Re‐shaping hysteretic behaviour—spectral analysis and design equations for semi‐active structures

Semi‐active dampers offer significant capability to reduce dynamic wind and seismic structural response. A novel resetable device with independent valve control laws that enables semi‐active re‐shaping of the overall structural hysteretic behaviour has been recently developed, and a one‐fifth scale prototype experimentally validated. This research statistically analyses three methods of re‐shaping structural hysteretic dynamics in a performance‐based seismic design context. Displacement, structural force, and total base‐shear response reduction factor spectra are obtained for suites of ground motions from the SAC project. Results indicate that the reduction factors are suite invariant. Resisting all motion adds damping in all four quadrants and showed 40–60% reductions in the structural force and displacement at the cost of a 20–60% increase in total base‐shear. Resisting only motion away from equilibrium adds damping in quadrants 1 and 3, and provides reductions of 20–40%, with a 20–50% increase in total base‐shear. However, only resisting motion towards equilibrium adds damping in quadrants 2 and 4 only, for which the structural responses and total base‐shear are reduced 20–40%. The spectral analysis results are used to create empirical reduction factor equations suitable for use in performance based design methods, creating an avenue for designing these devices into structural applications. Overall, the reductions in both response and base‐shear indicate the potential appeal of this semi‐active hysteresis sculpting approach for seismic retrofit applications—largely due to the reduction of the structural force and overturning demands on the foundation system. Copyright © 2006 John Wiley & Sons, Ltd.     

Semi‐active tuned mass damper building systems: Design

Passive and semi‐active tuned mass damper (PTMD and SATMD) building systems are proposed to mitigate structural response due to seismic loads. The structure's upper portion self plays a role either as a tuned mass passive damper or a semi‐active resetable device is adopted as a control feature for the PTMD, creating a SATMD system. Two‐degree‐of‐freedom analytical studies are employed to design the prototype structural system, specify its element characteristics and effectiveness for seismic responses, including defining the resetable device dynamics. The optimal parameters are derived for the large mass ratio by numerical analysis. For the SATMD building system the stiffness of the resetable device design is combined with rubber bearing stiffness. From parametric studies, effective practical control schemes can be derived for the SATMD system. To verify the principal efficacy of the conceptual system, the controlled system response is compared with the response spectrum of the earthquake suites used. The control ability of the SATMD scheme is compared with that of an uncontrolled (No TMD) and an ideal PTMD building systems for multi‐level seismic intensity. Copyright © 2009 John Wiley & Sons, Ltd.     

Full‐scale experimental verification of resetable semi‐active stiffness dampers

Because of many advantages over other control systems, semi‐active control devices have received considerable attention for applications to civil infrastructures. A variety of different semi‐active control devices have been studied for applications to buildings and bridges subject to strong winds and earthquakes. Recently, a new semi‐active control device, referred to as the resetable semi‐active stiffness damper (RSASD), has been proposed and studied at the University of California, Irvine (UCI). It has been demonstrated by simulation results that such a RSASD is quite effective in protecting civil engineering structures against earthquakes, including detrimental near‐field earthquakes. In this paper, full‐scale hardware for RSASD is designed and manufactured using pressurized gas. Experimental tests on full‐scale RSASDs have been conducted to verify the hysteretic behaviours (energy dissipation characteristics) and the relation between the damper stiffness and the gas pressure. The correlation between the experimental results of the hysteresis loops of RASADs and that of the theoretical ones has been assessed qualitatively. Experimental results further show the linear relation between the gas pressure and the stiffness of the RSASD as theoretically predicted. Finally, shake table tests have also been conducted using an almost full‐scale 3‐storey steel frame model equipped with full‐scale RSASDs at the National Center for Research on Earthquake Engineering (NCREE), Taipei, Taiwan, and the results are presented. Experimental results demonstrate the performance of RSASDs in reducing the responses of the large‐scale building model subject to several near‐field earthquakes. Copyright © 2007 John Wiley & Sons, Ltd.     

