damping force and energy dissipation under different loading displacements is within ±15%. Compared with the viscous damper (VD), the maximum damping force of SAVD and MAVD increased by 380% and 883%, respectively. Compared with the combined outrigger substructure system (COSS), the top displacement RMS of the combined outrigger and viscous damped substructure system (COVDSS), the combined outrigger and single‐layer amplified damped substructure system (COSAVDSS), and COMAVDSS are reduced by 11.76%, 30.66%, and 55.13%, respectively. Compared with the COVDSS, COSAVDSS and COMAVDSS increase the damper energy dissipation by 42% and 58%, respectively. The COMAVDSS utilizes the relative displacement difference between the main structure and substructure and the damping amplification mechanism to improve the energy dissipation efficiency.