Damped Outrigger Research Articles

Shaking table test and control effect analysis of structure with negative stiffness damped outrigger

A shaking table test was conducted on a negative stiffness damped outrigger (NSDO) structure, designed based on a real engineering project, to gain insights into the practical performance of the NSDO under earthquakes when equipped with nonlinear negative stiffness devices (NSD) and dampers. A low-friction NSD was designed, built, and verified by experiments to mitigate the potential issue adversely affecting its performance. The shaking table tests showed that NSD effectively increases the maximum deformation of the damper under moderate earthquakes. Nevertheless, the NSD had no influence on the initial and dynamic stiffness of the NSDO structure when the NSD was not activated due to low displacement. With the bell-shaped damping model to match modal damping ratios, a simplified fishbone numerical model was developed to simulate the response of the NSDO structure and to study the control effect of the NSDO through parametric analysis. The results revealed that the modal damping ratios were not uniform from mode to mode, and an inaccurate higher-mode damping ratio would significantly affect the response predictions during NSDO design. The initial tangential negative stiffness of the nonlinear NSD could be used to analyze the control effect under moderate earthquakes, while the secant stiffness was necessary for severe earthquakes. In addition, a combined seismic reduction curve was proposed for a two-level seismic mitigation analysis.

DNN-metamodeling and fragility estimate of high-rise buildings with outrigger systems subject to seismic loads

This paper proposed deep neural networks (DNNs) for the dynamic response of high-rise buildings with one-outrigger systems under two types of seismic hazards. Using an existing database, the hyperparameters for the architecture of the DNNs are determined finding a trade-off between accuracy and complexity. The performance of the proposed DNNs is compared with two metamodels in the literature, a probabilistic demand model and a kriging metamodel. Partial dependence plot and SHapley Additive exPlanations are used for the explanation of the marginal effect of each feature on the predicted outcome of a neural network from the perspective of global and local agnostic. Considering the uncertainty in the input features, the DNNs are then used to formulate fragility estimates for example high-rise buildings with three types of outrigger systems. The model-agnostic analysis suggests that the DNN targeting the inter-story drift and top acceleration shows extremely high sensitivity to variation in the seismic hazard features, earthquake magnitude, and rupture distance. The fragility curves objectively quantify the reliability of buildings with each of the three outrigger systems and show the effectiveness of damped outrigger systems in reducing fragilities.

Damping dissipation analysis of damped outrigger tall buildings with inerter and negative stiffness considering soil-structure-interaction

This paper analyzes the damping dissipation of damped outrigger tall buildings with inerter and negative stiffness considering soil-structure-interaction (SSI). A unified characteristic equation is established concerning different soil conditions and outrigger systems. By solving the unified characteristic equation, the multi-mode damping effect are parametrically investigated to evaluate the influence of SSI on tall buildings installing conventional outrigger (CO), conventional damped outrigger (CDO), negative stiffness damped outrigger (NSDO), and inerter damped outrigger (IDO). Then, the vibration performances of damped outrigger systems considering SSI are evaluated under both wind and earthquake loadings. Two key points are highlighted: (i) the interaction between the soil rocking behavior and the outrigger rotation in tall buildings; (ii) the influence of frequency variation caused by SSI on the damping effect of IDO and NSDO with frequency-dependent/independent features. Analyzing results indicate that a stronger CO would increase the damping effect of the foundation soil as long as the CO is not installed at lower stories. The SSI effect will render CDO itself undergo more dissipation for the first mode but limit CDO's damping effect on higher modes. IDO can be effective for the target mode, but is very sensitive to SSI effect due to its frequency-dependent feature; a re-optimization of IDO to proper vibration mode is always needed in resisting wind and earthquake. In contrast, NSDO's damping effect is less sensitive to the SSI effect and can be effective to multiple modes due to its frequency-independent feature. For example, the majority of the input energy from winds (over 90%) and earthquake (over 70 %) will be dissipated by NSDO, and such high values change little under SSI conditions, validating NSDO can provide effective and robust control to multiple hazards.

