Distributed Mass Damper System for Integrating Structural and Environmental Controls in Buildings

The writers recently proposed a new type of mass damper system to integrate structural and environmental control systems for buildings. External shading fins are used as mass dampers such that they can (1) control building energy consumption by adjusting the fins and, thus, the amount of sunlight entering the building; and (2) control structural movements by dissipating energy with the dampers during strong motions. Because shading fins are placed along the height of the building, the mass dampers are distributed along the building height instead of concentrated in one or a few locations like traditional tuned mass dampers (TMDs). The distributed mass damper (DMD) system is formulated and simulated for earthquake motions. Optimization is performed on damper parameters (i.e., masses, stiffness, and damping coefficients) of the passive DMD system to minimize structural responses. A near-optimal DMD system outperforms a single TMD system. The movable shading fins are also briefly discussed; they show a substantial savings in building energy consumption.     

Free Vibrations of Taut Cable with Attached Damper. II: Nonlinear Damper

Free vibrations of a taut cable with a nonlinear power-law damper attached near the end are considered. An approximate analytical solution for the amplitude-dependent effective damping ratios in each mode is developed by assuming the same form of solution as for the linear damper and minimizing the mean-square error in the force equilibrium at the damper. An asymptotic approximate solution for small frequency shifts reveals a nondimensional grouping of parameters allowing the development of an amplitude-dependent “universal estimation curve” for the power-law damper. The shape of the universal curve is slightly different for each value of the damper exponent, but for a given exponent the curve is nearly invariant over the same range of parameters as the universal curve for the linear damper. This formulation yields insights into the dependence of nonlinear damper performance on mode number and amplitude of oscillation, suggesting potential advantages that may be offered by a nonlinear damper over a traditional linear damper.     

Dynamic Load Simulator: Actuation Strategies and Applications

The development of a multiple-actuator dynamic load simulator (DLS), for the simulation of correlated dynamic loads on small-scale structural components and substructures, or on bench-scale system assemblage is presented in this paper. Conceptually, the DLS employs actuators to simulate a desired dynamic loading environment due to wind, waves, or earthquakes, which in special cases may serve as a replacement for conventional facilities such as wind tunnels, wave tanks and shaking tables. The actuation strategy of the DLS is based on force-control rather than the customary motion control (displacement/velocity) scheme. The load simulator is ideal for structural components and for systems that can be idealized as lumped mass systems. An actuation strategy for the DLS based on an innovative scheme that utilizes the coupled control system is developed. For implementation of this scheme, the nonlinear control system toolbox in MATLAB is used. In this scheme, the tuning of control parameters in the time domain is carried out by solving a constrained optimization problem. A suite of loading protocols that includes sinusoidal, two-point correlated fluctuations in wind loading, earthquake induced loading and loads characterized by strong non-Gaussian features is simulated by employing the control scheme introduced here. The load simulation examples presented here demonstrate that the loading time histories generated by utilizing the DLS matched the target values with high fidelity.     

Control Structure Interaction of Electromagnetic Mass Damper System for Structural Vibration Control

To investigate the effect of control-structure-interaction (CSI) between the innovative electromagnetic mass damper (EMD) control system and the test structure, three computational models are first developed in this paper. Then, typical driving voltages are applied to the servo-amplifier of the EMD system to excite the structure and to examine the dynamic behavior of the EMD system when it is implemented into the structure. Furthermore, the test results are compared with the predictions based on the proposed parametric models, namely on-line examination. Finally, shaking table tests of structural seismic response control employing the EMD control system are conducted to validate and compare the effectiveness of those parametric models. All the test results have shown that only when the CSI effect (especially the higher-order CSI effect) is fully considered, can the on-line dynamical property of the EMD system be accurately predicted and its control performance fully exerted. This is essential to achieve the highest performance when employing such EMD systems in suppressing structural vibrations.     

Exact Solution for Dynamic Response of Multi-Degree-of-Freedom Bilinear Hysteretic Systems

An exact solution technique for the response of a bilinear hysteretic multi-degree-of-freedom system subjected to arbitrary dynamic loadings is proposed. Each function in the loading vector is represented by a piecewise interpolation polynomial. By using the modal superposition method and the Duhamel integral procedure on each branch of the force-displacement relationship and matching transitional conditions, one can obtain a closed-form solution. When the system is subjected to such piecewise polynomial loadings as an earthquake acceleration, which usually can be represented by a series of straight line segments, an exact result can be obtained. Thus the proposed method can provide much higher accuracy, and requires less computational effort than the traditional step-by-step integration solution technique. The reason for these advantages is discussed and the related formulas are provided.     

Mathematical Model to Generate Asymmetric Pulses due to Human Jumping

A novel mathematical modeling has been proposed to generate synthetic vertical force signal induced by a single person jumping. This model can replicate much of the temporal and spectral features of the real jumping loading more reliably than the existing half-sine models coupled with Fourier series analysis. This includes lack of symmetry of individual jumping pulses and near-periodic nature of consecutive pulses. The model therefore offers way forward as to the development of a new generation of synthetic narrow-band jumping loads. In these, the shape and frequency content of the jumping force can be changed easily on a jump-by-jump basis, which simulates better on what is happening in reality during human jumping. The synthetic jumping loading can be used in assessing vibration serviceability of civil engineering structures for which such dynamic excitation is relevant, such as assembly structures and concert venues.     

