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A newly developed passive device that provides negative stiffness has been implemented within a quarter-scale highway bridge model and subjected to seismic loading via shake table testing. Details of the experimental results and their comparison with numerical simulations under a wide range of ground motions are presented. In addition, performance indices were developed to systematically evaluate the relative performance of different isolation system configurations that employ combinations of positive and negative stiffness as well as various levels of damping. Further, the influence of boundary conditions (rigid versus flexible bridge piers) on the effectiveness of employing negative stiffness devices has been evaluated.

In a companion paper, Pasala and Nagarajaiah analytically and experimentally validate the Adaptive Length Pendulum Smart Tuned Mass Damper (ALP-STMD) on a primary structure (2 story steel structure) whose frequencies are time invariant (Pasala and Nagarajaiah 2012). In this paper, the ALP-STMD effectiveness on a primary structure whose frequencies are time varying is studied experimentally. This study experimentally validates the ability of an ALP-STMD to adequately control a structural system in the presence of real time changes in primary stiffness that are detected by a real time observer based system identification. The experiments implement the newly developed Adaptive Length Pendulum Smart Tuned Mass Damper (ALP-STMD) which was first introduced and developed by Nagarajaiah (2009), Nagarajaiah and Pasala (2010) and Nagarajaiah et al. (2010). The ALP-STMD employs a mass pendulum of variable length which can be tuned in real time to the parameters of the system using sensor feedback. The tuning action is made possible by applying a current to a shape memory alloy wire changing the effective length that supports the damper mass assembly in real time. Once a stiffness change in the structural system is detected by an open loop observer, the ALP-STMD is re-tuned to the modified system parameters which successfully reduce the response of the primary system. Significant performance improvement is illustrated for the stiffness modified system, which undergoes the re-tuning adaptation, when compared to the stiffness modified system without adaptive re-tuning.

Due to the shift in paradigm from passive control to adaptive control, smart tuned mass dampers (STMDs) have received considerable attention for vibration control in tall buildings and bridges. STMDs are superior to tuned mass dampers (TMDs) in reducing the response of the primary structure. Unlike TMDs, STMDs are capable of accommodating the changes in primary structure properties, due to damage or deterioration, by tuning in real time based on a local feedback. In this paper, a novel adaptive-length pendulum (ALP) damper is developed and experimentally verified. Length of the pendulum is adjusted in real time using a shape memory alloy (SMA) wire actuator. This can be achieved in two ways i) by changing the amount of current in the SMA wire actuator or ii) by changing the effective length of current carrying SMA wire. Using an instantaneous frequency tracking algorithm, the dominant frequency of the structure can be tracked from a local feedback signal, then the length of pendulum is adjusted to match the dominant frequency. Effectiveness of the proposed ALP-STMD mechanism, combined with the STFT frequency tracking control algorithm, is verified experimentally on a prototype two-storey shear frame. It has been observed through experimental studies that the ALP-STMD absorbs most of the input energy associated in the vicinity of tuned frequency of the pendulum damper. The reduction of storey displacements up to 80 % when subjected to forced excitation (harmonic and chirp-signal) and a faster decay rate during free vibration is observed in the experiments.

Structural weakening and addition of damping is an approach previously proposed for the reduction of seismic forces and drifts in the retrofit of structures. It is also used in the design of new buildings with damping systems. While this approach is efficient, it does not significantly reduce and may even amplify inelastic excursions and permanent deformations of the structural system during a seismic event. This paper describes a negative stiffness device (NSD) that can emulate weakening of the structural system without inelastic excursions and permanent deformations. The NSD simulates yielding by engaging at a prescribed displacement and by applying a force at its installation level that opposes the structural restoring force. The NSD consists of (a) a self-contained highly compressed spring in a double negative stiffness magnification mechanism; and (b) a gap spring assembly (GSA) mechanism which delays the engagement of negative stiffness until the structural system undergoes a prescribed disp...

Yielding can be emulated in a structural system by adding an adaptive negative stiffness device (NSD) and shifting the yielding away from the main structural system, leading to the new idea of apparent weakening that occurs, ensuring structural stability at all displacement amplitudes. This is achieved through an adaptive negative stiffness system (ANSS), a combination of NSD and a viscous damper. By engaging the NSD at an appropriate displacement (apparent yield displacement that is well below the actual yield displacement of the structural system) the composite structure-device assembly behaves like a yielding structure. The combined NSD-structure system presented in this study has a recentering mechanism that avoids permanent deformation in the composite structure-device assembly unless the main structure itself yields. Essentially, a yielding-structure is mimicked with no, or with minimal, permanent deformation or yielding in the main structure. As a result, the main structural system suffers ...