Application of amplified damped outrigger in seismic design of high‐rise buildings

SummaryThe application of the outrigger technology effectively improves the lateral stiffness of buildings, reduces harmful deformation, enhances the seismic resistance of structures, and contributes to the rapid development of high‐rise buildings. To improve the response speed and energy dissipation of a viscous damping outrigger under seismic excitation, a viscous damping outrigger with an amplifier was proposed, and its effectiveness was verified by combining it with the seismic design of a 149.2 m high‐rise building in an 8.5‐degree intensity area. To determine the additional damping ratio of the building structure, investigations were carried out using both the code method and energy ratio method to evaluate the contribution of the damping outrigger. The damped outrigger equivalent stiffness determination method was studied, and the simplified engineering calculation method was compared against the refined finite element analysis results for engineering design purposes. The displacement amplification technique incorporated into the viscously damped outrigger can enhance the damper response speed, and increase the energy dissipation of the damped outrigger system. The application of an enlarged damped outrigger in engineering can result in an additional damping ratio of approximately 1% while simplifying the calculation method based on the additional damping and equivalent damper cut‐line stiffness, which can be useful in engineering design.

Robustness evaluation of the damped outrigger structure

Robustness is defined as the insensitivity of the structure to uncertainties like earthquakes, fire, cyclones, explosions, tsunamis, etc. Robustness analysis of Kalman observer with robust controller for damped outrigger structure is studied to analyze its design performance in the presence of various effects like an earthquake. This is a novel innovative study undertaken in evaluating the robustness of the proposed controller to signify its performance in the field of structural control. The damped outrigger structure is modeled using the finite element approach by finding mode shapes, fundamental natural frequency, and period. The Kalman observer is modeled according to the requirement of the structure with the Riccati equation. The robust proportional–integral–derivative controller is designed according to the input disturbance with Ziegler–Nichols ultimate gain approach. The issue of deterioration in the system performance due to saturation was observed during the analytical investigation of the robust proportional–integral–derivative controller with Kalman observer, which has been addressed by the anti-windup approach. The robustness index of the structure is calculated using sensitivity and complementary sensitivity. The maximum amplitude ratio of the sensitivity for viscous damper-controlled structure is 1.4723 and the value decreases for the other controllers, with a minimum value of 1.0 for the proposed anti-windup robust proportional–integral–derivative controller with Kalman observer. Respectively, the percentage overshoot for the uncontrolled case is 23.4% that values decreasing for other controlled cases, with a minimum of 7.8% for proposed anti-windup robust proportional–integral–derivative controller with Kalman observer. This robustness index and performance indices discriminate the significant robust performance of the proposed robust proportional–integral–derivative controller with Kalman observer-based damped outrigger structure in comparison with other controlled and uncontrolled cases.

Comparative study between inerter and negative stiffness damped outrigger structures

Recently, damped outrigger structures have shown great potentials in suppressing vibrations of tall buildings subjected to seismic and wind excitations. To gain insight into the seismic performance of damped outrigger structures, this paper proposes a stochastic optimization-based sensitivity analysis procedure (SOSAP) for comparative study of damped outrigger structures implemented with inerter dampers (ID) and negative stiffness dampers (NSD) subjected to stochastic seismic excitation. The novelty of this procedure is it integrates stochastic optimization with seismic excitation modeled using the Clough-Penzien spectrum, Pareto optimal fronts dealing with conflict objectives, and sensitivity analysis of objectives values with respect to both discriminative and common design variables. First, the state-space representations of stochastic seismic excitation and structures implemented either with inerter damped outriggers (IDO) or negative stiffness damped outriggers (NSDO) are combined to yield the representations of the augmented structure-damper-earthquake systems. Pareto optimal fronts are then used to examine the tradeoffs between competing optimization objectives, which are defined as harmful interstory drift and floor absolute acceleration via the solutions of the Lyapunov equations. Subsequently, the stochastic seismic responses of the IDO and NSDO systems are compared by investigating the sensitivity of objective values with respect to inertance, negative stiffness ratio and viscous coefficient. The obtained optimal parameters of comparative IDO and NSDO systems are further examined under real earthquake records from the perspectives of dynamic response and energy balance. These investigations demonstrate the efficacy of the proposed SOSAP, reveal the comparative seismic performance between the IDO and NSDO systems dependent on the optimization objectives and the available amount of ID and NSD, which provides insight into the optimal design of tall buildings with different design strategies and conflicting objectives subjected to stochastic seismic excitation.

