Pseudo-negative Stiffness Research Articles

Multimode vibration control of stay cables using pseudo negative stiffness MR damping system

At present the vibration control of stay cable suffers from low damping effectiveness in single mode vibration caused by the limitation of damper installation position as well as the poor modal compatibility, that is, a rapid degradation performance when the actual mode deviates from the designed optimal mode. In this paper, one practical semi-active magnetorheological (MR) damper based control solution is proposed to address the problems faced in multi-modal vibration control of stay cables. The semi-active pseudo negative stiffness (PNS) control strategy takes full account of the MR damper’s mechanical characteristics and the demands of the stay cable vibration control. Compared with the linear equivalent model, the proposed time-varying model exhibits more details of the damping force and the nonlinear response of the damped stay cable, which shows its essential role in the optimal design of MR-PNS scheme. Then the optimal design method of MR-PNS multi-modal vibration control for stay cable is summarized by taking the first three modes vibration control of the J20 cable in Nanjing Baguazhou Yangtze River Bridge as simulation examples. The simulations of cross-modal, multi-modal and wind-induced vibration cases are conducted respectively, while the results show that the optimal designed multi-modal MR-PNS scheme can simultaneously exceed the passive maximum modal damping ratio within first three modes. The advantages of the proposed MR-PNS method in high damping efficiency and modal compatibility could be verified by comparing with the passive multi-modal damping solution.

A programmable pseudo negative stiffness control device and its role in stay cable vibration control

Stay cables are prone to large amplitude vibrations, due to their low inherent damping and high lateral flexibility. In this study, one magnetorheological (MR) damper based programmable intelligent control device is developed to control the vibration of the stay cable more practically and efficiently. The proposed programmable scheme possesses the advantages of low energy consumption, less real time calculation and dynamic input. Its control oriented dynamic model integrated with programmable pseudo negative stiffness (PNS) strategy is built. And its beneficial role in the vibration control is explained in the complex eigenvalue theory analysis of stay cable with MR damper based programmable PNS force. Finally, the simulation of dynamic response of stay cable shows the superiority of programmable control scheme. Its realization demonstrates the feasibility of the single-input programmable PNS scheme experimentally. The dynamic response simulation of stay cable shows that MR damper based PNS scheme can offer better damping performance than conventional control method and its additional damping ratio is 1.63 times higher than that of optimal MR damper passive-on control.

Performance of RC elevated liquid storage tanks installed with semi‐active pseudo‐negative stiffness dampers

The effect of semi-active pseudo-negative stiffness dampers (SAPNSDs) on the seismic response mitigation in the reinforced concrete (RC) elevated liquid storage tanks is investigated. The SAPNSDs are operated in two modes: Passive-ON and Passive-OFF. The effect of placement (location) of the dampers is also studied by placing the dampers in three different configurations. Two aspect ratios of the tanks, viz., 0.5 and 2.0, are considered to study the effect of the variable level of the liquid in the container. Time history analysis is carried out for total of 18 different earthquake ground motions. The differential equations of motion are solved by the state-space approach. The response quantities such as peak base shear, overturning moment, container level displacements, and bracing level displacements, along with the damper forces, are obtained. It is found that the SAPNSDs (Passive-ON) effectively control the response of the RC elevated liquid storage tanks. Further, seismic energy input to the structure without SAPNSDs and the percentage energy dissipated by SAPNSDs is obtained. The placement of the dampers plays a significant role in response reduction during ground motion with high peak ground acceleration (PGA) than that with low PGA. The SAPNSDs installed at alternate levels (Configuration II) is the most efficient configuration for response control of the RC elevated liquid storage tank installed with the SAPNSDs. The seismic input energy reduces considerably by the installation of the semi-active pseudo-negative stiffness dampers (SAPNSDs).