Semi‐active tuned mass damper building systems: Application

Seismic performance attributes of multi‐story passive and semi‐active tuned mass damper (PTMD and SATMD) building systems are investigated for 12‐story moment resisting frames modeled as ‘10+2’ stories and ‘8+4’ stories. Segmented upper portion of the stories are isolated as a tuned mass, and a passive viscous damper or semi‐active resetable device is adopted as energy dissipation strategy. The semi‐active approach uses feedback control to alter or manipulate the reaction forces, effectively re‐tuning the system depending on the structural response. Optimum tuned mass damper control parameters and appropriate matching SATMD configurations are adopted from a companion study on a simplified two‐degree‐of‐freedom system. Statistical performance metrics are presented for 30 probabilistically scaled earthquake records from the SAC project. Time history analyses are used to compute response reduction factors across a wide range of seismic hazard intensities. Results show that large SATMD systems can effectively manage seismic response for multi‐degree‐of freedom systems across a broad range of ground motions in comparison to passive solutions. Specific results include the identification of differences in the mechanisms by which SATMD and PTMD systems remove energy, based on the differences in the devices used. Additionally, variability is seen to be tighter for the SATMD systems across the suites of ground motions used, indicating a more robust control system. While the overall efficacy of the concept is shown the major issues, such as isolation layer displacement, are discussed in detail not available in simplified spectral analyses, providing further insight into the dynamics of these issues for these systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Damping reduction factors and code‐based design equation for structures using semi‐active viscous dampers

This study uses a semi‐active viscous damper with three different control laws to reshape the structural hysteresis loop and mitigate structural response, referred to as 1–4, 1–3 and 2–4 devices, respectively. The 1–4 control law provides damping in all four quadrants of the force‐displacement graph (it behaves like a standard viscous damper), the 1–3 control law provides resisting forces only in the first and third quadrants, and the 2–4 control law provides damping in the second and fourth quadrants. This paper first outlines the linear single degree of freedom structural performance when the three types of semi‐active viscous dampers are applied. The results show that simultaneous reduction in both displacement and base‐shear demand is only available with the semi‐active 2–4 device. To enable guidelines for adding a 2–4 device into the design procedure, damping reduction factors (RF_ξs) are developed, as they play an important role and provide a means of linking devices to design procedures. Three methods are presented to obtain RF_ξ and equivalent viscous damping of a structure with a 2–4 semi‐active viscous damper. In the first method, the relationship between RF_ξ and the damping of a semi‐active structure can be obtained by calculating the area under the force‐deformation diagram. The second and third method modified the Eurocode8 formula of RF_ξ and smoothed results from analysis, respectively. Finally, a simple method is proposed to incorporate the design or retrofit of structures with simple, robust and reliable 2–4 semi‐active viscous dampers using standard design approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Market‐based control of linear structural systems

To limit the response of structures during external disturbances such as strong winds or large seismic events, structural control systems can be used. In the structural engineering field, attention has been shifted from active control to semi‐active control systems. Unlike active control system devices, semi‐active devices are compact, have efficient power consumption characteristics and are less expensive. As a result, an environment of a large number of actuators and sensors will result, rendering a complex large‐scale dynamic system. Such a system is best controlled by a decentralized approach such as market‐based control (MBC). In MBC, the system is modelled as a market place of buyers and sellers that leads to an efficient allocation of control power. The resulting MBC solution is shown to be locally Pareto optimal. This novel control approach is applied to three linear structural systems ranging from a one‐storey structure to a 20‐storey structure, all controlled by semi‐active hydraulic dampers. It is shown that MBC is competitive in the reduction of structural responses during large seismic loadings as compared to the centralized control approach of the linear quadratic regulation controller. Copyright © 2002 John Wiley & Sons, Ltd.     

