Design Of Nonlinear Viscous Dampers Research Articles

Simultaneous layout and size optimization of nonlinear viscous dampers for frame buildings under stochastic seismic excitation

Viscous dampers, as effective energy-dissipation devices, have been widely used for seismic mitigation of building structures. Due to the intrinsic uncertainties of structural parameters and earthquake ground motions, to obtain an optimal performance of structural control, the stochastic design optimization of viscous dampers for buildings is essential. This paper establishes a new dynamic reliability-based optimization framework to address the simultaneous layout and size design of nonlinear viscous dampers in frame buildings, considering the dual randomness of both nonstationary seismic excitations and uncertain structural model parameters. Firstly, a mixed integer optimization problem for nonlinear viscous dampers, including discrete and continuous design variables, is formulated, and the design target is to minimize the cost of the dampers subjected to performance constraints on dynamic reliability of building structures. Then, sequential approximate mixed integer programming with trust region is proposed to solve the optimization problem. Moreover, direct probability integral method is suggested to assess the dynamic reliability and its sensitivity with respect to design variables. Finally, accounting for both stochastic nonstationary seismic excitations and random structural parameters, the optimized results of two numerical examples indicate that the proposed method is a competitive choice for realizing the layout and size optimization of limiting types of nonlinear viscous dampers in frame buildings. To ensure the same target performance of buildings in terms of the probability of exceeding the target value of inter-story drift, the larger peak ground acceleration of stochastic ground motions is, the more cost of dampers is required for seismic protection of buildings.

Multi-objective optimum design of nonlinear viscous dampers in steel structures based on life cycle cost

An algorithm for optimum design of nonlinear viscous dampers with the goal of achieving minimum total cost is presented. An appropriate cost model is developed to determine the initial cost of equipping structures with viscous dampers, and the expected costs of the studied structures related to the possible earthquakes over their life time are estimated using life cycle cost analysis (LCCA). The results of this analysis are used in a multi-objective optimization algorithm with the aim of achieving minimum initial and life cycle cost. To evaluate the seismic behavior of structures, the Endurance Time (ET) method is used as a dynamic response-history analysis method which requires much less computational effort in comparison with conventional time history methods. To this end, the optimum arrangement of nonlinear viscous dampers along with their damping exponent (Alpha) for two weak steel moment frames with 4 and 8 stories are acquired using multi-objective genetic algorithm. Results from the proposed method are compared with two classic methods; uniform and stiffness proportional damping methods. With the aim of proposing an optimal Alpha value, a detailed discussion is provided on its effects on the overall performance of studied structures in terms of life cycle cost.

Stochastic optimal design of nonlinear viscous dampers for large-scale structures subjected to non-stationary seismic excitations based on dimension-reduced explicit method

Nonlinear fluid viscous dampers have been widely used in energy-dissipation structures. This paper is devoted to the stochastic optimal design of viscous dampers for large-scale structures under non-stationary random seismic excitations. The optimization problem is formulated as the minimization of the standard deviation of a target displacement component subjected to the constraint on the standard deviations of damping forces of viscous dampers, and the method of moving asymptotes (MMA), a gradient-based optimization method, is employed to solve the optimization problem involved. An effective dimension-reduced explicit method is first proposed for fast nonlinear time-history analysis of structural responses and the corresponding sensitivity analysis with respect to the parameters of viscous dampers, in which only a small number of degrees of freedom associated with the viscous dampers need to be considered in the iteration scheme, leading to extremely low computational cost in the nonlinear analysis. Then the proposed dimension-reduced explicit method is further used to conduct sample analyses with high efficiency in Monte-Carlo simulation (MCS) so as to obtain the statistical moments of critical responses and the relevant moment sensitivities required in the process of optimal design. To demonstrate the feasibility of the proposed method, the stochastic optimal design of viscous dampers is carried out for a large-scale suspension bridge with a main span of 1688 m, and the mean peak values of critical responses with the optimal parameters of viscous dampers are finally obtained for the design purpose of the bridge.