Seismic response control of core wall structures using tuned viscous mass damper (TVMD) outriggers

This paper presents research on the seismic response control of core wall structures through the installation of innovative damped outriggers known as tuned viscous mass damper (TVMD) outriggers. In this novel system, the TVMDs are arranged vertically between the outrigger trusses/beams and perimeter columns. A simplified model based on the distributed-parameter system was developed to represent a core wall structure equipped with TVMD outriggers. The dynamic properties and seismic responses of high-rise buildings were calculated through a dynamic analysis of the simplified model in MATLAB. The results indicate that TVMD outriggers designed by using fixed-point theory not only suppress the dynamic responses for the target tuning mode, but also supplement additional damping to lower-order modes. When tuned to the second mode, TVMD outriggers with a mass ratio of 0.1 reduce the maximum inter-story drift and floor acceleration responses by 23.48% and 35.80%, respectively. In addition, the control advantages of TVMD outriggers were demonstrated through energy dissipation analysis and damper force decomposition. The vibration control performance of multiple TVMD outriggers was also investigated and was found to achieve superior seismic control with a significantly reduced demand on the TVMD parameters.

Generalized Damped Outrigger Systems for Suppressing Multimode Vibrations of Tall Buildings

Damped outrigger is a viable means for reducing dynamic responses of tall buildings. This study focuses on generalized damped outrigger (GDO) systems. A GDO is composed of a damper for energy dissipation, a negative stiffness device and an inerter for damping enhancement. The GDO system incorporates GDOs at different floors of the tall building optimized to varied structural modes. Frequency equation of a tall building simplified as a cantilever beam with multiple GDOs is first derived by complex modal analysis. A finite different model of such a system is used for verification. Parametric analyses are then performed to compare damping effects of different GDO systems. It is found that a negative stiffness damped outrigger (NSDO) or inerter damped outrigger (IDO) needs to be optimized for maximizing damping of a specific mode. GDOs, respectively, tuned to different modes can largely improve the multimode damping effects. The optimal parameters of the GDOs are slightly different from those in the case when they are installed separately. With both negative stiffness and nonzero inertance, a GDO still needs to be tuned to a specific mode because multimode damping is sensitive to the damper coefficient. The combination of an NSDO optimized to the first mode and an IDO tuned to a higher mode seems the best solution. The IDO additionally improves the first mode damping provided by the NSDO and the two-mode damping is not sensitive to the damper coefficient of the NSDO. The findings are confirmed through seismic response analyses of a tall building with different GDO systems.

Energy sink outrigger control of a tall building under wind loads

The ability of the nonlinear energy sink (NES) device to suppress unwanted wind-induced vibrations in a tall building is investigated in this paper. This controller is an additional energy dissipation embedded within the inner surface of the perimeter column and the end boundary of the outrigger. The Timoshenko theory based on partial differential equations is used to model the dynamic response of the core-tube type structure. The root-mean-square (RMS) response of the structure, defined as the objective function, is used to evaluate the optimal placement of the damped outrigger. Subsequently, a detailed algorithm is proposed to better understand the numerical selection procedure of the suitable location. The effectiveness of the NES on the dynamics of the structural system is investigated through a comprehensive parametric study and compared to a TMD (Tuned Mass Damper) system. According to the results, it is found that the use of appropriate intrinsic parameters of the NES device improves its dynamic response to a considerable level. The presence of this control device is beneficial for the mechanical system and can minimize more than 79 % of the effects of wind-induced vibrations at the top of the structure.