Forced vibration test of a building with semi‐active damper system

The authors developed a semi‐active hydraulic damper (SHD) and installed it in an actual building in 1998. This was the first application of a semi‐active structural control system that can control a building's response in a large earthquake by continuously changing the device's damping coefficient. A forced vibration test was carried out by an exciter with a maximum force of 100 kN to investigate the building's vibration characteristics and to determine the system's performance. As a result, the primary resonance frequency and the damping ratio of a building that the SHDs were not jointed to, decreased as the exciting force increased due to the influence of non‐linear members such as PC curtain walls. The equivalent damping ratio was estimated by approximating the resonance curves using the steady‐state response of the SDOF bilinear hysteretic system. After the eight SHDs were jointed to the building, the system's performance was identified by a response control test for steady‐state vibration. The elements that composed the semi‐active damper system demonstrated the specified performance and the whole system operated well. Copyright © 2000 John Wiley & Sons, Ltd.     

Decentralized ℋ︁∞ controller design for large‐scale civil structures

Complexities inherent to large‐scale modern civil structures pose many challenges in the design of feedback structural control systems for dynamic response mitigation. With the emergence of low‐cost sensors and control devices creating technologies from which large‐scale structural control systems can deploy, a future control system may contain hundreds, or even thousands, of such devices. Key issues in such large‐scale structural control systems include reduced system reliability, increasing communication requirements, and longer latencies in the feedback loop. To effectively address these issues, decentralized control strategies provide promising solutions that allow control systems to operate at high nodal counts. This paper examines the feasibility of designing a decentralized controller that minimizes the ??_∞ norm of the closed‐loop system. ??_∞ control is a natural choice for decentralization because imposition of decentralized architectures is easy to achieve when posing the controller design using linear matrix inequalities. Decentralized control solutions are investigated for both continuous‐time and discrete‐time ??_∞ formulations. Numerical simulation results using a 3‐story and a 20‐story structure illustrate the feasibility of the different decentralized control strategies. The results also demonstrate that when realistic semi‐active control devices are used in combination with the decentralized ??_∞ control solution, better performance can be gained over the passive control cases. It is shown that decentralized control strategies may provide equivalent or better control performance, given that their centralized counterparts could suffer from longer sampling periods due to communication and computation constraints. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part II: Semi‐active mode

A magneto‐rheological (MR) damper is a semi‐active device where the damper force capacity is controlled by varying the input current into the damper. In this paper, the dynamics of MR dampers associated with variable current input is studied. Electromagnetic theory is used to model the dynamics of an MR damper including the eddy current effect and the nonlinear hysteretic behavior of damper material magnetization. A nonlinear differential equation that relates the input current to the damper with a constant equivalent current is proposed. The nonlinear differential equation is combined with the Maxwell Nonlinear Slider (MNS) model to create the variable current MNS model to predict the damper force under variable input current and random damper displacement loading. The model is evaluated by comparing the predicted response of a large‐scale MR damper to the measured damper response from experiments. The experiments include a real‐time hybrid simulation of a 3‐story building structure with a large‐scale MR damper subjected to the design earthquake. The exceptional agreement observed between the predicted and experimental results illustrate the robustness and the accuracy of the variable current MNS model. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance of a damage‐protected beam–column subassembly utilizing external HF2V energy dissipation devices

Ductile‐jointed connections, which generally require some form of supplementary energy dissipation to alleviate displacement response, typically employ mild steel energy dissipation devices. These devices run the risk of low‐cycle fatigue, are effective only for peak cycles that exceed prior displacements, are prone to buckling, and may require replacement following an earthquake. This study presents an experimental investigation employing an alternative to mild steel: a high force‐to‐volume (HF2V) class of damper‐based energy dissipation devices. Tests are performed on a near full‐scale beam–column joint subassembly utilizing externally mounted compact HF2V devices. Two configurations are considered: an exterior joint with two seismic beams and one gravity beam framing into a central column, and a corner joint with only one seismic beam and one gravity beam framing into a column. Quasi‐static tests are performed to column drifts up to 4%. The experiments validate the efficacy of the HF2V device concept, demonstrating good hysteretic energy dissipation, and minimal residual device force, allowing ready re‐centring of the joint. The devices dissipate energy consistently on every cycle without the deterioration observed in the yielding steel bar type of devices. The effectiveness of the HF2V devices on structural hysteretic behavior is noted to be sensitive to the relative stiffness of the anchoring elements, indicating that better efficiency would be obtained in an embedded design. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part I: Passive mode

