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This paper proposes a low-cost and efficient piezoelectric tuned mass damper (Piezo-TMD) for structural vibration reduction and energy harvesting. The Piezo-TMD consists of not only a proof mass, piezoelectric materials deforming in the d33 mode, and an electrical resistance, but also a spring and an inductor which enable the mechanical frequency and electrical frequency of the Piezo-TMD to be tuned to the structural resonance frequency. The equations of motion of a structure with the Piezo-TMD are derived, and an optimal design procedure for the Piezo-TMD is proposed to achieve a simultaneous maximum vibration reduction and energy harvesting. The performance of the Piezo-TMD is compared with that of a conventional optimal TMD installed in a footbridge under a pedestrian loading. The simulation results show that the Piezo-TMD performs better than the optimal conventional TMD in terms of vibration reduction while efficiently converting the absorbed mechanical energy to electricity with a high energy harvesting ratio. The innovative development of simultaneously tuning the mechanical and electrical systems leads to a much lower number of PZT stacks (saving 88% of piezoelectric materials in an illustrated case). The parametric study shows that the Piezo-TMD achieves the best performance when the optimal values for the spring stiffness, resistance, inductance, and the number of piezoelectric stacks are adopted from the proposed optimal design. If the selected spring stiffness and inductance are uncertain in a range between 0.94-1.07 times the optimal values, the vibration reduction performance of the Piezo-TMD remains similar, and the energy harvesting performance reduces less than 5%, as compared to the optimal performance. The effect of the number of piezoelectric stacks was also investigated. An insufficient number of piezoelectric stacks reduces the Piezo-TMD performance, and an excessive stack number does not improve the Piezo-TMD performance but increases the Piezo-TMD cost. Finally, the proposed Piezo-TMD employs inductance to significantly reduce the PZT stack number, thereby significantly reducing the cost of Piezo-TMDs.

This study develops the probabilistic seismic response and capacity models for the broad collection of standard pile designs that are routinely incorporated into bridges in California. A re...

Seismic responses of ordinary highway bridges that feature stiff superstructures have been shown to be strongly affected by abutment-backfill interactions. Seismic risk assessment of these bridges at the regional scale faces the added challenge of having to deal with the large uncertainty in backfill properties. In this regard, the study develops probabilistic backfill models to better quantify the uncertainties in modeling the abutment. First, efforts to establish the validity of the numerical method in predicting the pushover response of backfills are described. Advanced plasticity materials are used in finite element models (FEMs) to simulate sandy and clayey soils that yield consistent backfill force-displacement relationships against full-scale test results. Second, a probabilistic analysis framework is constructed to incorporate soil uncertainties that are identified from field investigations. Statistical moments are extracted from the resultant pushover curves to fully define the probabilistic backfill models, which are verified to bear appropriate uncertainty treatment and reasonable height adjustment factors. Further, statistical analysis tools are used to investigate the influences of different backfill models on the bridge demand estimates of two common bridge classes. The study reveals that backfill models will affect the response estimates of different bridge components in both diaphragm and seat-type abutment bridges. However, probabilistic models shall be especially considered on backfills for the bridge components that are expected to have dominant responses in the longitudinal direction. The proposed backfill models appear to outperform previous deterministic models in predicting realistic bridge responses. The models can be employed in the task of regional seismic assessment of various bridge classes.

Skewed bridges are often encountered in the highway bridge system when the geometry cannot accommodate straight (unskewed) bridges. The objective of this study is to investigate the influence of skew angle on the seismic response of bridges using nonlinear time-history analysis and probabilistic seismic assessments. Six types of skewed and straight bridges (including multi-span simply supported, multi-span continuous, and single-span skewed bridges with steel or concrete girders together with non-integral abutments) commonly used in the central and southeastern United States (CSEUS) are considered for establishing three-dimensional numerical bridge models. The six bridge types are further categorized as: (1) non-seismically designed (NSD) bridges, (2) bridges with seismically designed (SD) columns, (3) bridges retrofitted by (i) column jackets, (ii) isolator bearings (IBs) and keeper plates (KPs), (iii) restrainer cables (RCs) and shear keys (SKs), or (iv) seat extenders (SEs) and shear keys (SKs). Probabilistic seismic demand models incorporating geometric and material uncertainty parameters for the bridges under a suite of ground motions are established to develop corresponding sets of fragility curves in terms of vulnerable bridge components. System fragility curves are further developed through a combination of the component fragility curves in the bridges. Comparisons of the fragility curves between the straight and skewed bridges indicate that the larger the skew angle, the more vulnerable the bridges, regardless of NSD bridges, bridges with SD columns, and retrofitted bridges. Formulas that consider effect of skew on the values of fragility parameters in the fragility curves are derived for each bridge class, component type, and limit state. Finally, the retrofit of columns and seismically designed columns can reduce column damage probabilities without significantly increasing demands to the other bridge component types, leading to a lower bridge system risk than that for the NSD bridges. However, although the other three retrofits (IB&KP, RC&SK, and SE&SK) can reduce transverse and/or longitudinal demands on the bearings, the column demands remain a similar or worse damage level than that for the NSD bridges, resulting in a similar or higher risk for the three retrofitted bridge systems.