Viscous inertial mass damper (VIMD) for seismic responses control of the coupled adjacent buildings

Many research studies have focused on a novel kind of damper involved with an inertial/gyro mass component, called the inertial mass damper (IMD). Different realizations of the IMD share common standard features: a sizeable apparent mass and the pseudo-negative dynamic stiffness. The connected control method (CCM) has been proven effective for mitigating vibration between adjacent flexible structures. This paper explores the efficacy of using an IMD in parallel with a viscous damper (termed VIMD) configured in the sky bridge to control the vibration of two adjacent towers under random earthquake excitation. First, numerical models of two buildings are developed using a Timoshenko beam model, which can accommodate both bending and shear deformation. Key damper parameters are explored through a parametric study. Then, stochastic optimization is performed to determine optimum damper parameters and the most effective configuration. The optimization results are analyzed in detail, and guidelines for the damper configuration are recommended. By comparing the optimal control performance between the VIMD and traditional viscous damper (VD), the following conclusions can be drawn: due to its pseudo-negative stiffness characteristics and large damper force, the VIMD can achieve better control performances for a wide range of the axial stiffness of the sky bridge; the VIMD requires a smaller damping coefficient and axial stiffness, which can result in smaller damper sizes and member sections of the sky bridge. Therefore, the VIMD is demonstrated to be a useful alternative for engineering practice in CCM vibration mitigation strategies.

Single input magnetorheological pseudo negative stiffness control for bridge stay cables

The bridge stay cable, one of the most critical components in cable-stayed bridges, is vulnerable to vibrations owing to its low inherent damping capacity. Thus effective vibration control technology for bridge stay cables is extremely critical to safe operations of cable-stayed bridges. Several countermeasures have been presented and/or implemented to mitigate this vibration; however the passive method can only add a small amount of damping to the cables, excessive energy demand of active control devices severely limits its practicality, the semi-active control methods still have the drawbacks of complex state estimation module and a large amount of control algorithm calculation. This paper proposes a practical magnetorheological pseudo negative stiffness (MR-PNS) control system coupled with control strategy for bridge stay cables. The current reference point is introduced in the dynamic modeling of the MR-PNS control system to characterize the current control strategy. This paper investigates the adjustable of MR-PNS control system performance and energy consumption caused by different current strategies. Taking the vibration control of the Nanjing Second Yangtze River Bridge J20 cable as an example, the simulation results highlight the advantages of the MR-PNS control system that the failure area is small, the quasi-optimal area is wide, and it can still keep sort of vibration damping performance in the degenerate area. The model cable vibration control test proves the feasibility and efficiency of the single input MR-PNS bridge stay cables control method.

GENETIC ALGORITHM OPTIMAL ARRANGEMENT OF POSITIVE AND NEGATIVE STIFFNESS DAMPERS FOR HYBRID DAMPING BASED ON SEISMIC WAVES METHOD

Increasing negative stiffness may lead to enhanced interlayer displacement. Therefore, the influence of many factors between pseudo-negative stiffness dampers and interlayer displacement should be analyzed. In order to reveal the qualitative relationship between hybrid damping and structural parameters, a novel method that optimizes the structural parameters of dampers based on based on seismic waves method with the help of MATLAB and the SAP2000 OAPI function platform is proposed. First, a negative stiffness damper was approximately simulated by the combination of a parallel damper unit and a multiline elastic unit, and the corresponding benchmark model was investigated. Second, the optimization program of structural damper damping based on a genetic algorithm was developed. Optimization analysis of the mixed damping of positive and negative stiffness dampers was conducted on the 20-story steel frame benchmark model. The damping of different stiffness was summarized on the basis of the analysis results, and the general arrangement principle of the device in the high-rise structure was discussed in the study. Finally, the hybrid damping was formed by the pseudo-negative stiffness damper and the traditional positive stiffness damper. The layout principle and vibration reduction effect of the hybrid damping were verified by experiments under MATLAB and the SAP2000 OAPI function platform. Results show that the top floor acceleration of the structure under the action of the El Centro wave and Kobe wave is reduced by approximately 15% when the pseudo-negative stiffness damper is used. Meanwhile, the displacement of the lower part of the structure is increased by only 5%. Furthermore, enhanced control results can be obtained by the different control strategies and a thorough analysis of the influencing factors used in layers 2–12 and 13–20. The proposed method provides references for optimizing the experimental platform construction and experimental evaluation of hybrid damping dampers. Keywords: Negative stiffness damper, Structural parameter damping, Interlayer displacement peak, Genetic algorithm, Parameter optimization