Effectiveness evaluation and optimal design of nonlinear viscous dampers for inelastic structures under pulse‐type ground motions

SummaryThis paper addresses the effectiveness and optimal design of nonlinear viscous dampers for inelastic structures. First, a nonlinear damping index is derived by using the dimensional analysis to estimate the damping induced by supplemental nonlinear dampers on inelastic single degree of freedom (SDOF) structures. Subsequently, the effects of the added nonlinear damping on the seismic responses of inelastic SDOF systems are analyzed in dimensionless forms when subject to various near‐fault ground motions. The structure‐to‐motion frequency ratio, the motion characteristics, and the structural nonlinearity are the main factors that will affect the damping effectiveness. Especially, it is shown that adding nonlinear viscous dampers will decrease displacement demands yet sometimes lead to amplified acceleration responses. Furthermore, an equivalency procedure is developed to match the inelastic multi‐degree of freedom (MDOF) structure that is equipped with multiple nonlinear viscous dampers to its corresponding SDOF system. Such equivalency justifies that the analysis results for the viscous damping efficiency on SDOF systems can be congruously applied to realistic multi‐story structures. Finally, the optimal designs of nonlinear dampers for MDOF inelastic structures are identified by implementing a hybrid genetic optimization framework along with a robust performance index.

Reliability-based optimal design of nonlinear viscous dampers for the seismic protection of structural systems

Viscous dampers are widely employed for enhancing the seismic performance of structural systems, and their design is often carried out using simplified approaches to account for the uncertainty in the seismic input. This paper introduces a novel and rigorous approach that allows to explicitly consider the variability of the intensity and characteristics of the seismic input in designing the optimal viscous constant and velocity exponent of the dampers based on performance-based criteria. The optimal solution permits controlling the probability of structural failure, while minimizing the damper cost, related to the sum of the damper forces. The solution to the optimization problem is efficiently sought via the constrained optimization by linear approximation (COBYLA) method, while Subset simulation together with auxiliary response method are employed for the performance assessment at each iteration of the optimization process. A 3-storey steel moment-resisting building frame is considered to illustrate the application of the proposed design methodology and to evaluate and compare the performances that can be achieved with different damper nonlinearity levels. Comparisons are also made with the results obtained by applying simplifying approaches, often employed in design practice, as those aiming to minimize the sum of the viscous damping constant and/or considering a single hazard level for the performance assessment.

Optimal design of nonlinear viscous dampers for frame structures

It is well-known that in order to decrease displacements and accelerations in a frame structure during earthquakes, purely viscous dampers can be effectively employed, allowing for a remarkable dissipation of seismic input energy. The design of such devices, however, is still an open issue, since it is often carried out by means of inefficient trial-and-error procedures, or simplified analytical approaches which do not guarantee the optimal exploitation of the dampers. This work investigates the use of an optimisation-based approach for the design of nonlinear purely viscous dampers, aimed at improving the seismic behaviour of frame structures. The potential and the flexibility of the method are shown through an illustrative example displaying how different structural requirements (limitation or minimisation of inter-storey drifts and/or forces transferred by the devices) can be easily taken into account by means of a suitable formulation of a constrained optimisation problem.

Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems

This study is concerned with the analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Analytical algorithms are derived using the Ritz–Galerkin method to evaluate the transmissibility of SDOF displacement vibration isolation and force vibration isolation systems where a nonlinear viscous damper is used as an energy dissipating device. The results reveal that compared to linear dampers, nonlinear viscous dampers can more significantly improve the system vibration isolation performance in a wider frequency range. A procedure is then proposed based on the analysis results to facilitate the design of nonlinear viscous dampers for system vibration isolation purposes. These results have significant implications for the design of vibration isolation systems in many engineering applications.

Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.

