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Nonviscous damping models in which the damping forces depend on the history of velocities via convolution integrals over some kernel functions have risen in many different subjects. The aim of this paper is to extend the Newmark method from viscously damped structure systems to nonviscously damped structure systems. The proposed analysis method for nonviscously damped structure systems is derived based on Newmark's assumption of acceleration. The convolution integral term is calculated directly using the trapezoidal rule. The computational procedure of the proposed direct time integration method for nonviscously damped structure systems is given in detail. Finally, the dynamic responses of two nonviscously damped structure systems are computed using the proposed method. The accuracy and efficiency of the proposed method are discussed through comparison with another developed method. [ABSTRACT FROM AUTHOR]

Recent developments of a distributed mass damper (DMD) system integrate structural and environmental control systems for buildings. This system simultaneously improves building safety and sustainability by using external shading fins as mass dampers, controlling the amount of sunlight coming into the building for energy efficiency, and reducing structural movements during strong motions. Unlike traditional mass dampers, which are usually placed at the tops of structures, the shading fin mass dampers (SFMDs) are distributed throughout structures because fins are placed along the entire heights of buildings. A recent paper by the authors shows that the passive DMD system is as effective in response mitigation as a conventional tuned mass damper (TMD). In this paper, active control strategies for mass damper control are analyzed and simulated to show further response reductions. Nonpassive controls are of interest for the SFMD system because actuators are already needed to control the positions of the shading fins to affect sunlight for energy efficiency. Several active control strategies [linear quadratic regulator (LQR)-based] are compared with an optimal passive strategy. A 20-story shear structure with 20 DMDs is used as a testbed for active control. The results illustrate that the active DMD system can outperform conventional active systems (e.g., a fully active system and a single active mass damper system) while using a similar level of control forces. [ABSTRACT FROM AUTHOR]

It has been experimentally identified that a stationary crowd or an individual acts like a mass-spring-damper in structural vibration. However, experiments have shown that only one resonance frequency or damped natural frequency of human-structure systems are observed on structures, such as grandstands or floors with crowds. This paper studies the presence of the two resonance frequencies in a heavily damped, two-degree-of-freedom (TDOF) system in theory and in experiment. The invisibility, or nonpresence, of a resonance frequency is defined by investigating a heavily damped single-degree-of-freedom (SDOF) system subjected to a harmonic load. By using frequency response functions (FRFs) for acceleration, it is demonstrated that the observable presence of the two resonance frequencies of the TDOF system depends on the mass ratio and frequency ratio of the upper SDOF model to the lower SDOF model and the damping ratio of the upper SDOF model. The conditions for the presence of the two resonance frequencies are presented graphically based on a study of over 5,000 cases that covered reasonable ranges for these three parameters. Two sets of human-structure interaction experiments, whose design was based on the conditions for observing the resonance frequencies, demonstrated qualitatively the effect of the mass ratio of the system and damping ratio of the human body on the presence of the resonance frequencies, thus verifying the theoretical results. These limiting conditions are discussed and the observation of only one resonance frequency in experiments on some human-structure systems is explained. [ABSTRACT FROM AUTHOR]

This paper focuses on the benchmark problem application regarding the vibration control of tall buildings under cross wind excitation. The building under consideration is the 76-story, 306-m tall reinforced concrete office tower proposed for the city of Melbourne, Australia. The adopted control scheme consists of an active tuned mass damper (ATMD) where the control action is achieved by a fuzzy logic controller (FLC). The main advantage of the FLC is its inherent robustness and ability to handle any nonlinear behavior of the structure and the fact that its implementation does not require a mathematical model of the structure. This benchmark study is based on specified design constraints for the ATMD to be considered in the design of the proposed control scheme. The performance of the controller has been demonstrated through the uncertainty in stiffness (+15 and -15% variation from initial stiffness) of the building. The results of the simulation show a good performance by the fuzzy controller for all cases tested. Also the results show that the fuzzy controller performance is similar to the linear quadratic Gaussian (LQG) controller, while possessing several advantages over the LQG controller. [ABSTRACT FROM AUTHOR]

A nonlinear finite-element formulation for the static and dynamic behavior of flexible beams was developed by appropriately modifying and extending the three-dimensional (3D) finite-deformation beam model originally developed by Simo. By introducing energy dissipation in a physically consistent way through a linear viscoelastic constitutive equation, the main contribution in this paper lies in the derivation of a tangent stiffness operator that includes the effect of damping. Moreover, a solution to issues concerning the interpolation of total rotation vectors of magnitude greater than is proposed, along with an alternative approach for the update of curvatures based on total rotation vectors, taking advantage of special features of Lie groups and of the notion of right-trivialized derivative. Both two-dimensional (2D) and three-dimensional (3D) numerical examples are presented. In particular, static and dynamic analyses of an electrical conductor commonly used in power substations were performed. Energy balance calculations and the convergence rate of Newton's method illustrate the accuracy of the computed solutions. [ABSTRACT FROM AUTHOR]