Experimental and numerical studies on pseudo-negative-stiffness control of a base isolated building using magneto-rheological dampers

This article presents a series of experimental and numerical studies on the feasibility and effectiveness of pseudo-negative-stiffness (PNS) control system using magneto-rheological (MR) dampers. First, a MR damper with nominal force capacity of 10 kN was self-developed. A set of experiments was conducted to study the dynamic performance of the MR damper. Then, a PNS control system was established with NI Compact RIO as hardware platform and Labview as software platform. The displacement-based PNS (DPNS) control algorithm was employed to control the MR damper. Dynamic performance tests were performed to investigate the hysteretic behavior of DPNS control force under different excitation conditions and with different control parameters. Next, shaking table tests were conducted on a four-floor steel frame base isolated structure model employing the PNS control system. The seismic responses under uncontrolled case, passive off case, passive on case and DPNS control case were compared. For each control type, the control efficacy was verified for the El Centro, Ji Ji, Kobe_FN and Kobe_FP with increasing peak ground acceleration. The test results show that the DPNS control can further reduce the isolation displacement compared to the passive off case with no accompanying increase of superstructure responses under seismic excitation with different intensities and spectral characteristics. Finally, numerical studies were conducted to compare the effectiveness of DPNS and clipped-optimal control and investigate the effect of time delay of DPNS control. Results indicate that the DPNS control outperforms the clipped-optimal control and the time delay of the DPNS control leads to the adjustment of the DPNS control force at zero displacement, which is beneficial to control efficacy.

Experimental evaluation of an inertial mass damper and its analytical model for cable vibration mitigation

Cables are prone to vibration due to their low inherent damping characteristics. Recently, negative stiffness dampers have gained attentions, because of their promising energy dissipation ability. The viscous inertial mass damper (termed as VIMD hereinafter) can be viewed as one realization of the inerter. It is formed by paralleling an inertial mass part with a common energy dissipation element (e.g., viscous element) and able to provide pseudo-negative stiffness properties to flexible systems such as cables. A previous study examined the potential of IMD to enhance the damping of stay cables. Because there are already models for common energy dissipation elements, the key to establish a general model for IMD is to propose an analytical model of the rotary mass component. In this paper, the characteristics of the rotary mass and the proposed analytical model have been evaluated by the numerical and experimental tests. First, a series of harmonic tests are conducted to show the performance and properties of the IMD only having the rotary mass. Then, the mechanism of nonlinearities is analyzed, and an analytical model is introduced and validated by comparing with the experimental data. Finally, a real-time hybrid simulation test is conducted with a physical IMD specimen and cable numerical substructure under distributed sinusoidal excitation. The results show that the chosen model of the rotary mass part can provide better estimation on the damper

Performance evaluation of existing isolated buildings with supplemental passive pseudo-negative stiffness devices

A new configuration for passive pseudo-negative stiffness device (PPNSD) is proposed to work as a supplemental device for the seismic protection of existing isolated buildings. The proposed PPNSD reproduces the hysteretic behaviors of semi-active pseudo-negative stiffness devices (PNSD). Using the ratchet-pawl mechanism, a prototype was realized and tested under cyclic loading, validating the feasibility of the proposed PPNSD. Seismic reduction effect of the PPNSD on single-degree-of-freedom (SDOF) systems was verified through seismic response analysis. The PPNSD shows superiority in suppressing the peak acceleration response of long period structures, which is unlikely to be achieved even with large supplemental damping. Then, the performance of isolated buildings with PPNSD was evaluated in comparison to those of isolated buildings with traditional passive isolators under far-field (FF), near-fault pulse-like (NFP), and near-fault non-pulse-like (NFNP) ground motions. It is shown that the use of PPNSD not only simultaneously reduced the base drift and the acceleration of superstructures, but also was effective for all the FF, NFNP, and NFP motions.