Dimensionnement simplifié d'amortisseurs visqueux non linéaires pour ponts en zone sismique

ABSTRACT At the moment, the design of non-linear viscous dampers used to reduce forces and displacements of bridges in seismic areas can only be done through non-linear time history analyses. We suggest here a very simple design tool based on elastic response spectra, given by the code, and a linearisation of the dashpot behaviour. This technique, developed for single degree-of-freedom oscillators is then extended to more complex bridge structures whose behaviour involves more than one mode and to other dynamic actions such as turbulent wind loads.

?Fundamental consideration for the design of non-linear viscous dampers?.Earthquake Engineering and Structural Dynamics 1999;28:1405-1425

Earthquake Engineering & Structural DynamicsVolume 29, Issue 7 p. 1076-1076 ErratumFree Access ‘Fundamental consideration for the design of non-linear viscous dampers’. Earthquake Engineering and Structural Dynamics 1999; 28:1405–1425 First published: 19 June 2000 https://doi.org/10.1002/1096-9845(200007)29:7<1076::AID-EQE962>3.0.CO;2-RAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The original article to which this erratum refers was published in Earthquake Engineering and Structural Dynamics 1999; 28:1405–1425. Volume29, Issue7July 2000Pages 1076-1076 RelatedInformation

Fundamental considerations for the design of non‐linear viscous dampers

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2000; 29(7):1076. Two interrelated issues related to the design of non-linear viscous dampers are considered in this paper: structural velocities and equivalent viscous damping. As the effectiveness of non-linear viscous dampers is highly dependent on operating velocities, it is important to have reliable estimates of the true velocity in the device. This should be based on the actual relative structural velocity and not the commonly misused spectral pseudo-velocity. This is because if spectral pseudo-velocities (PSV) are used, they are based on design displacements (Sv=ω0Sd) and are thus fundamentally different from the actual relative structural velocity. This paper examines the difference between these two velocities, and based on an extensive study of historical earthquake motions proposes empirical relations that permit the designer to transform the well-known spectral pseudo-velocity to an actual relative structural velocity for use in design. Non-linear static analysis procedures recommended in current guidelines for the design of structural systems with supplement damping devices are based on converting rate-dependent device properties into equivalent viscous damping properties based on an equivalent energy consumption approach. Owing to the non-linear velocity dependence of supplemental devices, an alternative approach for converting energy dissipation into equivalent viscous damping is advanced in this paper that is based upon power consumption considerations. The concept of a normalized damper capacity (ϵ) is then introduced and a simple design procedure which incorporates power equivalent linear damping based on actual structural velocities is presented. Copyright © 1999 John Wiley & Sons, Ltd.

Fundamental considerations for the design of non-linear viscous dampers

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2000; 29(7):1076. Two interrelated issues related to the design of non-linear viscous dampers are considered in this paper: structural velocities and equivalent viscous damping. As the effectiveness of non-linear viscous dampers is highly dependent on operating velocities, it is important to have reliable estimates of the true velocity in the device. This should be based on the actual relative structural velocity and not the commonly misused spectral pseudo-velocity. This is because if spectral pseudo-velocities (PSV) are used, they are based on design displacements (Sv=ω0Sd) and are thus fundamentally different from the actual relative structural velocity. This paper examines the difference between these two velocities, and based on an extensive study of historical earthquake motions proposes empirical relations that permit the designer to transform the well-known spectral pseudo-velocity to an actual relative structural velocity for use in design. Non-linear static analysis procedures recommended in current guidelines for the design of structural systems with supplement damping devices are based on converting rate-dependent device properties into equivalent viscous damping properties based on an equivalent energy consumption approach. Owing to the non-linear velocity dependence of supplemental devices, an alternative approach for converting energy dissipation into equivalent viscous damping is advanced in this paper that is based upon power consumption considerations. The concept of a normalized damper capacity (ϵ) is then introduced and a simple design procedure which incorporates power equivalent linear damping based on actual structural velocities is presented. Copyright © 1999 John Wiley & Sons, Ltd.