After a brief review of the problems entailed by the so-called proportional damping matrices, this paper elaborates on a simple technique to construct damping matrices that guarantee the fraction of damping in each mode to be positive and adequate and accomplishes this without solving for either the modes or the natural frequencies. Although the resulting matrices do not generally satisfy the proportionality condition, this fact is irrelevant for the purposes to which such matrices are put. [ABSTRACT FROM AUTHOR]

Lattice transmission towers are vital components of transmission line systems, which play an important role in the operation of electrical power systems. This paper proposes a new type of tuned mass damper (TMD), the pounding tuned mass damper (PTMD), to upgrade the seismic resistant performance of a transmission tower. In the PTMD, a limiting collar with viscoelastic material laced on the inner rim is installed to restrict the stroke of the TMD and to dissipate energy through collision. The pounding force is modeled based on the Hertz contact law, whereas the pounding stiffness is estimated in a small-scale test. A multimass model of a 55-m tower is established to verify the effectiveness of the PTMD numerically. Harmonic excitation and time-history analysis demonstrate the PTMD's superiority over the traditional TMD. Finally, a parametric study is performed for the optimal design. [ABSTRACT FROM AUTHOR]

The evaluation of loss mechanisms in microscale mechanical resonators is addressed. Among various dissipation causes, thermoelastic loss is considered as a fundamental dissipation mechanism in microbeam resonators packed in a near-vacuum environment. However, the standard thermoelastic analysis is unable to interpret the size effect experimentally evidenced in resonators when the dimensions become very small, below several microns. In this paper we propose an enhanced nonlocal thermoelastic model, based on a thermodynamical formulation, which incorporates internal characteristic material lengths. Analytical results obtained with this nonlocal theory are compared with experimental results reported in the literature. It is shown how nonlocality can better interpret the observed behavior, at least in a certain range of resonators dimensions. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of unidirectional and bidirectional tuned liquid dampers (TLDs) under random excitation. The performance of the tuned liquid dampers is measured in terms of efficiency and robustness. A series of experimental tests are conducted on model scale structure-tuned liquid damper systems to evaluate their performance, which is then compared to that of the well known tuned mass damper. The effective damping is calculated for each test conducted and the efficiency and robustness are subsequently examined. The performance of a mistuned TLD is experimentally investigated to highlight the robustness of these passive dynamic vibration absorbers. A nonlinear numerical model is used to conduct an extensive parametric study on the performance of a tuned liquid damper. This study has resulted in the development of performance charts for a tuned liquid damper. These charts allow the efficiency of a tuned liquid damper to be examined for a number of varying parameters, which include the excitation amplitude, water depth, and building frequency. These charts are particularly useful for the initial design of a tuned liquid damper when the precise frequency of the structure is not known. [ABSTRACT FROM AUTHOR]

This paper summarizes the results from a comprehensive experimental program in an effort to better understand the phenomenon of viscous heating of fluid dampers under small-stroke (wind loading) and large-stroke (earthquake loading) motions. Two dampers, one with 15-kip and one with 250-kip force output at peak design velocity, have been instrumented and tested under various amplitudes and frequencies. Temperature histories at different locations along the damper casing and within the silicon fluid that undergoes the shearing action have been recorded. Experimental data under small-stroke motions of the 250-kip damper showed that a single closed-form expression derived from first principles is capable of predicting the temperature rise at different locations of the damper with fidelity. The recorded data under long-stroke motions suggest a two-parameter law of cooling that allows the estimation of the internal temperature of the silicon oil once the external temperature on the damper casing is known. The presented cooling law is an extension of Newton’s law of cooling. The study concludes that for both dampers, the same values of the model parameters provide a good approximation of the cooling behavior. The study presents a valuable formula that can be used in practice to estimate the internal fluid temperature of the damper given the external shell temperature. [ABSTRACT FROM AUTHOR]

Response of structures to static and dynamic loads may be assessed in terms of energy. The energy evaluation depends on hysteretic models used to describe inelastic behavior of structures and their elements. One of the hysteretic models often employed in structural analysis is the Ramberg–Osgood model. In the paper a physically motivated model, which leads to the Ramberg–Osgood force–displacement relationship under monotonic loading and exhibits Masing type of behavior for unloading/reloading, is described. Based on the model formulas to calculate recoverable elastic strain energy and irrecoverable hysteretic energy for systems/elements under monotonic loading are derived. It is also shown how recoverable elastic strain energy and irrecoverable hysteretic energy can be evaluated at any point of unloading/reloading curves for a system/element of Masing type. The application of the derived formulas is illustrated by evaluating the energy of a single-degree-of-freedom system subjected to impulse and seismic loading. [ABSTRACT FROM AUTHOR]

