Publications

The application of Bayesian system identification in the context of a hysteretic negative stiffness system for seismic protection of structures is presented. The negative stiffness system employs the concept of apparent weakening to decrease the effective lateral stiffness of structures subjected to strong earthquakes, resulting in a significant reduction of the base shear and other seismic demands. In this paper, results from large-scale experimental testing performed by Rice University and the University at Buffalo - SUNY are used to estimate the parameters that define the nonlinear models of structures equipped with negative stiffness systems. For this purpose, an unscented Kalman filter for augmented-state nonlinear estimation is employed for structural identification. It is shown that the identified models have the capability to accurately predict the nonlinear hysteretic behavior of the modified structure. The predicted response quantities include lateral drifts and accelerations, base shear, restoring forces, and internal forces in structural members. The identified models provide benchmark parameters that can be used to predict the performance of negative stiffness systems, which is useful for the future design of structures equipped with this type of earthquake protection devices.

High-rise structures and large-span bridges have low vibration frequencies and low intrinsic damping and hence are subjected to multimode vibrations under environmental excitation. Supplementing damping is a viable means to suppress such vibrations. The amount of supplemental damping is nevertheless limited as the damping devices in practice can only be attached to the structure at positions while the displacements or relative displacements in vibrations are small. Introducing negative stiffness, passively by negative stiffness devices (NSDs) or inerters, at the damping device positions is an effective damping enhancement approach. This study focuses on the multimode damping effects of dampers enhanced by NSDs and inerters for flexible structures, with emphasis on the frequency-independence (NSDs)/dependence (inerters) of the introduced negative stiffness. Tall buildings/bridges with outrigger systems incorporating NSDs (NSDOs) and inerters (IDOs) are taken as examples for demonstration of the multimode response mitigation performance. First, the principle of equal modal damping is applied for tuning IDOs to achieve maximal damping for a target mode. Then, an equivalent NSDO is determined to achieve the same level of damping of the target mode. Subsequently, multimode damping ratios for the first several modes are compared for the building respectively with the tuned IDOs and the equivalent NSDOs. The results show that the IDOs when tuned to a particular mode (e.g., the second mode) have almost no effect on the damping of a lower mode (first mode)—as compared to what can be achieved by conventional damped outriggers (CDOs). IDOs tend to lock the relative motion between the outrigger and the perimeter columns in higher structural modes because of their frequency dependence. However, NSDOs achieve comparable damping enhancement for all modes as compared to CDOs because of their frequency independence. It is also found that for a higher mode it might be preferable to use IDOs with small inertance to achieve a target level of damping that requires a large absolute negative stiffness value, although NSDs can be enhanced by adding levers to achieve large negative stiffness values as demonstrated recently by the first author. The findings have also been confirmed by numerical analyses of a typical building under seismic and wind loading. Practical and implementable NSD with rate-independent damping is developed based on the classical Maxwell—Weichert model to help mitigate vibrations in several modes, which is the subject of a future study.

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.

Sliding base-isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near-source pulse-type earthquakes. It is common practice to incorporate supplemental passive non-linear dampers into the isolation system to counter increased bearing displacements. Non-linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi-active controllable non-linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a 'smart' sliding isolation system, used in a 1:20 scaled bridge model, employing semi-active controllable magneto-rheological (MR) dampers is investigated, analytically and experimentally, under several near-fault earthquakes. A non-linear analytical model, which incorporates the non-linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low- and high-damping cases, while maintaining isolation level forces less than the passive high-damping case. Copyright © 2005 John Wiley & Sons, Ltd.

Modal parameter identification has received much attention recently for their usefulness in earthquake engineering, damage detection and structural health monitoring. The identification method based on Matrix Pencil technique is adopted in this paper to identify structural modal parameters, such as natural frequencies, damping ratios and modal shapes using impulse vibration responses. This method can also be applied to dynamic responses induced by stationary and white-noise inputs since the auto- and cross-correlation function of the two outputs has the same form as the impulse response dynamic functions. Matrix Pencil method is very robust to noise contained in the measurement data. It has a lower variance of estimates of the parameters of interest than the Polynomial Method, and is also computationally more efficient. The numerical simulation results show that this technique can identify modal parameters accurately even if the noise level is high.