Magneto‐rheological (MR) dampers are a promising device for seismic hazard mitigation because their damping characteristics can be varied adaptively using an appropriate control law. During the last few decades researchers have investigated the behavior of MR dampers and semi‐active control laws associated with these types of dampers for earthquake hazard mitigation. A majority of this research has involved small‐scale MR dampers. To investigate the dynamic behavior of a large‐scale MR damper, characterization tests were conducted at the Lehigh Network for Earthquake Engineering Simulation equipment site on large‐scale MR dampers. A new MR damper model, called the Maxwell Nonlinear Slider (MNS) model, is developed based on the characterization tests and is reported in this paper. The MNS model can independently describe the pre‐yield and post‐yield behavior of an MR damper, which makes it easy to identify the model parameters. The MNS model utilizes Hershel–Bulkley visco‐plasticity to describe the post‐yield non‐Newtonian fluid behavior, that is, shear thinning and thickening behavior, of the MR fluid that occurs in the dampers. The predicted response of a large‐scale damper from the MNS model along with that from existing Bouc–Wen and hyperbolic tangent models, are compared with measured response from various experiments. The comparisons show that the MNS model achieves better accuracy than the existing models in predicting damper response under cyclic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Study of a semi‐active stiffness damper under various earthquake inputs

Semi‐active stiffness damper (SASD) is one of many semi‐active control systems with the capability to mitigate the dynamic response using only a small amount of external power. The system consists of a hydraulic damper connected to the bracing frame in a selected story unit. In this paper, study of a SASD in two building models of five‐stories under four benchmark earthquake records is reported. The purpose of this study is to evaluate the effectiveness of the control system against structure type and varying earthquake inputs. Various control laws are chosen to work with SASD, such as: resetting control, switching control, linear quadratic regulator (LQR) and modified LQR, and the results are compared with no control and passive control cases. Numerical results show that the use of a SASD is effective in reducing seismic responses. Control effectiveness is dependent on the type of structure and earthquake excitation. Passive control is less effective than other control cases as expected. Resetting control, switching control and LQR generally perform similarly in response reduction. While modified LQR is more efficient and robust compared with other control algorithms. Copyright © 2002 John Wiley & Sons, Ltd.     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

Spectral analysis for a semi‐active–passive net‐zero base‐shear design concept

Passive high force‐to‐volume (HF2V) dampers offer significant displacement reduction and energy dissipation, but cannot customise overall response. Semi‐active resettable devices offer adaptive, custom hysteresis loops that reduce displacement and base shear, but have limited dissipation. This paper presents a new, combined concept to maximise displacement reduction without increasing base shear – a net‐zero base‐shear concept. HF2V devices, up to a maximum of 10% structural weight, are combined with fixed stiffness resettable devices. Spectral analyses are run for the three SAC ground motion suites that iteratively size the HF2V device at each structural period to achieve maximum displacement reductions without increasing median base shear. HF2V velocity dependence and the need to scale HF2V capacity to spectral velocity are examined in terms of their impact on the results of these analyses. The net‐zero approach reduces base shear by up to 50% and displacements by 30–70% over all ground motions, exceeding reductions obtained by either device separately by 30–50% (relative). The net‐zero condition is not reached within the device limits defined, except at relatively long periods (>3.5 s) because of a virtuous circle of reduced displacement from the resettable and HF2V devices outweighing the increased base shear from the HF2V devices alone. These results are independent of HF2V device scaling, design and velocity dependence. The overall net‐zero concept offers a significant advantage in a combination that cannot be achieved by passive or semi‐active solutions alone. Copyright © 2011 John Wiley & Sons, Ltd.     