Multimode damping optimization of a long-span suspension bridge with damped outriggers for suppressing vortex-induced vibrations

Long-span suspension bridges are subjected to wind-induced vibrations due to their large flexibility and low damping. Damped outriggers have been proposed recently to supplement damping and suppress multimode vibrations of main girders of long-span bridges, e.g., vortex-induced vibrations. However, when installed at multiple positions including tower-girder junction points and girder ends to further improve multimode damping effect, damping effects of the damped outriggers are interdependent. Additionally, the frequency curves of adjacent modes with respect to varying parameters of the damping devices could approach and intersect with each other, making it difficult to track mode orders and modal damping variations in design optimization. This study therefore proposes an optimization method to design damped outrigger parameters for maximizing multimode damping of the bridge. First, the bridge with damped outriggers is modeled generally using finite element method for dynamic analysis. Subsequently, two critical issues in the design, i.e., the mode tracking and multi-objective optimization, are respectively addressed by using the modal assurance criterion and the genetic algorithm. The proposed method is then applied to the Xihoumen Bridge with a main span of 1650 m. The results show that through the proposed optimization, 6 out of 7 modes vulnerable to vortex-induced vibrations can reach a damping ratio over 1.0%, which cannot be achieved by using damped outriggers of a uniform size. Furthermore, the required damper coefficients are decreased by 49.4%. The flexibility of the outriggers has been considered in the design. The developed method is promising in the design of other types bridge damping devices, e.g., multiple tuned mass dampers.

Frequency independent damped outrigger systems for multi‐mode seismic control of super tall buildings with frequency independent negative stiffness enhancement

AbstractDamped outrigger system is effective for improving energy dissipation for tall buildings. However, conventional damped outrigger (CDO) system with viscous damping has two limitations: (i) its maximum damping ratio cannot be improved when outrigger/column stiffness is inadequate; (ii) different modes achieve their maximum damping ratios at different outrigger damping values, and thus the dampers cannot be optimized to simultaneously reduce vibrations of multiple modes of concern to their minimum. In this paper, a purely frequency‐independent negative stiffness damped outrigger (FI‐NSDO) system is proposed by combining frequency‐independent damper (FID) and negative stiffness device (NSD). The damped outrigger with FID can achieve the maximum damping ratio for all modes as compared to frequency‐dependent damper like viscous damper. As the NSD has the features of assisting and enhancing motion and frequency‐independence, the utilization of NSD will considerably improve the maximum damping ratios when outrigger/column stiffness is inadequate and maintain the frequency‐independent feature of the whole system. Therefore, the FI‐NSDO has the capability of simultaneously increasing the damping ratios of all target modes to their maximum values. Analysis in frequency domain and time domain, demonstrate that the proposed FI‐NSDO performs better in controlling the multi‐mode vibration of seismic responses.

Frequency domain-based analytical framework for seismic performance of viscously damped outrigger systems based on continuous Timoshenko beam theory

This paper proposes a frequency domain-based analytical framework for seismic performance of viscously damped outrigger systems. Based on a core–outrigger–damper–column simplified model, the global dynamic stiffness matrix is assembled from the core modeled as a Timoshenko beam, damped outriggers as complex rotational stiffness comprising outriggers, dampers, and perimeter columns, and inherent damping using Leung’s theory and modal damping construction. A general numerical method combining Wittrick-Williams algorithm and Newtonian iteration is developed to study the dynamic characteristic of such systems with multiple damped outriggers. The fast Fourier transformation (FFT) and the inverse Fourier transformation (IFFT) are then integrated with the principle of potential energy to obtain the equivalent nodal force and thus the time history response by transformations between time and frequency domains. Finally, the stochastic analysis is conducted via the transfer function resulting from the global stiffness matrix with the stochastic seismic excitation following Kanai-Tajimi spectrum. The proposed approach is verified by comparison with the finite element method through a case study of a tall building implemented with viscously damped outriggers. This study shows that the proposed analytical framework could serve as a powerful tool for evaluating the performance of viscously damped outrigger systems.