A regenerative force actuation (RFA) network consists of multiple electromechanical forcing devices distributed throughout a structural system and actuated in such a way as to reduce the response of the structure when it is subjected to an excitation. The associated electronics of the devices are connected together such that they are capable of sharing electrical power with each other. This makes it possible for some devices to extract mechanical energy from the structure while others reinject a portion of that energy back into the structure at other locations. The forcing capability of an RFA network is constrained by the requirement that the total network must always dissipate energy. As such, it differs from fully active control devices in that its operation requires only a small amount of external power. Furthermore, its power-sharing capability gives it a forcing versatility beyond that attainable with semiactive and traditional passive damping systems. In this paper, RFA networks are analyzed in the context of their ability to apply supplemental linear structural damping, taking into account dissipation due to electrical resistances and viscous damping associated with the actuators. It is shown that these systems can be used to produce nonlocal damping (i.e., damping forces between distant degrees of freedom) and asymmetric damping matrices. By comparison, semiactive and passive devices can only impose local damping forces. The more generalized linear damping capabilities of RFA networks are shown to yield significant improvements in linear-quadratic optimal performance in stationary response. Examples are given in which a RFA network is used in various configurations to reduce the stationary response of the three-story shear structure to stochastic base excitation. [ABSTRACT FROM AUTHOR]

Under pulse-type ground motions modal analysis is not quite efficient for estimating the elastic response of multi-degree-of-freedom systems, in particular when the effects of higher modes are significant. This paper first shows that the assumption of nondispersive damped waves for shear beams leads to inconsistent response estimation. Subsequently, a closed form time domain dispersive damped wave solution to the partial differential equation of motion is presented and it is verified with frequency domain solutions. Finally, using the solutions to the differential equation of motion, the response of frame structures with energy dissipating devices is studied. [ABSTRACT FROM AUTHOR]

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. However, only minimal damping can be added if the attachment point is close to the bridge deck. For longer bridge cables, the relative attachment point becomes increasingly smaller, and passive damping may become insufficient. A recent analytical study by the authors demonstrated that “smart” semiactive damping can provide increased supplemental damping. This paper experimentally verifies a smart damping control strategy employing H2/linear quadratic Gaussian (LQG) clipped optimal control using only force and displacement measurements at the damper for an inclined flat-sag cable. A shear mode magnetorheological fluid damper is attached to a 12.65 m inclined flat-sag steel cable to reduce cable vibration. Cable response is seen to be substantially reduced by the smart damper. [ABSTRACT FROM AUTHOR]

In this paper, we study the control effect for a 20-story benchmark building and apply passive and semiactive control devices to the building. First, we take viscous damping walls as a passive control device which consists of two outer plates and one inner plate, facing each other with a small gap filled with viscous fluid. The damping force is related to the interstory velocity, temperature, and the shearing area. Next, we take a variable oil damper as a semiactive control device which can produce the control forces by little electrical power. We propose a damper model in which the damping coefficient changes according to the response of the damper and control forces calculated by the controller based on a linear quadratic Gaussian control theory. It is demonstrated from the results of some simulations that both passive device and semiactive device can effectively reduce the response of the structure in various earthquake motions. [ABSTRACT FROM AUTHOR]

This paper addresses the third-generation benchmark problem on structural control, and focuses on the control of a full-scale, nonlinear, seismically excited, 20-story building. A semiactive design is developed in which magnetorheological (MR) dampers are applied to reduce the structural responses of the benchmark building. Control input determination is based on a clipped-optimal control algorithm which employs absolute acceleration feedback. A phenomenological model of an MR damper, based on a Bouc–Wen element, is employed in the analysis. The semiactive system using the MR damper is compared to the performance of an active system and an ideal semiactive system, which are based on the same nominal controller as is used in the MR damper control algorithm. The results demonstrate that the MR damper is effective, and achieves similar performance to the active and ideal semiactive system, while requiring very little power. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method for identifying the optimal damper distribution to control the seismic response of a 20-story benchmark building. A genetic algorithm with integer representation was used to determine the damper locations. Both H[sub 2]- and H[sub ∞]-norms of the linear system transfer function were utilized as the objective functions. Moreover, frequency weighting was incorporated into the objective functions so that the genetic algorithm emphasized minimization of the response in the second mode of vibration instead of the dominant first mode. The results from numerical simulations of the nonlinear benchmark building show that, depending on the objective function used, the optimal damper locations can vary significantly. However, most of dampers tend to be concentrated in the lowermost and uppermost stories. In general, the damper configurations evaluated herein performed well in terms of reducing the seismic response of the benchmark building in comparison to the uncontrolled building. [ABSTRACT FROM AUTHOR]

A new control algorithm is proposed in this paper to control the responses of a seismically excited, nonlinear 20-story building with piezoelectric friction dampers. The passive friction damping mechanism is used for low-amplitude vibration while the active counterpart takes over for high-amplitude vibration. Both the stick and sliding phases of dampers are taken into account. To effectively mitigate the peak story drift and floor acceleration of the 20-story building, multiple dampers are placed on the 20-story building based on a sequential procedure developed for optimal performance of the dampers. Extensive simulations indicate that the proposed semiactive dampers can effectively reduce the seismic responses of the uncontrolled building with substantially less external power than its associated active dampers, for instance, 67% less under the 1940 El Centro earthquake when the passive friction force is equal to 10% of the damper capacity. [ABSTRACT FROM AUTHOR]

