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Summary Current models describing the behavior for the triple friction pendulum (TFP) bearing are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply as a direct consequence of equilibrium. This paper presents a revised model of behavior of the TFP bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact. To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces. Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior. The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity and temperature can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made. This paper presents (a) the development of the revised TFP bearing model, (b) the analytic solution for the force–displacement relations of two configurations of the TFP bearing, (c) a model that incorporates inertia effects of the TFP bearing components and other effects that are useful in advanced response history analysis, and (d) examples of implementation of the features of the presented model. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Summary The friction pendulum system is a sliding seismic isolator with self-centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity-dependent friction coefficient. The participation of the nonlinear springs is governed by stick-slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force-deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D-BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.

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 ...

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.

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.