Yielding can be emulated in a structural system by adding an adaptive “negative stiffness device” (NSD) and shifting the “yielding” away from the main structural system-leading to the new idea of “apparent weakening” that occurs ensuring structural stability at all displacement amplitudes. This is achieved through an adaptive negative stiffness system (ANSS), a combination of NSD and a viscous damper. By engaging the NSD at an appropriate displacement (apparent yield displacement that is well below the actual yield displacement of the structural system) the composite structure-device assembly behaves like a yielding structure. The combined NSD-structure system presented in this study has a re-centering mechanism thereby avoids permanent deformation in the composite structure-device assembly unless, the main structure itself yields. Essentially, a yielding-structure is “mimicked” without any, or with minimal permanent deformation or yielding in the main structure. As a result, the main structural system suffers less accelerations, less displacements and less base shear, while the ANSS “absorbs” them. This paper presents comprehensive details on development and study of the ANSS/NSD. Through numerical simulations, the effectiveness and the superior performance of the ANSS/NSD as compared to a structural system with supplemental passive dampers is presented. A companion paper presents the NSD and its mechanics in detail.

The concept of apparent weakening by adding true negative stiffness to a structure has been previously introduced by the authors in order to reduce simultaneous drifts, accelerations, and displacements in a structure without yielding or permanent deformation in the main system. A novel negative stiffness device (NSD) that generates true negative stiffness has been developed, built, and tested and has been previously described by the authors in terms of operation and analytical and numerical modeling. This paper presents results that represent proof-of-concept for weakening with the use of the NSD based on the shake table testing of a 3-story seismically isolated structure, equipped with these devices complemented by viscous dampers. The NSD is shown to have a significant effect on the superstructure response by reducing floor accelerations, story drift, and the base shear and upon the addition of dampers, also results in a reduction in isolator displacements. Moreover, this paper provides validati...

The peak deformation, acceleration, and the base shear experienced by the structures can be reduced by simulating yielding in an elastic system—also referred as apparent weakening. The negative stiffness device (NSD), used in this study, exhibits nonlinear-elastic negative stiffness behavior; by adding NSD to the elastic structure (primary structure), the resulting structure-device assembly behaves like a bilinear-elastic structure. In an elastic structure, the acceleration and base shear experienced by the structure can be reduced by adding the negative stiffness device, and the additional deformations caused from the reduced stiffness can be contained by adding viscous dampers. Previously, the authors have carried out experimental studies to demonstrate the effectiveness of apparent weakening in elastic structures, but little is known about the behavior of these systems when the primary structure itself yields. This paper focuses on the issues that may emanate with the addition of NSD to the sys...

The acceleration and base shear of structures during strong ground motion can be attenuated by achieving bilinear-elastic behavior without any permanent displacement—also referred to as “apparent weakening.” The negative stiffness device (NSD), used in this study, exhibits nonlinear-elastic negative stiffness behavior; by adding NSD to the elastic structure, the resulting structure-device assembly behaves like a bilinear-elastic structure. Peak acceleration and base shear experienced by the structures can be reduced by adding the negative stiffness device, and the additional deformations caused by the reduced stiffness can be contained by adding a viscous damper. This paper presents the experimental study on a three-story fixed-base structure (3SFS), acting as a single-degree-of-freedom (SDOF) system (because of bracing in the top two stories), that demonstrates the concept of apparent weakening in elastic structural systems. Two NSDs and a viscous damper are installed in the first story of 3SFS. ...

In recent years, it has been recognized that Negative Stiffness Devices (NSD) may be suitable for seismic protection of structures. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (i.e., 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 the NSD's rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the adaptive stiffness device. The combination of adaptive 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 bridge model that is subjected to various strong earthquake ground motions. The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. The seismic performance of the bridge model is being investigated as part of the NEES-ADAPT Project which includes shaking table tests of the bridge to validate the results from the numerical simulations.

Weakening and damping of structures has proven to be an effective method for mitigating the structure's response. This approach has drawn further attention after the invention of negative stiffness device (NSD), developed by the authors. Preliminary analytical and experimental studies reported on the NSD have revealed that by adding the NSD to a single story structure the base shear demands and peak acceleration of the main structure are reduced significantly and the inter-story deformations are contained by adding a passive damper. In this paper an analytical study is carried on an inelastic multistoried shear building to demonstrate the effectiveness of placing NSDs and dampers at multiple locations along the height of the building. It has been shown that by placing a NSD in a particular story the superstructure above that story can be isolated. It has also been shown through simulation studies that the NSD will limit the amount of energy transmitted to the superstructure from the ground excitation. Essentially, NSD acts as a vibration isolator. Large base deformations is one major limitation in base-isolating the structural systems but using NSDs this can be overcome as the isolation is achieved over the height of the building and not confined to the base. It has been shown through the simulation studies that by placing NSDs in all the lower story's the acceleration of the superstructure and base shear can be reduced significantly without affecting the drifts. Simulation results of a nine-storied 1:3 scale inelastic shear building subjected to periodic ground motion and Kobe fault normal ground motion