Seismic response control of a building by negative stiffness devices

Two analytical studies for the seismic response of a multi-degree-of-freedom shear model controlled by pseudo-negative stiffness (PNS) device and true negative stiffness (TNS) device are presented. The first study intends to optimise the parameters of the control devices for maximum response reduction. The optimal number and location of devices required to achieve the optimal reduction of seismic responses are investigated. In the second study, the performance of the negative stiffness devices, TNS and PNS, are compared with each other and also with a conventional viscous fluid damper (VFD) based on their seismic response reduction capability; different control strategies are adopted for the comparison. The building model considered is a shear type, lumped mass one with a lateral degree-of-freedom at each floor. The governing equations of motion are solved using Newmark’s beta method for a linear variation at a small time interval for six earthquake ground motions. The results indicate that the PNS and TNS devices performed better than the conventional VFD. However, the negative stiffness behaviour of the devices tends to increase certain responses as compared to the conventional damper. Furthermore, the addition of a conventional damper was found to improve the negative stiffness device’s performance as the possible increase in deformation due to such devices is controlled.

Seismic Response Reduction in Liquid Storage Tanks by Simple Smart Base Isolation Systems

In this paper, a nonlinear autonomous algorithm is proposed to control the variable dampers and to provide semi-active control of a liquid storage tank by taking advantage of similarity to friction models and avoiding demerits. Friction mechanism in sliding bearings shows rigid-perfectly plastic behavior with limited damping force. However, transition of vibrations of high frequencies and appearance of residual displacements after the excitation are the drawbacks of such systems. Considering a performance-based seismic design approach, the proposed damping mechanism is capable of controlling the system in a two-level seismic design criterion. The performance and applicability of both the proposed algorithm and a variable oil damper under this command were experimentally verified in previous research. The effect of passive and semi-active seismic control of a liquid storage tank on the response of the structure and sloshing liquid is analytically investigated. Three base isolation systems with passive viscous or sliding dampers are applied and compared with three hybrid semi-active base isolation systems. Pseudo-negative stiffness, skyhook and a proposed control strategy by author are utilized as the control systems. A lumped mass–spring model is employed to represent the dynamic behavior of the tank and the contained liquid. The structural response and sloshing are calculated and compared. It is shown that the smart base isolation system is effective in reduction in the base shear and displacement of the structure. The sloshing response observed through the displacement and kinetic energy of the convective mass is reduced by the hybrid control systems.

Probabilistic seismic risk assessment of modified pseudo-negative stiffness control of a base-isolated building

Pseudo-negative stiffness (PNS) control of a base-isolated structure, which has a large damping ratio at the isolation level, is used to suppress isolator displacement without large force transmission to the superstructure during extreme earthquakes. However, potential increases in floor acceleration in the superstructure are induced by the large damping ratio, especially for low-to-moderate seismic input level. In consideration of structural functionality and safety, a modified PNS (MPNS) control scheme based on the ‘ideal isolation control principle’ is proposed, considering different seismic intensity levels. The effect of the MPNS control is investigated from three aspects, namely floor acceleration, inter-storey drift and isolator displacement within a probabilistic performance-based seismic engineering framework. Comparisons are made between MPNS control, conventional PNS control and passive damping control. A benchmark base-isolated building is used as a case study. In the seismic performance evaluation, the seismic intensity measures for different response parameters are optimised. An extensive parametric study is also conducted to identify the optimal control parameter to conform to the ideal isolation control principle. Results demonstrated that the MPNS control is an effective solution to the challenging problem of improving structural functionality at low seismic intensity, as well as structural safety from collapse at extreme seismic intensity.