The effect of damping on progressive collapse responses of structures is typically ignored. However, the margin of conservatism resulting from ignoring damping is not well known. Therefore, in this paper, a nonlinear single-degree-of-freedom (SDOF) model is developed with a piecewise linear resistance function, viscous damping, and a loading function consisting of a ramp part and ensuing constant load. The closed-form analytical solutions are derived with Laplace transform techniques and verified with experimental results of steel beam-column assemblies under column-removal scenarios (CRS). The model is then used to investigate the damping effect on the dynamic displacement responses of structures under CRS with different initial conditions, structural resistance types, and levels of applied load. The results indicate that the effect of damping on displacement responses depends not only on the structural resistance but also on the level of applied load. For structural responses involving elastic and plastic hardening resistance, ignoring conventional global damping (e.g., a damping ratio of 3–5%) is reasonably conservative, but it is suggested that for structures with severe plastic softening resistance (e.g., softening stiffness greater than 10% elastic stiffness) and high damping ratio (e.g., more than 10%), the damping should be explicitly considered in the progressive collapse analysis; otherwise, it is too conservative, resulting in unnecessary cost. [ABSTRACT FROM AUTHOR]

This paper presents a simplified coupled thermal-mechanical model for the modelling of viscoelastic dampers with temperatureand frequency-dependent properties subjected to long-term and short-term dynamic loading due to wind and earthquakes. In this numerical model, the self-heating effect caused by molecular-level friction in the viscoelastic (VE) material is captured explicitly using a finite volume thermal diffusion model based only on the physical properties of the steel and VE material. The thermal model is coupled to a single degree of freedom (SDOF) mechanical model, which produces an efficient computational scheme for time-history analyses of VE dampers under both long-term and short-term loading scenarios. The predictions from the proposed model are compared with full-scale experimental results of long-duration wind loading ranging from design level events to extremely rare events, and for shorter but more intense seismic loading scenarios. It is shown that results obtained using this proposed simplified model with idealized geometry predicted well the dynamic response of the damper for all ranges of experimental results thus validating a robust physics based tool for predicting the response of VE dampers. [ABSTRACT FROM AUTHOR]

Dynamic response of mechanical structures is significantly affected by joints. Joints introduce remarkable frictional damping and localized flexibility to the structure; hence, to obtain a more accurate representation of a system's dynamics, it is crucial to take these effects into account. This paper investigates the application of finite-element model updating on characterization of a nonlinear joint interface. A thin layer of virtual elements is used at a joint location to represent the nonlinear behavior of the coupling in the tangential direction. The material properties of the elements are described by a nonlinear constitutive stress-strain equation that defines the nonlinear state of the joint interface. In this study, Richard-Abbot elastic-plastic material was considered, which is capable of characterizing energy dissipation and softening phenomena in a joint at a nonlinear state. Uncertain material parameters are adjusted to minimize the residual between the numerical and experimental nonlinear frequency responses. Minimization was carried out based on iterative sensitivity-based optimization. The procedure was implemented on an assembled structure consisting of two steel threaded pipes coupled to each other by a nut interface. It was demonstrated that the proposed technique significantly reduced the uncertainties in the joint modeling and led to a more reliable description of the assembled structure. [ABSTRACT FROM AUTHOR]

This paper presents a mathematically exact solution of the continuum to the transient response of a vertical single beam buried partly in a nonlinear foundation because of a support displacement. The foundation has a nonlinear property between reaction and displacement similar to elastoplastic foundation and viscous damping of the Voigt type. Winkler's hypothesis can be produced from the relative displacement based on a foundation displacement, which may be imitated by behavior of a one-dimensional shear wave in the medium. The approach, which involves the classical beam theory and the method of eigenfunction expansion, is simple and clear for seeking solutions and solving equations of motion under the boundary and initial conditions. The connection conditions on the mechanics at the interface and the continuity for displacement and its velocity at the changing time are effectively applied to the relationship between the governing equations of motion satisfied in an elastic domain and those satisfied in a plastic domain. [ABSTRACT FROM AUTHOR]