Free Vibrations of Taut Cable with Attached Damper. I: Linear Viscous Damper

Free vibrations of a taut cable with an attached linear viscous damper are investigated in detail using an analytical formulation of the complex eigenvalue problem. This problem is of considerable practical interest in the context of stay-cable vibration suppression in bridges. An expression for the eigenvalues is derived that is independent of the damper coefficient, giving the range of attainable modal damping ratios and corresponding oscillation frequencies in every mode for a given damper location without approximation. This formulation reveals the importance of damper-induced frequency shifts in characterizing the response of the system. New regimes of behavior are observed when these frequency shifts are large, as is the case in higher modes and for damper locations further from the end of the cable. For a damper located sufficiently near the antinode in a given mode, a regime of solutions is identified for which the damping approaches critical as the damper coefficient approaches a critical value. A regime diagram is developed to indicate the type of behavior in each mode for any given damper location.     

Vibration of Tensioned Beams with Intermediate Damper. I: Formulation, Influence of Damper Location

Exact analytical solutions are formulated for free vibrations of tensioned beams with an intermediate viscous damper. The dynamic stiffness method is used in the problem formulation, and characteristic equations are obtained for both clamped and pinned supports. The complex eigenfrequencies form loci in the complex plane that originate at the undamped eigenfrequencies and terminate at the eigenfrequencies of the fully locked system, in which the damper acts as an intermediate pin support. The fully locked eigenfrequencies exhibit “curve veering,” in which adjacent eigenfrequencies approach and then veer apart as the damper passes a node of an undamped mode shape. Consideration of the evolution of the eigenfrequency loci with varying damper location reveals three distinct regimes of behavior, which prevail from the taut-string limit to the case of a beam without tension. The second regime corresponds to damper locations near the first antinode of a given undamped mode shape; in this regime, the loci bend backwards to intersect the imaginary axis, and two distinct nonoscillatory decaying solutions emerge when the damper coefficient exceeds a critical value.     

Dynamic Ratcheting in Elastoplastic Single-Degree-of-Freedom Systems

In dynamic analysis, hysteretic damping often provides a reasonable model of the inelastic behavior of a structure. Nonlinearity presented by hysteretic damping, however, introduces the possibility of developing complicated motions not expected in linear dynamics. In this study, motions of a single-degree-of-freedom system with hysteretic damping under dual-frequency sinusoidal excitations are investigated through numerical simulation. Hysteretic damping behavior is represented by three different plasticity models: the elasto-perfectly-plastic model; the linear kinematic hardening model; and the two-surface model. Under certain conditions, the resultant motions from the elasto-perfectly-plastic model and the two-surface model exhibit a continual increment of plastic deformation in successive cycles. Parametric study shows that this dynamic ratcheting develops when applied frequencies are commensurable (i.e., related to each other with integer ratio), and the product of terms comprising the ratio is an even number. In the Poincaré section, motion from commensurable frequencies shows limit cycle behavior, whereas the boundedness of motion for incommensurable frequencies is depicted by having quasi-periodicity. On the other hand, the response of the linear kinematic hardening model is qualitatively different and, in particular, dynamic ratcheting does not develop, irrespective of the frequency commensurability. These findings suggest that model selection may have unanticipated consequences for the analysis and design of structural systems subjected to severe dynamic loadings, such as major earthquakes.     

Vibration of Tensioned Beams with Intermediate Damper. II: Damper near a Support

Analytical solutions are used to investigate the free vibrations of tensioned beams with a viscous damper attached transversely near a support. This problem is of particular relevance for stay-cable vibration suppression, but no restrictions on the level of axial load are introduced, and the results are quite broadly applicable. Characteristic equations for both clamped and pinned supports are rearranged into forms suitable for numerical solution by fixed-point iteration, whereby the complex eigenfrequencies and corresponding damping ratios can be accurately computed within a few iterations. Explicit asymptotic approximations for the complex eigenfrequencies are also obtained, subject to restrictions on the closeness of the eigenfrequencies to their undamped values. These asymptotic approximations are expressed in the same “universal” form identified in previous studies. It is observed that the maximum attainable modal damping ratios and the corresponding optimal values of the damper coefficient can be significantly affected by bending stiffness and by the nature of the support conditions, and a nondimensional parameter grouping is identified that enables an assessment of when bending stiffness should be considered.     