In recent years, magneto-rheological (MR) dampers have been used to control the response of structures. This paper presents the design and application of an H ∞ fault detection and isolation (FDI) filter and fault tolerant controller (FTC) for truss vibration control systems using MR dampers. A linear matrix inequality formulation is used to design a full order robust H∞ filter to estimate faulty input signals. A fault tolerant H ∞ controller is designed for the combined system of plant and filter, minimizing the control objective selected in the presence of disturbances and faults. A truss structure with an MR damper is used to validate the FDI and FTC controller design through numerical simulations. The residuals obtained from the filter through simulation clearly identify the fault signals. The simulation results of the proposed FTC controller confirm its effectiveness for vibration suppression of the faulty truss system.

A negative stiffness device (NSD) has been proposed as an innovative way for seismic protection of structures. It was shown both numerically and experimentally to improve the performance of inelastic structures when it is appropriately designed for the given application. In order to systematically evaluate the effects of a NSD, dimensional analysis is used in this study to quantify the structural responses as the function of input ground motion characteristics, model parameters of structure and NSD, as well as supplemental damping. To facilitate this, a simplified yet parameterized numerical model is first proposed to mimic the observed responses of the tested prototype NSD. The dimensional analysis is then conducted on a single degree of freedom (SDOF) system equipped with both a NSD and a nonlinear damper. By comparing the dimensionless structural responses for the cases of (1) inelastic structure only, (2) inelastic structure with nonlinear damper, and (3) inelastic structure with both nonlinear damper and NSD when subject to various pulse type motions, the effectiveness of a NSD is investigated thoroughly. Finally, the optimal ranges of NSD model parameters are also identified.

A new control algorithm is developed for reducing the response of smart base isolated buildings with variable friction semiactive control systems in near-fault earthquakes. The central idea of the control algorithm is to design a H∞ controller for the structural system and use this controller to determine the optimum control force in the semiactive device. The H∞ controller is designed using appropriate input and output weighting filters that have been developed for optimal performance in reducing near-fault earthquake responses. A novel semiactive variable friction device is also developed and with the H∞ controller shown to be effective in achieving response reductions in smart base isolated buildings in near-fault earthquakes. The new variable friction device developed consists of four friction elements and four restoring spring elements arranged in a rhombus configuration with each arm consisting of a friction–stiffness pair. The level of friction force can be adjusted by varying the angle of the arms of the device leading to smooth variation of friction force in the device. Experimental results are presented to verify the proposed analytical model of the device. The H∞ algorithm is implemented analytically on a five storey smart base isolated building with linear elastomeric isolation bearings and variable friction system located at the isolation level. The H∞ controller along with the weighting filters leads to the smooth variation of friction force, thus eliminating the disadvantages associated with rapid switching. Several recent near-fault earthquakes are considered in this study. The robustness of the H∞ controller is shown by considering a stiffness uncertainty of ±10%. Copyright © 2006 John Wiley & Sons, Ltd.

As a useful class of techniques for structural health monitoring, vibration-based structural damage detection has been intensively studied in civil engineering community for decades. Structural damage is commonly assumed to be linear stiffness reduction, which cannot represent nonlinear damage from the real world, such as plastic deformation, cracks, and joint looseness. Novelty detection-based and supervised classification-based methods have been used for nonlinear damage detection, but direct physical interpretation of the damage cannot be accessed. To address this limitation, the major scope of this work is to detect and physically characterize linear/nonlinear-type structural damage in a semi-supervised way. The proposed method first uses previously proposed sparse identification to establish a baseline (undamaged) model. Then, damage is considered as a variation of restoring forces in the structural system. It can be further treated as a pseudoforce along with the external disturbance force applied to the structural system. Thus, the damaged system is transformed into an equivalent linear system and nonlinear restoring force. By comparing the corresponding outputs from the prediction of baseline model and newly measured data, a variation of mass-normalized restoring (pseudo) force is identified, which can be used for further damage characterization. An illustrative example and three experimental tests are introduced in this work to verify the effectiveness of the proposed method.