Classical quasi-steady galloping analysis deals exclusively with cases of across-wind vibrations, leaving aside the more general situation where the wind and motion may not be normal. This can arise in many circumstances, such as in the motion of a power transmission cable about its equilibrium configuration that is swayed from the vertical plane as a result of the mean wind or in a tall slender structure in a skewed wind. Furthermore, the generalization to such situations, when this had been made, has only considered special issues. In this paper, the correct equations for the quasi-steady aerodynamic damping coefficients for a rotated system or wind are derived, and the differences from other variants are highlighted. Motion in two orthogonal structural planes is considered, potentially giving coupled translational galloping, for which previous analysis has often been limited or has even arrived at erroneous conclusions. For the two-degree-of-freedom case, the behavior is dependent on the structural as well as the aerodynamic parameters, in particular the orientation of the principal structural axes and the relative natural frequencies in the two planes. For the first time, the differences in the aerodynamic damping and zones of galloping instability are quantified between solutions from the correct perfectly tuned, well detuned, and classical Den Hartog equations (and also an incorrect generalization of the latter) for a variety of typical cross-sectional shapes. It is found that although the Den Hartog summation often gives a reasonable estimate for the actual aerodynamic damping, even in the rotated situation, in some circumstances the differences can be quite large. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical investigation on the energy dissipation in a nearly saturated poroviscoelastic soil column under quasi-static compressional excitations. Different components of the energy dissipation are evaluated and compared. The magnitude of fluid- induced energy dissipation is primarily a function of a normalized excitation frequency . For small values of , a drained soil column is fully relaxed and essentially behaves as a dry column with negligible pore pressure. For such a soil column, fluid-induced energy dissipation is negligible, and the total damping ratio of the column is essentially the same as that of the solid skeleton. For very high values of , a drained soil column is fully loaded and the excitation-generated pore pressure decreases as the fluid becomes more compressible. For such a soil column, the fluid pressure gradient only exists in a thin boundary layer near the drainage boundary, where drainage occurs and fluid induces energy dissipation, whereas the rest of the column is essentially undrained. Significant fluid-induced energy dissipation occurs for moderate values of because of a combination of moderate fluid pressure, pressure gradient, and fluid relative motion throughout the soil column. The effects of the boundary drainage condition, saturation, porosity, and skeleton damping ratio on fluid-induced energy dissipation are discussed. [ABSTRACT FROM AUTHOR]

Vibration reduction in stay cables by means of viscous dampers is of great interest in cable damage prevention and serviceability of structural system supported by such cables. The paper presents a study on the effectiveness, as well as the limits, of rotational viscous dampers and springs inserted at the two ends of a bending-stiff taut cable; influence of rotational stiffness of the springs is also investigated. After a nondimensional expression of the equation of motion has been obtained, as in other cases of nonproportionally damped continuous structures, complex modal analysis is pursued, obtaining complex eigenvalues and eigenfunctions. Comparison with intermediate dampers, widely used in bridge engineering, is performed showing the range of nondimensional parameters for which the proposed approach is of interest. Finally, a numerical technique based on complex mode superposition is presented in order to evaluate time domain responses for transversal distributed excitation. As an example, the procedure is applied to a wind-exposed cable. [ABSTRACT FROM AUTHOR]

Hysteretic damping is often modeled by means of linear viscoelastic approaches such as “nearly constant attenuation” models (e.g. NCQ model). These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. The aim of this paper is to propose a mechanical model involving nonlinear viscoelastic behavior for isotropic materials under dynamic excitations. This model simultaneously takes into account nonlinear elasticity and nonlinear damping. On one hand, the shear modulus is a function of the excitation level; on the other, the description of viscosity is based on a generalized Maxwell body involving nonlinearity. This formulation (X-NCQ) is implemented into a one-dimensional finite-element approach for a dry soil. The validation of the model shows its ability to retrieve low amplitude seismic ground motion. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content). [ABSTRACT FROM AUTHOR]

This paper presents both the centralized and decentralized control strategies by using semiactive control devices (magnetorheological dampers) for building structural control under seismic excitations. The control algorithms used in this study only focus on the linear quadratic Gaussian control theory with acceleration measurements as feedback signals. In the centralized control, the control force is generated directly from the measurement in each degree of freedom, while in the decentralized control, only measurement from local subsystems is used to calculate the control force with respect to the locations of control devices and measurements. Four groups of centralized/decentralized control algorithms are studied: fully centralized control, fully decentralized control, half-centralized control, and partially decentralized control. The ASCE 20-story benchmark building is selected as an example to evaluate the control performance among different control strategies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A model for hysteretic dynamics is proposed in the current paper. Hysteresis is treated as an input–output relation for a dynamic system. The Lagrangian of the dynamic system is constructed on the basis of a nonconvex potential energy and governing equations of the system dynamics are obtained using the Lagrangian equation. Bifurcations will be induced in the nonlinear dynamics due to the nonconvexity of the potential energy. It is shown that when the coefficients are chosen appropriately, the bifurcation diagram will lead to hysteretic behavior. Both the third- and fifth-order nonlinear terms are investigated and it is shown that the fifth-order nonlinearity is able to give a perfect prediction of experimental hysteretic behaviors. Hysteretic damping force of a magneto-rheological fluid damper and polarization hysteresis in piezoelectric materials are modeled successfully using the current model. The parameter identification for the model is also presented. [ABSTRACT FROM AUTHOR]

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. Several studies have investigated optimal passive linear viscous dampers; however, even the optimal passive device can only add a small amount of damping to the cable when attached a reasonable distance from the cable/deck anchorage. This paper investigates the potential for improved damping using semiactive devices. The equations of motion of the cable/damper system are derived using an assumed modes approach and a control-oriented model is developed. The control-oriented model is shown to be more accurate than other models and facilitates low-order control designs. The effectiveness of passive linear viscous dampers is reviewed. The response of a cable with passive, active, and semiactive dampers is studied. The response with a semiactive damper is found to be dramatically reduced compared to the optimal passive linear viscous damper for typical damper configurations, thus demonstrating the potential benefits using a semiactive damper for absorbing cable vibratory energy. [ABSTRACT FROM AUTHOR]