Experimental testing revealed that installing concealed vertical slits in reinforced concrete (RC) infill walls enabled the RC infill walls to behave in a more ductile manner (as compared t...

The present study aims at proposing an innovative phase control methodology for semi-active tuned mass dampers (SA-TMDs) that intend to minimize the off-tuned problems associated with passive tuned mass dampers (P-TMDs). The phase control algorithm is first developed, the essential of which is to apply the variable friction force to slow down the mass block at specific moments when the phase lag of the SA-TMD with respect to the structure is different from 90°, resulting in the SA-TMD back to the desired phase lag, i.e., −90° phase deviation, so that the SA-TMD has the maximum power flow to reduce the structural vibration. The feasibility of the application of the phase control in SA-TMDs is verified by performing numerical analyses of a simplified Taipei 101 structure model with a SA-TMD subjected to sinusoidal loads and design level wind loads. The numerical simulation results show that the SA-TMD implemented with phase control can enable the mass block to vibrate in a manner with a phase lag close to the −90° when the structure model is under sinusoidal excitations with frequencies different from the structural fundamental mode. The SA-TMD with phase control not only exhibits better performance than the optimal P-TMD in terms of suppressing the structural vibration, but also enhances its robustness, particularly when the SA-TMD is off-tuned to the structure.

This study develops seismic fragility curves for vertical-pile-supported wharves commonly found in the western United States. Nonlinear time-history analyses of a two-dimensional numerical model under two ground motion suites are performed. The results show that the jumbo container cranes increase by 10.8% in the wharf deck drift. By using the experiment-based limit states, the proposed fragility curves demonstrate that, at a PGA of 0.50 g, the probabilities of exceeding slight, moderate, extensive, and complete limit states are approximately 23.0%, 7.0%, 4.0%, and 3.0%, respectively, while at a PGA of 1.00 g, the exceeding probabilities increase to 44.0%, 19.0%, 14.0%, and 11.0%, respectively.

SUMMARY Optimal design for tuned mass dampers (TMDs) with linear or nonlinear viscous damping is formulated in order for design practitioners to directly compute the optimal parameters of a TMD in a damped structure subjected to wind excitations. The optimal TMD tuning frequency ratio and damping coefficient for a viscous TMD system installed in a damped structure under 10 white noise excitations are determined by using the time-domain optimization procedure, which minimizes the structural response. By applying a sequence of curve-fitting schemes to the obtained optimal values, design formulas for optimal TMDs are then derived. These are expressed as a function of the mass ratio and damping power-law exponent of the TMD as well as the damping ratio of the structure. The feasibility of the proposed optimal design formulas is verified in terms of formulary accuracy and of comparisons with existing formulas from previous research works. In addition, one numerical example of the Taipei 101 building with a nonlinear TMD, which is redesigned according to the proposed optimal formulas, is illustrated in effort to describe the use of the formulas in the TMD design procedure and to investigate the effectiveness of the optimal TMD. The results indicate that the proposed optimal design formulas provide a convenient and effective approach for designing a viscous TMD installed in a wind-excited damped structure. Copyright © 2011 John Wiley & Sons, Ltd.

The algorithm of modified predictive control (MPC) is derived with the partial-state concept of direct output feedback (DOF) to reduce the number of sensors for real implementation. The feasibility of using modified predictive control with direct output feedback (MPCwDOF) is verified through numerical and experimental study. According to the MPCwDOF algorithm, the online control forces are simply generated from the actual output measurements that are multiplied by a prescribed constant output feedback gain matrix. An off-line numerical method is introduced to find the feedback gain systematically and efficiently. Numerical examples of two control systems with respect to single-controller and multiple-controller systems are illustrated for validating the feasibility of using the MPCwDOF algorithm and the application of the decentralized control strategy to the MPCwDOF algorithm. An experiment of a large-scale 5-story structural model with an MPCwDOF-controlled active mass damper on the roof is also performed. Results indicate that the controlled structures achieve good performance under environmental excitations. Simple online calculations and a small number of sensors make the proposed control algorithm more favorable to real implementation. Copyright © 2010 John Wiley & Sons, Ltd.

A hybrid seismic device that provides both energy-absorbing and re-centering capabilities to overcome external forces is developed and evaluated. The hybrid device is composed of three main components: (1) a set of re-centering wires fabricated from shape memory alloy (SMA) material, (2) two energy-absorbing struts, and (3) two high-strength steel tubes to guide the movement of the hybrid device. The SMA wires are located within the guiding high-strength steel tubes and designed to be sufficiently long such that their deformation strain is within the 6% target strain limit. A conservative value of 6% strain, instead of 8%, or 10%, is adopted to (1) avoid the SMA stiffening phase that increases strength up to 5 times that of its forward transformation yield forces, resulting in a serious damage to the adjacent structural members, and (2) to retain the full re-centering capability of the SMA wires even when the hybrid device is under large displacement. The energy-absorbing struts are pin-connected outside of the guiding steel tubes and may be fabricated of mild steel or low strength aluminum. To reduce the possibility of buckling in the energy-absorbing struts when subjected to compression, they are designed to be stocky and seismically compact, or buckling restrained. An optimal proportion of the SMA wires and energy-absorbing struts is formulated such that the hybrid device retains re-centering capability, while maximizing energy dissipation. Results obtained through the seismic analysis reveal that the hybrid braced frame system exhibits a similar energy dissipation capacity to the buckling restrained braced system, while also having excellent re-centering capabilities.