Stochastic Optimization and Sensitivity Analysis of the Combined Negative Stiffness Damped Outrigger and Conventional Damped Outrigger Systems Subjected to Nonstationary Seismic Excitation

In recent years, various kinds of damped outrigger systems, particularly with the negative stiffness devices, have been shown to effectively suppress excessive vibration induced by earthquake and wind. To gain insight into such systems, this paper proposes a stochastic optimization method to investigate optimal configurations of combined negative stiffness damped outriggers (NSDOs) and conventional damped outriggers (CDOs) subjected to nonstationary stochastic seismic excitation. The simplified analysis model of various combinations of damped outriggers is developed, and the state-space representation of outrigger systems is then formulated. The nonstationary seismic excitation is modeled as a uniformly modulated stationary Gaussian process with a time-modulating function following Clough–Penzien spectrum, and combining equations of motions of outrigger systems and seismic excitation gives rise to the augmented state-space representation of structure-damper-excitation and subsequently the differential Lyapunov equation. The optimal designs of damped outriggers are defined via the solution of the differential Lyapunov equation. The multiobjective optimization with Pareto optimal fronts is adopted to deal with conflicting objectives between harmful interstory drift and floor absolute acceleration. The sensitivity of negative stiffness devices on optimal objectives is also investigated. The optimal designs are further examined under real typical and near-fault earthquake records. The results demonstrate the efficacy of the proposed method and provide insight into the systems subjected to nonstationary seismic excitation. While the purely NSDO systems could have better performance with adequate negative stiffness devices, the proposed combined NSDO and CDO systems prove to be more effective with limited negative stiffness devices and thus provide more design flexibilities tailored to different application situations.

Optimal parameters for tall buildings with a single viscously damped outrigger considering earthquake and wind loads

SummaryTall buildings suffer from low inherent damping and high flexibility. Therefore, a core‐outrigger system is often used to stiffen such buildings. A modified form, known as the damped outrigger system, wherein vertically oriented dampers are installed between outriggers and perimeter columns, has been recently developed to supplement the damping. This paper studies the efficacy of a viscously damped outrigger system through dynamic analysis of a 60‐story tall building subjected to nonconcurrent earthquake and wind excitations. Two ground motion sets (100 accelerograms) are used for the former and wind tunnel test data for the latter. Effects of three building parameters, namely, (i) the core‐to‐column stiffness ratio, (ii) the outrigger location, and (iii) the damper size, on the dynamic characteristics and seismic and wind responses are evaluated. Effects of damper nonlinearity on seismic and wind responses are also investigated considering energy‐equivalent nonlinear viscous dampers. Finally, the optimum values of these parameters are determined. For example, the optimum outrigger location is found to be between to , where is the height of the building. The results also show that the damped outrigger system significantly outperforms the conventional one for seismic excitation, and it is very effective in reducing the wind‐induced floor accelerations, provided the parameters are chosen appropriately.

Reliability Analysis of Stochastic System using Stochastic Spectral Embedding based Probability Density Evolution Method

This study presents a reliability analysis of stochastic system using the probability density evolution method (PDEM). The PDEM is formulated according to the principle of probability conservation where generalized density evolution equations (GDEEs) are completely decoupled. To estimate the probability density function accurately, a set of representative points of random variables are generated using the GF-discrepancy scheme. A large number of representative points is needed to obtain satisfactory accuracy, which becomes computationally expensive. To reduce the computation burden, a stochastic spectral embedding (SSE) is used as a surrogate model which approximates the original response surface. To illustrate the proposed SSE-based PDEM, two numerical examples are investigated, including the reliability analysis of four-branch problem, and the reliability-based design optimization of a shape memory alloy based damped outrigger tall timber building. Numerical results show that the proposed SSE-based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs.