Use of pseudo-negative stiffness dampers for reducing the seismic response of bridges: a benchmark study

Seismic response control of the benchmark Highway Bridge with a variable damper employing pseudo-negative stiffness (PNS) control algorithm; referred as PNS damper is investigated under the six earthquake ground motions. PNS damper is used as a semi-active control device. The study is based on the finite-element model of the 91/5 highway bridge located in Southern California. The prime aim of the study is to investigate the effectiveness of PNS damper for seismic response mitigation of the benchmark highway bridge. Numerical simulations are conducted by installing the control devices between the deck-end and abutments of the bridge. The response of the bridge with PNS damper is compared with the corresponding uncontrolled response and the sample controllers. Combined effect of the PNS damper and elastic stiffness of the existing structural member produces a broad hysteresis loop, leading to higher seismic energy dissipation at low control force. From the results of the numerical simulations, it is concluded that PNS dampers are quite effective in reducing the pier base shear, deck displacement, acceleration and bearing displacements, thereby reducing damages during near-fault earthquake ground motions.

Nature of seismic control force in acceleration feedback

Active control methods have been applied to numerous civil structures in recent years. A significant amount of the research on active control methods has been based on full-state feedback using the linear quadratic regulator (LQR) control algorithm; because measurement of the full state (i.e., the displacements and velocities of all DOFs) is difficult, such algorithms are impractical in full-scale implementations. Output feedback strategies based on measured acceleration at a limited number of points has been proposed and validated. However, a thorough understanding of the dissipative nature of the associated control forces and the way in which these forces protect the structure have been elusive. This paper considers the hysteric behavior of the control forces produced by the widely employed linear quadratic Gaussian (LQG)-based acceleration feedback control strategies and explores parallels with the pseudo-negative stiffness (PNS) semi-active damping systems. Numerical simulation studies carried out on one-story and three-story buildings with active bracing show that the LQG-based algorithms are quite versatile and can produce controllers with a variety of behaviors, including the PNS, depending upon the control objectives chosen. Copyright © 2012 John Wiley & Sons, Ltd.

Seismic performance of structures incorporating magnetorheological dampers with pseudo-NEGATIVE STIFFNESS

SUMMARY Pseudo-negative stiffness control is a control scheme that is aimed to track, in a passive energy dissipation fashion, a target spring force with negative stiffness when possible. In this study, it is proved that systems with pseudo-negative stiffness control have the property of homogeneity even though they are nonlinear systems. The harmonic response analyses reveal that the pseudo-negative stiffness reduces the resonant frequency of the system. Seismic response spectrum analyses show that both acceleration and displacement can be reduced with the pseudo-negative stiffness control when the structural period is long and damping level is not high. Pseudo-negative stiffness control of a five-story base-isolated structure incorporating magnetorheological damper is studied through analytical and real-time hybrid test methods. The results show that displacement and acceleration responses with pseudo-negative stiffness control are lower than those with passive-off control and isolator alone, whereas the displacement response with pseudo-negative stiffness is greater than the passive-on control. Copyright © 2011 John Wiley & Sons, Ltd.

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.

Passive and semi‐active seismic response control of a cable‐stayed bridge

AbstractEffectiveness of passive and semi‐active seismic response control on a cable‐stayed bridge was studied by numerical analyses. An existing cable‐stayed bridge which has fixed‐hinge connections between deck and towers is modeled and its connections were replaced by isolation bearings and dampers. The isolation bearings are of elastic and hysteretic type. The dampers are of linear and variable type. The variable damper uses semi‐active control that incorporates a pseudo‐negative stiffness algorithm. A pseudo‐negative stiffness hysteretic loop produced by the variable damper, combined with a positive stiffness curve of the deck‐tower connections, creates nearly rigid–perfectly plastic force–deformation characteristics with a large damping ratio. The damping ratio for the main mode of the bridge for both passive and semi‐active control was also calculated. Soil‐structure interaction and three‐dimensional effects on structural responses were studied. Copyright © 2002 John Wiley & Sons, Ltd.