Column forces, displacements and accelerations experienced by the structure during strong ground motions can be reduced by weakening and (or) softening the structure and adding a supplemental damper. Although this approach proved to be promising analytically, the concept of “structural strength reduction” leads to inelastic behavior and large permanent deformations in the main structural system. In this paper a new concept is developed to emulate weakening in a structural system by adding an “adaptive negative stiffness device” (NSD) and shifting the “yielding” away from the main structural system; leading, to the new idea of “apparent weakening” with reduced inelastic excursions in the main structural system. This is achieved through an adaptive negative stiffness system (ANSS), which is a combination of NSD and a damper. Engaging the NSD at an appropriate displacement (simulated yield displacement), that is well below the actual yield displacement of the structural system, will result in a composite structure-device assembly that behaves like a yielding structure. The NSD has a re-centering mechanism thereby avoiding permanent deformation in the composite structuredevice assembly unless, the main structure itself yields. Essentially, a yieldingstructure is “mimicked” without any, or with minimum yielding and permanent deformation in the main structure. In summary, the main structural system undergoes less acceleration, less displacements and less base shear, while the ANSS “absorbs” them. This paper presents the working principle and details on development and study of the ANSS/NSD. Through numerical simulations, the effectiveness and the superior performance of the ANSS/NSD as compared to a structural system with supplemental passive dampers is presented.

This paper addresses tracking-control of hysteretic systems using a gain-scheduled (GS) controller. Hysteretic system with variable stiffness and damping is represented as a quasi linear parameter varying (LPV) system. Designed controller is scheduled on the measured/estimated stiffness and damping in real-time. GS controller is constructed from the parameter dependent Lyapunov matrices, which are obtained as optimal solutions of linear matrix inequalities (LMIs) that ensures the feasibility solution for closed loop system performance. The proposed method is worked on semiactive independently variable stiffness (SAIVS) device. It is shown that the gain-scheduled controller developed for the quasi-LPV system results in excellent tracking performance even in the cases where robust-H∞ controller failed to function.

This paper presents a Linear Parameter Varying (LPV) gain-scheduling controller to control the response of a Semiactive independently variable stiffness (SAIVS) system. Effectiveness of the LPV Gain-scheduling controller is verified analytically. Simulation results shows that the nonlinear, time-varying stiffness properties of the SAIVS device can be tracked, even when the mathematical model of nonlinear system is only piecewise continuously differentiable, by representing the system in LPV form and by choosing the spring angle of SAIVS as the scheduling parameter. LPV controller is scheduled based on the real-time estimate of the spring stiffness of SAIVS. It is further shown that the adapted method is more effective in response reduction compared to a robust controller. Introduction Many electromechanical, structural and material systems at the macro-, mesomicroand nano-scale exhibit nonlinear hysteresis properties. Example of such systems includes gear systems, vibrating systems with umbilicals and smart materials like piezoceramic materials, magnetostrictive materials, electro-active polymers, electro-rheological and magneto-rheological fluids. Nonlinear hysteresis hinders the applicability of traditional control methods on these systems despite having a fairly accurate mathematical model of the plant. Approximation of this nonlinearity can cause a number of undesirable effects including poor performance, steady-state errors, limit cycle behavior and loss of stability. Current control analysis and design methods to address non-smooth nonlinear effects are limited. The most widely used approach is inverse compensation. The idea behind inverse compensation is to use the exact or appropriate inverse models to cancel the effects of the nonlinearity by including these inverse models in the controller dynamics. Many inverse models were developed for this purpose (Galinaitis and Rogers, 1998; Mittal and Menq, 2000; Krejci and Kuhnen, 2001). However, this approach suffers from several limitations. This method can not be used if nonlinearity is sandwiched between two blocks, the nonlinearity cannot be cancelled by adding the inverse model to the controller. The inverse models are difficult to obtain and contain significant uncertainty due to the uncertainty in the modeling.

A negative stiffness device has been tested within a quarter-scale highway bridge model on the seismic shaking table at the University at Buffalo Network for Earthquake Engineering Simulation (NEES) site. Based on the experiments, numerical models have been developed, calibrated, and used to simulate the response of the bridge under a wide range of ground motions. In addition, performance indices have been developed to systematically and quantitatively evaluate the relative performance of different isolation system configurations that employ combinations of positive and negative stiffness as well as various levels of positive damping. Further, the influence of boundary conditions (rigid versus flexible bridge piers) on the effectiveness of employing negative stiffness devices has been evaluated. Finally, concepts for graphical interpretation of the performance indices are presented and used to demonstrate the degree to which employing negative stiffness may be beneficial in improving the seismic response of bridge structures.