Centralized semi‐active control of post‐tensioned steel frames

Centralized semi‐active control is a technique for controlling the whole structure using one main computer. Centralized control systems introduce better control for relatively short to medium high structures where the response of any story cannot be separated from the adjacent ones. In this paper, two centralized control approaches are proposed for controlling the seismic response of post‐tensioned (PT) steel frames. The first approach, the stiffness control approach, aims to alter the stiffness of the PT frame so that it avoids large dynamic amplifications due to earthquake excitations. The second approach, deformation regulation control approach, aims at redistributing the demand/strength ratio in order to provide a more uniform distribution of deformations over the height of the structure. The two control approaches were assessed through simulations of the earthquake response of semi‐actively and passively controlled six‐story post‐tensioned steel frames. The results showed that the stiffness control approach is efficient in reducing the frame deformations and internal forces. The deformation regulation control approach was found to be efficient in reducing the frame displacements and generating a more uniform distribution of the inter‐story drifts. These results indicate that centralized semi‐active control can be used to improve the seismic performance of post‐tensioned steel frames. Copyright © 2014 John Wiley & Sons, Ltd.     

Predictive control of seismic structures with semi‐active friction dampers

In this paper a predictive control method especially suitable for the control of semi‐active friction dampers is proposed. By keeping the adjustable slip force of a semi‐active friction damper slightly lower than the critical friction force, the method allows the damper to remain in its slip state throughout an earthquake of arbitrary intensity, so the energy dissipation capacity of the damper can be improved. The proposed method is formulated in a discrete‐time domain and cast in the form of direct output feedback for easy control implementation. The control algorithm is able to produce a continuous and smooth slip force for a friction damper and thus avoid exerting the high‐frequency structural response that usually exists in structures with conventional friction dampers. Using a numerical study, the control performance of a multiple degrees of freedom (DOF) structural system equipped with passive friction dampers and semi‐active dampers controlled by the proposed method are compared. The numerical case shows that by merely using a single semi‐active friction damper and a few sensors, the proposed method is able to achieve better acceleration reduction than the case using multiple passive dampers. Copyright © 2004 John Wiley & Sons, Ltd.     

Semi‐active neuro‐control for base‐isolation system using magnetorheological (MR) dampers

Vibration mitigation using smart, reliable and cost‐effective mechanisms that requires small activation power is the primary objective of this paper. A semi‐active controller‐based neural network for base‐isolation structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (INV‐MR) is constructed to replicate the inverse dynamics of the MR damper. Next, linear quadratic Gaussian (LQG) controller is designed to produce the optimal control force. Thereafter, the LQG controller and the INV‐MR models are linked to control the structure. The coupled LQG and INV‐MR system was used to train a semi‐active neuro‐controller, designated as SA‐NC, which produces the necessary control voltage that actuates the MR damper. To evaluate the proposed method, the SA‐NC is compared to passive lead–rubber bearing isolation systems (LRBs). Results revealed that the SA‐NC was quite effective in seismic response reduction for wide range of motions from moderate to severe seismic events compared to the passive systems. In addition, the semi‐active MR damper enjoys many desirable features, such as its inherent stability, practicality and small power requirements. The effectiveness of the SA‐NC is illustrated and verified using simulated response of a six‐degree‐of‐freedom model of a base‐isolated building excited by several historical earthquake records. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of hysteretic smoothness on inelastic response spectra with constant‐ductility

This paper presents an efficient methodology for computing constant‐ductility inelastic response spectra. The computation of constant‐ductility spectra involves numerical root‐finding algorithms to find the strongest structure providing a desired ductility response. Smooth inelastic structural behavior is modeled using a first‐order nonlinear differential equation and the transient structural response is solved using an implicit algorithm requiring Newton iterations at each time step. For structural models with smooth hysteretic behavior (not piece‐wise linear), a simple root‐finding method involving a combination of hyperbolic fits, linear interpolation, and Newton's method converges upon the highest strength (conservative) solution with a small number of iterations. The effect of the hysteretic smoothness on the occurrence of multiple roots is examined for two near‐fault and two far‐fault earthquake records, and for two measures of ductility and for normalized hysteretic energy. The results indicate how the smoothness of the hysteretic behavior affects ductility demand and constant‐ductility response spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection

A new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an ‘apparent weakening and softening’ of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non‐damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter‐scale highway bridge model. Copyright © 2014 John Wiley & Sons, Ltd.