Vibration Serviceability of a Building Floor Structure. I: Dynamic Testing and Computer Modeling

Buildings with large column-free floors or long-cantilevered structures can be susceptible to annoying vibrations due to everyday occupants’ activities such as walking. Computer modeling and analytical representation of building structural properties to predict the floor response subjected to excitations due to human activities are important issues that require further studies. Vibration testing and analysis of built structures can assist in more accurate estimation of structure dynamic properties. This paper presents the results of the modal testing conducted on an office building floor and analysis of the collected vibration measurements. It compares these results with the structural response using computer analyses. It also presents a sensitivity study to assess the importance of various structural parameters on the floor dynamic response. From the results presented, it is concluded that for the structure used in this study the raised flooring and nonstructural elements acted mainly as added mass and did not contribute to the floor damping. Conclusions are also made on the importance of various structural parameters on floor response and the analysis of the modal test results.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

General Realization Algorithm for Modal Identification of Linear Dynamic Systems

The general realization algorithm (GRA) is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. The GRA extends the well known eigensystem realization algorithm (ERA) based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least-squares optimization to get the minimum prediction error for the response. The statistical properties (i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors) of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with nonclassical damping.     

Applications and Issues of GIS as Tool for Civil Engineering Modeling

A tool that has proliferated within civil engineering in recent years is geographic information systems (GIS). The goal of a tool is to supplement ability and knowledge that already exists, not to serve as a replacement for that which is lacking. To secure the benefits and avoid misuse of a burgeoning tool, engineers must understand the limitations, alternatives, and context of the tool. The common benefits of using GIS as a supplement to engineering modeling are summarized. Several brief case studies of GIS modeling applications are taken from popular civil engineering literature to demonstrate the wide use and varied implementation of GIS across the discipline. Drawing from the case studies, limitations regarding traditional GIS data models and the implementation of civil engineering models within current GIS are identified and countered by discussing the direction of the next generation of GIS. The paper concludes by highlighting the potential for the misuse of GIS in the context of engineering modeling and suggests that this potential can be reduced through education and awareness. The goal of this paper is to promote awareness of the issues related to GIS-based modeling and to assist in the formulation of questions regarding the application of current GIS. The technology has experienced much publicity of late, with many engineers being perhaps too excited about the usefulness of current GIS. An undoubtedly beneficial side effect of this, however, is that engineers are becoming more aware of GIS and, hopefully, the associated subtleties. Civil engineers must stay informed of GIS issues and progress, but more importantly, civil engineers must inform the GIS community to direct the technology development optimally.     

Modified Sturm Sequence Property for Damped Systems

This technical note presents a method of checking the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues for nonproportionally damped system. A Schur–Cohn matrix is constructed from the coefficients of the characteristic polynomial for the damped system, and LDLT factorized using some standard numerical algorithms. By observing signs of the diagonal elements of the above diagonal matrix D, we can determine the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues, which is very similar to the well-known Sturm sequence property for undamped systems. To verify the applicability of the proposed method, two numerical examples are considered.     

Nonlinear System Modeling and Velocity Feedback Compensation for Effective Force Testing

Effective force testing (EFT) is a test procedure that can be used to apply real-time earthquake loads to large-scale structural models. The implementation of the EFT method requires velocity feedback compensation for the actuators in order to apply forces accurately to test structures. Nonlinearities in the servosystem have a significant impact on the velocity feedback compensation and test results when large flow demands are present, which can be caused by large structural velocities and/or large forces applied to the test structure. This paper presents a nonlinear servosystem model, upon which a nonlinear compensation scheme is proposed. The model and compensation scheme are experimentally verified. The results indicate that the proposed model accurately describes the servosystem behavior, and with the nonlinear velocity feedback compensation, real-time dynamic testing can be conducted using the EFT method.     

Improvement of Eigensolution Method for Nonproportionally Damped Systems by Step Length

This study presents an efficient eigensolution method for nonproportionally damped systems. The proposed method is obtained by applying the accelerated Newton–Raphson technique and the orthonormal condition of the eigenvectors to the linearized form of the quadratic eigenproblem. In the Newton–Raphson scheme, a step length and a selective scheme are introduced to increase the convergence of the solution. The step length can be evaluated by minimizing the norm of the residual vector using the least-squares method. While the singularity may occur during the factorizing process in other iteration methods such as the inverse iteration method and the subspace iteration method if the shift value is close to an exact eigenvalue, the proposed method guarantees the nonsingularity by the orthonormal condition of eigenvectors, which can be proved analytically. A numerical example is presented to demonstrate the effectiveness of the proposed method.     

Wind Response Control of Building with Variable Stiffness Tuned Mass Damper Using Empirical Mode Decomposition/Hilbert Transform

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.     

Dynamic Modeling of Pressure Reducing Valves

Models are currently available for representing the dynamical behavior of most water network components. Such models are relatively simple, accurate and can be easily solved. However, there is no generally accepted dynamic model of a pressure reducing valve (PRV). The key contributions of this paper are the development of several dynamic models—two phenomenological, one behavioral, and one linear—to represent the behavior of PRVs. The models vary in complexity but perform similarly. Experimental data is used to assess the accuracy of the models. The phenomenological models are derived from physical laws and provide an excellent but complex representation of a PRV. The behavioral model is simpler and sufficient for most practical purposes. The linear model does not take the needle valve setting (which controls the valve’s speed) into account and therefore has limited use.