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping. [ABSTRACT FROM AUTHOR]

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings. [ABSTRACT FROM AUTHOR]

This paper presents an overview and problem definition of a benchmark problem for the response control of wind-excited tall buildings. The building considered is a 76-story 306 m concrete office tower proposed for the city of Melbourne, Australia. The building is slender with a height to width ratio of 7.3; hence, it is wind sensitive. Wind tunnel tests for such a 76-story building model have been conducted at the University of Sydney and the results of across-wind data are used in the present benchmark problem. Either active, semiactive, or passive control systems can be installed in the building to reduce the wind response, although only an active control sample problem has been worked out to illustrate the control design. In the case of active control systems, either an active tuned mass damper or an active mass driver can be installed on the top floor. In the case of passive or semiactive systems, such as viscous dampers, viscoelastic dampers, electrorheological, or magnetorheological dampers, etc., control devices can be installed in selected story units. Control constraints and evaluation criteria are presented for the design problem. A simulation program based on the linear quadratic Gaussian technique has been developed and made available for the comparison of the performance of various control strategies. [ABSTRACT FROM AUTHOR]

The dynamic response of a rectangular plate on a viscoelastic foundation under moving loads with varying velocity is investigated. Three types of moving loads, including acceleration, deceleration, and uniform speed are discussed. Analytical solutions of the dynamic deflection of a plate with general boundary conditions subjected to moving loads are presented by means of dealing with the governing equation. In the numerical analysis, a plate with four edges simply supported is selected to study the dynamic response yielded by the moving loads. The deflection distributions in the range of the plate for the accelerated and decelerated load cases are illustrated. The time histories of the deflection response corresponding to different acceleration and deceleration levels are investigated in detail. The effects of the initial speed of the moving load and the damping of the foundation on the response are also discussed. [ABSTRACT FROM AUTHOR]

Models of varying complexities are being used to represent the frequency-dependent dynamic force deformation characteristics of viscoelastic dampers. More sophisticated models with real or complex fractional derivatives can definitely capture the frequency-dependent properties better. However, since these advanced models add complexity in the analysis of structures, the use of two classical models—a Kelvin chain and a Maxwell ladder—consisting of usual dashpots and springs is suggested. In this technical note, we provide explicit steps and necessary formulas to calculate the parameters of these two proposed models to provide desired frequency-dependent characteristics represented by the storage and loss moduli. [ABSTRACT FROM AUTHOR]

Theoretical and laboratory studies were presented for the water column oscillation in a vertical tube partially immersed in a reservoir. Three types of oscillations were studied, with the top of the tube being fully open (free oscillation), the top capped with a hose for ventilation (damped oscillation), and the top fully capped (capped oscillation). Governing equations of the oscillations were established and good estimations of the oscillatory characteristics were obtained. In the experiments, the periods of the free oscillations and the damped oscillations were close, whereas the period of the capped oscillations was shorter, which was due to the effect of the trapped air in the tube above the water column. The damped oscillation had quicker decay than the free oscillation. Due to the finite size of the reservoir used in the experiments, the recorded oscillations were the superposition of the water column movement in the vertical tube and the surface wave of the reservoir. The former dominated the oscillation at the beginning, whereas the latter became dominant in the end. By approximating the two components as sinusoidal waves, the beats in the recorded oscillations were estimated, and the results were in good agreement with the experiments. [ABSTRACT FROM AUTHOR]

Recent research has shown the viability of using nonlinear energy-sink (NES) devices for vibration mitigation in mechanical and structural systems. When attached to a primary structure, these lightweight passive devices can effectively reduce the structural vibration response through their nonlinear stiffness properties. In this research, a two-degree-of-freedom NES device is designed using innovative elastomeric bumpers as the critical components providing nonlinear restoring forces. A number of elastomeric bumper configurations are evaluated experimentally, and the effect of geometric bumper parameters is investigated with a focus on their influence on the stiffness properties of the bumper. A NES device employing different bumpers is then implemented on a 6-story model building and tested using impulse-like base motion. Nonlinear system identification of the NES device shows that nonlinear stiffness properties are achieved using the elastomeric bumpers. Shake-table testing of the building equipped with the NES device demonstrates that the device is capable of dissipating and redistributing the induced vibration energy in a rapid, effective, and robust fashion. [ABSTRACT FROM AUTHOR]

Based on the methods of variable separation and matching eigenfunction expansions for velocity potential, analytical solutions are developed for a water wave radiation problem by a submerged vertical cylinder in finite water depth. They are validated by comparison with results from the higher order boundary element method and convergent examinations on the number of expansion models. Numerical analysis is carried out to investigate the influence submerged depth, cylinder length, and water depth on added mass and radiation damping. When the submerged depth is large, the added mass approaches a stable value, and radiation damping tends to zero. At high frequency range, the heave and pitch of the added mass of the submerged cylinder is about twice that of the floating cylinder. The influence of cylinder length for hydrodynamic coefficients is quite complex and shows the various properties at different frequency ranges. Added mass can be increased with the decrease of water depth, whereas the effect of water depth on radiation damping is quite small. [ABSTRACT FROM AUTHOR]