Over the past decades moderate/severe earthquakes often caused great damage to bridge decks due to their mutual collision and large residual deck offset due to yielding in the traditional steel restrainers. This issue raises a need of developing a smart expansion joint with a high recentering strength to prevent decks from collision and to restore the original configuration. Buckling restrained shape memory alloy (SMA) can provide a much higher recentering strength than unconfined SMA (approximately 1.2 ∼ 1.5 times), which significantly reduces the amount of SMA and thereby the cost of the smart expansion joint proposed herein. The other important feature is that the proposed recentering mechanism always causes the confined SMA compressive, rather than tensile, when the expansion joint is in either tension or compression. This innovative recentering mechanism eliminates the issue of SMA’s break due to tensile strain limitation (approximately 0.12 strain). To verify the proposed buckling-restrained SMA symmetrical expansion joint, an individual recentering bucking restrained SMA device was quasi-statically tested in a uniaxial MTS 810 testing machine. The observed hysteresis of the device under cyclic loading shows high strength symmetrical tension/compression loops, together with a relative large ductility. The obtained experimental results were used to calibrate a confined SMA model in OpenSees. Finally, a three-span simply supported steel bridge with the proposed buckling restrained SMA expansion joints that have a high recentering tension/compression strength was numerically investigated using incremental dynamic analysis. The results reveal the high recentering ability of the bridge.

Power outage after an earthquake would cause an additional chaos to the existing aftermath, greatly aggravating the situation if the outage lasts for an extended period. This research aims at developing an innovative piezoelectric brace, which provides both passive energy-dissipating and energy-harvesting capabilities—a passive suppression of structural vibrations and conversion of vibration energy into reusable electricity. The piezoelectric brace has compression modules that exert compressive loads on the piezoelectric material regardless if the brace is in compression or in tension. The compression module consists of a piezoelectric stack and rubber pads. The rubber pads are used to limit the maximum strain in the piezoelectric material below the allowable operational strain. The electro-mechanical equations of motion are derived for a 1-story and a 3-story frame model with the piezoelectric braces. To evaluate the structural behavior and the energy harvesting performance, numerical simulations are executed for the two model buildings (in downtown Los Angeles) that are equipped with the piezoelectric braces. The effects of design parameters including the geometry of the piezoelectric stack and rubber pads and the electric resistance in the electro-mechanical conversion circuit on the performance are investigated. The numerical results indicate that the piezoelectric braces passively dissipate energy through inclined oval-shaped hysteretic loops. The harvested energy is up to approximately 40% of the input energy. The structural displacements are significantly reduced, as compared to the original frames without the piezoelectric braces. Finally, a design procedure for a frame with the proposed passive piezoelectric braces is also presented.

This paper presents results from two experimental programs of quasi-static testing and dynamic testing which investigate the re-centering and energy-dissipating behavior of a one-tenth-scale smart hybrid brace. Smart hybrid braces, that tend to prevent a soft-story mechanism, restore the original configuration and can be rapidly rehabilitated, are composed of three main components: (1) a set of superelastic shape memory alloy (SMA) wires anchored in a re-centering mechanism, (2) two struts with energy-absorbing capabilities, and (3) two high-strength steel tubes to guide the movement of the smart hybrid brace. A prototype smart hybrid brace was designed in compliance with the optimal proportion design methodology. The 1/10-scale smart hybrid brace was fabricated according to the similarity rules and then was tested in a uniaxial MTS 810 material testing machine. When the smart hybrid brace without the energy-dissipation struts was conducted under a series of quasi-statically cyclic tests, a double-flag-shaped hysteresis was clearly revealed. Subsequently, the energy-dissipation aluminum struts were added into the hybrid brace and then the same low-frequency cyclic tests was performed until the SMA strain approached the design strain limitation of 6%. The maximum residual displacement, 0.02 in, is smaller than the reverse transformation yield displacement of 0.03 in, meeting the proposed design concept. The hysteretic response in the last cycle exhibits a similar double-flag shape with nearly zero residual displacement, indicating that both the recentering SMA-wire mechanism and brace main body in the smart hybrid brace remain intact. The smart hybrid brace was further tested using dynamic loading with a frequency of 0.25 Hz. The dynamic results reveal a similar hysteresis to that under the quasi-static tests, except for the increased strain hardening. These tests reveal the features of the smart hybrid braces – repeatable SMA wire recentering mechanism and replaceable energy-dissipation components.