Determination of optimum design parameters of non-linear damped outrigger system for high-rise buildings

Determination of optimum design parameters of non-linear damped outrigger system for high-rise buildings

Vibration mitigation of long-span bridges with damped outriggers

Long-span bridges have low vibration frequencies and small intrinsic damping, and hence are subjected to large-amplitude vibrations, e.g., vortex-induced vibrations (VIVs), which jeopardize the serviceability and safety of the bridge structures. This study proposes a novel concept to supplement damping to such bridges for multimode vibration mitigation, by damping rotations of the bridge girder during vertical and torsional vibrations instead of translational displacements that have been previously the focus of relevant studies. A salient advantage of the concept is that bridge girder rotations near its ends are relatively large during vibrations enabling adequate supplemental damping and also convenient implementation. The concept is realized by a damped outrigger, consisting of a stiff outrigger rigidly connected to the bridge girder and horizontal dampers connecting the end of the outrigger to a bridge tower or a pier. A tensioned beam with rotational constraints is first used to demonstrate damping effects of damped outriggers on suspension bridges. Considering practical parameter ranges, the maximal damping ratio provided by one damped outrigger to a specific mode is about 1.0%. Influences of the relative importance of axial tension and bending stiffness and outrigger stiffness are studied. Furthermore, finite element analyses of an existing suspension bridge with damped outriggers are conducted to verify the damping performance. Numerical results show that by installing one damped outrigger, 6 out of 7 modes that have been involved in VIV events of the bridge can achieve a damping ratio of approximately 1.0% or above. By installing damped outriggers at the two towers, more modes can achieve a relatively large damping ratio, suggesting excellent performance of damped outriggers in suppressing multimode vibrations of long-span bridges.

Damping Performance Analysis of the Damped Outrigger System Based on H∞

A cantilever beam with multiple rotation spring-dampers was utilized to simulate the damped outrigger system. Two new methods, namely, the “Maxwell dampers type method” and the “virtual small mass method,” were proposed to present the simplified seismic response analysis of the damped outrigger system. Corresponding dynamic characteristic equations based on the proposed methods were also given. Subsequently, [Formula: see text] performance index was employed to obtain the optimal damper parameters. The numerical analysis shows that the proposed methods agree well with the finite-element method and have relatively accurate results. Stiffness ratios of the perimeter columns have a significant effect on the pseudo frequencies and system damping ratios. Lower stiffness ratios of the perimeter columns commonly lead to higher pseudo frequencies and system damping ratios. Furthermore, the damped outrigger system has excellent seismic mitigation performance when applied with appropriate damping parameters based on [Formula: see text].

A novel crosswind mitigation strategy for tall buildings using negative stiffness damped outrigger systems

A novel crosswind mitigation strategy for tall buildings using negative stiffness damped outrigger systems

Observer-based anti-windup robust PID controller for performance enhancement of damped outrigger structure

This study presents an observer-based anti-windup robust proportional–integral–derivative controller with state estimator method for damped outrigger structure using magneto-rheological damper to mitigate the seismic response. In this approach, full-order Kalman observer is designed for estimating the states of the damped outrigger system from the feedback of the system output with optimum observer gain. However, due to the computational complexity, the integral windup is observed in the loop; therefore, integral anti-windup is introduced for the internal stability in the loop to produce the desired output. The semi-active magneto-rheological damper is integrated with the proposed system, to produce the required force by the system that ranges between the maximum and minimum values as regulated by the voltages produced by the controller in action for every instant of the seismic energy. The proposed strategy is designed in MATLAB and Simulink to find the adequacy of the damped outrigger system in terms of mitigating the following seismic responses like displacement, velocity, and acceleration. The dynamic analysis of the damped outrigger structure with the proposed control strategy shows enhanced performance in reducing the response of the structure as observed in peak response values. The evaluation criteria show a significant reduction in the vibration of the structure.