The focus of this work is on methods for modal identification of civil structures using output data only. An important family of time domain methods uses autoregressive time series models and exploits formulations developed in the field of system control. Another strategy consists of using methods well tested in the identification of structures on the basis of impulse response or free decay and extending them to the analysis of response signals generated by excitations of a more general nature. A third option refers to the Ho-Kalman minimal realization algorithm, which was extended by Akaike and Aoki to stochastic systems. These approaches, or their combinations, include a sizable proportion of the methods actually used in output-only identification of civil structures subjected to natural excitation, and most of them are based on stationarity assumptions. The question that prompted this study was as follows: what degrees of reliability and accuracy can such methods ensure when they are used, as is often the case in actual practice, in nonstationary conditions? An answer to this question was sought numerically by focusing on nonstationary conditions deemed typical of the actions naturally applied to civil structures. [ABSTRACT FROM AUTHOR]

Vibration reduction or damping capability is highly desired for structural stability when hazardous impact loads are applied to a concrete structure. Damping capability of concrete structures depends primarily on the viscoelastic response of concrete material to the magnitudes and frequencies of impact loads, which in turn requires a minimum level of stiffness and damping capacity of concrete. A common industrial byproduct material-silica fume that showed certain antishock potential when mixed with concretes-was modified with silane in this study toward improved capabilities in both stiffness and damping. To evaluate the effectiveness of the modified silica fume (MSF), a series of dynamic flexural tests and numerical analyses were conducted, of which the results are presented. A three-dimensional micromechanical model was developed based on the discrete element method (DEM), which was then employed to study the stiffness and damping behavior of the admixed concrete. A 10% usage of MSF (by weight of cement) was found to significantly enhance the storage and loss moduli and the loss tangent of concrete. The DEM model developed can be used for evaluating and designing energy-absorbing concretes for general military and civil uses. [ABSTRACT FROM AUTHOR]

This note deals with three aspects of nonproportional damping in linear damped vibrating systems in which the stiffness and damping matrices are not restricted to being symmetric and positive definite. First, we give results on approximating a general damping matrix by one that commutes with the stiffness matrix when the stiffness matrix is a general diagonalizable matrix, and the damping and stiffness matrices do not commute. The criterion we use for carrying out this approximation is closeness in Euclidean norm between the actual damping matrix and its approximant. When the eigenvalues of the stiffness matrix are all distinct, the best approximant provides justification for the usual practice in structural analysis of disregarding the off-diagonal terms in the transformed damping matrix. However, when the eigenvalues of the stiffness matrix are not distinct, the best approximant to a general damping matrix turns out to be related to a block diagonal matrix, and the aforementioned approximation cannot be justified on the basis of the criterion used here. In this case, even when the damping and stiffness matrices commute, decoupling of the modes is not guaranteed. We show that for general matrices, even for symmetric ones, the response of the approximate system and the actual system can be widely different, in fact qualitatively so. Examples illustrating our results are provided. Second, we present some results related to the difficulty in handling general, nonproportionally damped systems, in which the damping matrix may be indefinite, by considering a simple example of a two degrees-of-freedom system. Last, we use this example to point out the nonintuitive response behavior of general nonproportionally damped systems when the damping matrix is indefinite. Our results point to the need for great caution in approximating nonproportionally damped systems by damping matrices that commute with the stiffness matrix, especially when considering general damping matrices. Such approximations could lead to qualitatively differing responses between the actual system and its proportionally damped approximation. [ABSTRACT FROM AUTHOR]

Viscoelastic dampers are being used in structures to mitigate dynamic effects. The models of varying complexities from simple maxwell element to differential models with fractional and complex order derivatives have been used to represent their frequency-dependent force deformation characteristics. More complex models are able to capture the frequency dependence of the material properties better, but are difficult to use in analyses. However, the classical models consisting of assemblies of Kelvin and/or Maxwell elements with an adequate number of parameters can be formed to capture the frequency dependence as accurately as the more sophisticated fractional derivative models can do. The main advantage in adopting these classical models is a simpler and smaller system of equations, which can be conveniently analyzed for nonlinear and linear systems. In this study, the two classical mechanical models consisting of Kelvin chains and Maxwell ladder are used. It is shown that these mechanical models are as effective as the fractional derivative model in capturing the effect of the frequency dependence of the material properties in response calculations and are more convenient to use in dynamic response analyses. [ABSTRACT FROM AUTHOR]

