This paper performs a unified analysis of multimode damping effects of negative stiffness and inerter mechanisms when combined with a viscous damper for cable vibration control. They are referred to as negative stiffness dampers (NSDs) and inerter-based vibration absorbers (IVAs), respectively. Multimode control of cable vibrations is of practical importance because wind-rain induced cable vibrations typically have frequencies in the range of 1 Hz to 3 Hz which covers a number of modes of long cables. The NSD and IVAs have been extensively studied for enhancing damping of a particular cable mode while multimode cable vibration control using such devices is still absent in the literature. Therefore, this study begins with a discussion of an ideal NSD for multimode cable vibration control. Dynamic properties of a typical NSD and four typical IVAs with respect to vibration frequency are then examined with reference to the ideal NSD. Subsequently, multimode damping effects of all the devices when attached to a cable respectively are investigated in details using an analytical method. Their performances and tuning conditions are discussed in depth. Analytical results show that theoretically an NSD improves damping for each cable mode equally and hence it can achieve multimode damping enhancement per design requirement. To balance damping effects for multiple cable modes, an upper bound of damping enhancement exists when using an IVA. Particularly, an IVA with an inerter and a viscous damper with intrinsic stiffness in series (so-called tuned inerter damper) has the best performance among the investigated IVAs. The characteristic frequency of this type of IVA needs to be close to the lowest frequency of target cable modes and a relatively large inertance is needed. The analytical results are then exemplified by a case study for damper design of a real cable of 454.1 m long. The analytical findings have further been verified by numerical analyses on multimode responses of the cable with the investigated devices respectively.
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.
This paper presents an on-line learning failure-tolerant neural controller capable of controlling buildings subjected to severe earthquake ground motions. In the proposed scheme the neural controller aids a conventional H∞ controller designed to reduce the response of buildings under earthquake excitations. The conventional H∞ controller is designed to reduce the structural responses for a suite of severe earthquake excitations using specially designed frequency domain weighting filters. The neural controller uses a sequential learning radial basis function neural network architecture called extended minimal resource allocating network. The parameters of the neural network are adapted on-line with no off-line training. The performance of the proposed neural-aided controller is illustrated using simulation studies for a two degree of freedom structure equipped with one actuator on each floor. Results are presented for the cases of no failure and failure of the actuator on each of the two floors under several earthquake excitations. The study indicates that the performance of the proposed neural-aided controller is superior to that of the H∞ controller under no actuator failure conditions. In the presence of actuator failures, the performance of the primary H∞ controller degrades considerably, since actuator failures have not been considered for the design. Under these circumstances, the neural-aided controller is capable of controlling the acceleration and displacement structural responses. In many cases, using the neural-aided controller, the response magnitudes under failure conditions are comparable to the performance of the H∞ controller under no-failure conditions.
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.
Abstract This study applied adaptive negative stiffness devices in the application of braced‐damper systems to propose an adaptive negative stiffness amplifying damper (NSAD), and investigated its effectiveness and robustness for controlling the inelastic seismic responses of yielding structures. The adaptive stiffness behavior of the proposed NSAD perform negative stiffness and damping magnification effect within a certain displacement threshold, thus controlling both structural acceleration and drift at elastic stage; when subjected to strong earthquakes, the proposed NSAD would adaptively develop positive stiffness, which limits the inelastic deformation of yielding structures. A set of nonlinear seismic spectra are established for responses including acceleration, ductility, energy dissipation, and residual deformation. Numerical results validated that the proposed adaptive NSAD is effective for both elastic and inelastic structures. In addition, influences of key parameters like flexible support, negative stiffness ratio, and displacement threshold ratio (ratio of displacement threshold to yielding displacement), are carefully studied. From the point of controlling both acceleration and ductility demands of inelastic structures, the displacement threshold ratio is recommended to have a value close to a unit; typically, a reasonable upper limit of displacement threshold ratio is recommended to be lower than 1.5 to avoid amplifying residual deformation.
This paper presents a new and innovative semi-active variable stiffness tuned mass damper (SAIVS-TMD). The system has the distinct advantage of retuning in real time thus making the system robust to changes in building stiffness and damping, whereas the passive tuned mass damper (TMD) can only be tuned to a fixed frequency. The SAIVS-TMD is based on a novel semi-active variable stiffness control (SAIVS) device. SAIVS system requires nominal power for operation as compared to active tuned mass dampers. The SAIVS-TMD is retuned using a new control algorithm based on instantaneous frequency estimation using Hilbert transform and short-time Fourier transform (STFT). An analytical model of a three-story structure with SAIVS-TMD is developed. Numerical simulations are performed using the analytical model. The system is implemented in a 1:10 scale three-story scale model in real time using a digital signal processing system and controller. Shake table test results of the system with the SAIVS-TMD are presented. It is shown that the SAIVS-TMD is very effective in reducing the response and providing retuning capability when the building stiffness changes, whereas the TMD is mistuned and loses its effectiveness. Analytical modeling and comparisons between analytical and experimental results are also presented.