The ability to use multiple tuned mass dampers (TMDs) in improving inelastic structural performance to dissipate the earthquake input energy is investigated. Inelastic structural behavior is modeled using the force analogy method, which is the backbone of analytically characterizing the plastic energy dissipation in the structure. Both tuning period and placement of the multiple TMDs are studied to give the best structural performance in terms of plastic energy dissipation. Numerical simulations are performed to study the energy responses of structures with and without TMD installed, and the effectiveness of TMDs in the reduction of energy responses is also studied by using tuned mass spectra. Results show that the installation of TMDs gives the structure additional capability of dissipating a large amount of damping energy and at the same time reducing the amount of plastic energy demand and therefore reducing damage in the structure. More important, TMDs have the ability to draw the plastic energy dissipation at the lower stories and release it to the upper stories. This is particularly beneficial for structures that would otherwise suffer more damage at the lower stories than the upper stories. However, the reduction in plastic energy dissipation is quite sensitive to the earthquake vibration characteristics, and TMDs should not be used for structures with weak upper stories. [ABSTRACT FROM AUTHOR]

This note proposes an improved eigenvalue-counting method based on the argument principle by introducing Rombouts’ algorithm, which is a stable, efficient, and accurate algorithm to calculate the coefficients of the characteristic polynomial of a general square matrix. In addition, this note comprehensively investigates the effectiveness of the proposed method from the viewpoint of the practical consideration by comparing with the modified Sturm sequence property-based counting method which has been recently developed and also known as the well-proven method. In this note, the operation counts in each method are carefully compared and numerically verified. According to analytical and numerical comparison, the argument principle-based counting method is much better than the modified Sturm sequence property-based method from a practical point of view, even if the latter method is much well-established one theoretically. [ABSTRACT FROM AUTHOR]

The dynamic instability of doubly curved panels with a centrally located circular cutout, subjected to nonuniform compressive in-plane harmonic edge loading is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to single (mode) resonances in parametrically excited doubly curved panels with a central circular cutout. The method of multiple scales is used to obtain analytical expressions for the single (mode) and combination resonance instability regions. It is shown that other cases of the combination resonance can be of major importance and yield a significantly enlarged instability region in comparison to the principal instability region. The effects of nonuniform edge loading, centrally located circular cutout, damping, the static, and dynamic load factors on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as single (mode) resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which doubly curved panels cannot become dynamically unstable. A central circular cutout has the destabilizing effect on the dynamic stability behavior of doubly curved panels subjected to nonuniform edge loading. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures. [ABSTRACT FROM AUTHOR]

Dynamic characteristics are analytically investigated for a single degree of freedom structure with a Maxwell element (SSME). Eigenvalues are obtained analytically and approximated by a perturbation method. Then, cases are sorted by a stiffness ratio λ: the ratio of a structural spring to an auxiliary spring. For a small λ, the optimal damping [lowercase_phi_synonym]c provides the maximum damping ratio. For a large λ, the lower and upper critical dampings [lowercase_phi_synonym]a and [lowercase_phi_synonym]b provide duplex eigenvalues. These values are approximated by simple terms. To reduce transient response, λ should be large, and [lowercase_phi_synonym] should be around [lowercase_phi_synonym]c, [lowercase_phi_synonym]a, and [lowercase_phi_synonym]b, which provide the SSME with large damping. For a stationary excitation, the optimal damping [lowercase_phi_synonym]d is introduced to produce the minimum peak deformation. In fact, [lowercase_phi_synonym]d is larger than [lowercase_phi_synonym]c and [lowercase_phi_synonym]b, and provides larger stiffness and a smaller damping ratio. For a seismic excitation, some cases with [lowercase_phi_synonym]d might reduce deformation more than those with [lowercase_phi_synonym]c and [lowercase_phi_synonym]b, but must support larger stress in the Maxwell element. Thus, [lowercase_phi_synonym] should be based on design constraints. [ABSTRACT FROM AUTHOR]

A theoretical study of the steady-state response of a saturated poroelastic soil column during compressional and rotational harmonic vibrations is presented. Hydraulic damping due to Biot flow is evaluated for top-drained and double-drained boundary conditions and for compressional and rotational motions using the theory of a damped single-degree-of-freedom system. For compressional motions, the dynamic response of gravels and sands is highly influenced by the compressibility of the pore fluid. More hydraulic damping occurs as soil hydraulic conductivity increases and as the column boundary conditions change from top drained to double drained. On the other hand, hydraulic damping for rotational motions is significantly less than that for compressional motions and is dependent on a dimensionless hydraulic conductivity parameter Ks. For Ks within the range of 10-3–100, hydraulic damping may have an important contribution to total soil damping, especially at small strain levels. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Analyses and simulations of the coupled surge-and-heave motions of a nonlinear, moored, experimental, submerged structure subjected to random waves are presented here. The random wave excitations examined include periodic waves with additive noise and narrow-band random waves. Characteristic experimental results include noisy subharmonic and superharmonic responses, and transition behaviors among multiple coexisting responses. This investigation applies a systematic, stochastic analysis procedure to further the deterministic study presented in Part I. Good agreement between the analytical predictions and experimental results is shown. Effects of random perturbations in waves on nonlinear response phenomena are examined, especially for the cases of multiple responses coexisting with chaos. It is found that chaotic responses are sensitive and of weak strength compared to other coexisting responses, and the system response trajectories mainly stay in the stronger, periodic attracting domains. Numerical results indicate perturbation-induced response transitions leading to very large-amplitude response beyond the experimental model limitations. [ABSTRACT FROM AUTHOR]