Predicting the response of elastomeric seismic isolation bearings when subjected to severe ground motions is challenging due to the highly nonlinear behavior associated with the bearings under a combination of large displacements and axial loads. In particular, the horizontal stiffness of the bearings is a function of both horizontal displacement as well as axial load that varies due to overturning moments. Previous analytical models or formulations to model these bearings were mainly developed to estimate critical loads at the stability limit. Only few of these models are capable of estimating the correct nonlinear behavior of bearings observed at horizontal displacements in excess of the bearing width. In this study, a nonlinear analytical model is presented that is capable of modeling the dynamic response of bearings more accurately at all displacement ranges, especially beyond the stability limit and is verified with experimental data from an earlier experimental study. It was observed in the dynamic experiments that the bearings have a far larger capability to sustain horizontal loads at displacements exceeding their stability limit than predicted by earlier models and more importantly the bearings re-centered after these large displacement excursions. This behavior is captured using the analytical model developed in this study.
An online identification of variation of stiffness in structural systems has been presented in this study. The proposed technique is based on wavelet analysis. The time-frequency characteristics of the wavelets have been used in the formulation of online identification. The basis function used is a modified version of the Littlewood—Paley wavelet. The bases generated from this wavelet at different scales have the advantage of non-overlapping frequency bands which has been utilized in the frequency tracking algorithm. Further, an algorithm for detection of variation in modes shapes in time-varying linear multi-degree-of-freedom (MDOF) systems has been developed. Several types of changes in stiffness, such as a sudden jump, a ramp (gradual) change, or a sudden change with subsequent restoration of stiffness have been considered as illustrative eXamples in case of single-degree-of-freedom (SDOF) and MDOF systems. It has been found that the proposed technique for wavelet based online identification is efficient in tracking different types of cases considered and has potential for application in adaptive control.
The effectiveness of a novel semiactive variable stiffness-tuned mass damper (SAIVS-TMD) for the response control of a wind-excited tall benchmark building is investigated in this study. The benchmark building considered is a proposed 76-story concrete office tower in Melbourne, Australia. It is a slender building 306 m tall with a height to width ratio of 7.3; hence, it is wind sensitive. Across wind load data from wind tunnel tests are used in the present study. The objective of this study is to evaluate the new SAIVS-TMD system, that has the distinct advantage of continuously retuning its frequency due to real time control and is robust to changes in building stiffness and damping. In comparison, the passive tuned mass damper (TMD) can only be tuned to a fixed frequency. A time varying analytical model of the tall building with the SAIVS-TMD is developed. The frequency tuning of the SAIVS-TMD is achieved based on empirical mode decomposition and Hilbert transform instantaneous frequency algorithm developed by the writers. It is shown that the SAIVS-TMD can reduce the structural response substantially, when compared to the uncontrolled case, and it can reduce the response further when compared to the case with TMD. Additionally, it is shown the SAIVS-TMD reduces response even when the building stiffness changes by ±15% and is robust; whereas, the TMD loses its effectiveness under such building stiffness variations. It is also shown that SAIVS-TMD can reduce the response similar to an active TMD; however, with an order of magnitude less power consumption.
Nanotubes form clusters and are found in curved bundles in nanotube films and nanocomposites. Separation phenomenon is suspected to occur in these curved bundles. In this study, the deformation of a single-wall carbon nanotube (SWCNT) interacting with curved bundle nanotubes is analyzed. It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes. A new method of modeling geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method (CFEM) formulation, combined with small deformation beam theory, with the inclusion of axial force. Current developed CFEM method overcomes the limitation of linear Finite Element Method (FEM) formulation regarding large rotations and deformations of carbon nanotubes. This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregularities in the electronic transport properties of adsorbed nanotubes in nanocomposites.
Sample controllers for a three-dimensional smart base-isolated building benchmark problem with linear and frictional isolation system are presented in this paper. A Kalman filter is used to estimate the states based on absolute acceleration measurements. Input filters are used to better inform the controller of the spectral content of the earthquake excitations. A reduced order control-oriented model of the benchmark structure with a linear isolation system is developed. A H2/linear quadratic Gaussian controller is presented for the active case; additionally, a clipped optimal controller is presented for the semiactive case. A preliminary 'skyhook' semiactive controller is also presented for the benchmark problem. Magnetorheological fluid dampers are used for control in the semiactive case and ideal actuators are used for control in the active case. The focus of this phase I study is on the linear isolation system only. Computed results for the passive, semiactive, and active cases are presented. Detailed comparisons of benchmark performance indices for base-isolated structures with a nominal linear isolation system, with and without control, for a set of strong near-field earthquakes are presented. The modeling and sample control designs demonstrated in this paper can be used to form the basis for studying a wide variety of active and semiactive control strategies—to be developed by the participants in the benchmark study—for linear base-isolated buildings. Copyright © 2005 John Wiley & Sons, Ltd.
Response of sliding isolated bridges with smart dampers in near fault earthquake ground motions is evaluated in this study. The smart damper used is a magnetorheological (MR) damper. A 1:20 scale single span sliding isolated bridge model with four sliding bearings and a MR damper is studied. New sliding mode controller is developed and implemented in real time. Several near fault ground motions recorded in the Northridge earthquake are used in the testing. Shake table test results of the scaled sliding isolated bridge model with MR damper are presented to demonstrate the effectiveness of the dampers. It is shown that the smart MR dampers can reduce displacements and forces in the piers further than the passive dampers. While these displacement reductions can be achieved by increasing the passive damping further, it can only be done at the expense of greater forces in the piers.
