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Passive dampers play a key role in the smart and reliable design of building structures under uncertain earthquake loading. Passive dampers enable structural designers to enhance the potential of their structural design techniques and acquire the powerful methodologies for more reliable structures under unpredictable uncertainties. While there exist many review articles on optimization of passive dampers, this review is aimed at introducing a new perspective that most passive damper algorithms can be classified based on the combination of several component approaches with different objectives. Mixed approaches considering input uncertainties are particularly highlighted. Research focused on comparison among different optimization methods is also investigated. [ABSTRACT FROM AUTHOR]

The editorial discusses Nature-based Solutions (NbS) in the built environment, emphasizing the importance of working with nature to address societal challenges effectively. NbS involve actions to protect, manage, and restore ecosystems while providing benefits for human wellbeing and biodiversity. The article highlights the role of green infrastructure in climate adaptation and the need for a holistic approach that integrates ecological engineering with traditional grey infrastructure. Various studies presented in the editorial explore the application of NbS at different scales, from mesocosms to regional systems, to address challenges such as disaster risk reduction and sustainable urban development. [Extracted from the article]

Basin presence is believed to affect the ground surface response due to earthquakes, particularly in areas around the basin edge. Previous studies showed that 1-D and 2-D wave propagation analyses resulted in significant differences in amplification at the basin edge. However, the link between 1-D and 2-D responses has not been studied for engineering practices. In practical application, seismic studies were commonly performed using 1-D analysis, for example, to develop a city micro-zonation map. Based on practical considerations, it is necessary to estimate the scaling factor for the 1-D analysis by considering the basin presence, particularly for one containing soft soil. There are three stages carried out in this study. The first stage: collecting data on some basin geometries for the 2-D modeling references and then defining selected site class and input motions. The second stage: modeling 1-D and 2-D wave propagation using D-MOD and Fast Lagrangian Analysis of Continua (FLAC), respectively. The third stage: comparing spectral acceleration resulting from the 1-D and 2-D analyses to obtain the scaling factors. This research studied and reported the relationship between PGA values varied as 0.2 g, 0.3 g, 0.4 g, and 0.5 g, basin geometry (e.g., the angle was set to 5°, 10°, 15°, 30°, and 45°, with depth and width variations of 0.0125, 0.025, 0.05, 0.075, 0.1, 0.2, and 0.4, while the basin width was adjusted to 500 m, 1 km, 2 km, and 4 km), and the spectral acceleration in several observation points on the ground surface. Based on this evaluation, a series of scaling factors are proposed. These factors can be used for spectral acceleration from available hazard maps, commonly developed based on 1-D analysis. The application example of this scaling factor is presented in this study, using the Bandung Basin case. [ABSTRACT FROM AUTHOR]

This paper proposes an accurate and efficient reliability evaluation method for robust design optimization using a probabilistic approach. First, the validity of this method is verified using two benchmark functions. This method is then applied to the robust design optimization problem of building‐connecting damper parameters, and the effect of robust design is verified. The variation in the natural period and structural damping ratio of buildings is considered, and the criteria satisfaction rate (CSR) are directly evaluated using the response value calculated by time history response analysis. [ABSTRACT FROM AUTHOR]

An explicit design procedure of cross‐sections of framed tube high‐rise buildings via an inverse problem approach is presented. In the formulation, interstory drift ratios and net deformations of beams are prescribed. The derived expressions clearly express the three‐dimensional effect (tube effect) from the orthogonal frame. The expressions are helpful for the preliminary design because cross‐sections are rationally and rapidly provided for a set of target deformations without trial‐and‐error repetition. In the proposed design method, a 2×2‐bay basic model under a set of static horizontal loads is designed at first. Then, this 2×2‐bay model is transformed into a multi‐bay model. The second moments of cross‐section of the multi‐bay model can be obtained based on the equivalence of the responses of those two models in the case where the elongation of columns is neglected. In addition, assumptions of axial strains of columns are introduced to obtain the equivalent parameters of cross‐sections of the 2×2‐bay model. It is demonstrated through numerical examples that the proposed method has reasonable accuracy. [ABSTRACT FROM AUTHOR]

Summary: A pseudo‐multi impulse (PMI) is proposed as an extension of the ordinary base‐input multi impulse substituting a long‐duration, long‐period ground motion which can often be simulated by a multi‐cycle sine wave (MSW). PMI is treated as a multitude of impulsive lateral forces and hardly excites the higher‐mode responses of elastic multi‐degree‐of‐freedom (MDOF) models because the undamped fundamental participation vector is adopted as the influence coefficient vector. It is shown that the critical time interval of PMI can be obtained without any repetition. This enables a smart derivation of the critical response. The displacement transfer functions are derived for elastic MDOF models, where two kinds of the influence coefficient vectors are adopted: (1) one at every component (conventional one) and (2) the undamped fundamental‐mode participation vector. It is demonstrated that the critical PMI can efficiently and accurately evaluate the maximum responses under MSW and the critical input period of MSW for elastic–plastic MDOF models. Furthermore, PMI is extended to treat the critical case for the second eigenmode. Finally, the critical PMI is applied to high‐rise buildings for the investigation into the input energy and the cumulative plastic deformation ductility demand. [ABSTRACT FROM AUTHOR]

A new model reduction method is presented for moment‐resisting frames with viscous dampers. The proposed method considers (1) the interactive effect of added damping between the horizontal‐vertical directions and (2) the direct effect with regard to the vertical direction different from the conventional static condensation method. When brace‐type dampers are treated, these effects cannot be neglected originally. The proposed method gives a better correspondence of the fundamental eigenmode with that of the non‐reduced moment frame than the static condensation method. In addition, the proposed reduced model can accurately evaluate the maximum interstory drifts of the non‐reduced moment frame. The proposed model reduction method is formulated in the frequency domain. The frequency dependency of the stiffness matrix and the damping matrix of the reduced model is investigated. The influences of the added damping matrix by viscous dampers on the natural circular frequencies, the damping ratios and the participation vectors are also investigated. Finally, it is demonstrated through a numerical example that the displacement‐based optimization of the damper allocation can be accurately and rapidly conducted by using the reduced models throughout the optimization process. [ABSTRACT FROM AUTHOR]

A simple evaluation method of building resilience is proposed, and the resilience of elastic‐plastic high‐rise buildings is evaluated under resonant long‐duration ground motions. The concept of availability is incorporated into the evaluation model of the building resilience, which was proposed in the previous paper. Not only in‐building components but also external factors such as lifelines and redundancy of facility systems are considered in the evaluation model. Based on the evaluation model, the following probabilistic indices are formulated: (1) the expected value of the total recovery time, (2) the expected values of the availability of the structural frame, facilities, and non‐structural components just after an earthquake event, and (3) the maximum likelihood recovery curves (MLRCs) of the structural frame, facilities, and non‐structural components. Numerical examples are presented for evaluating the resilience of elastic‐plastic high‐rise building models under a pseudo‐multi impulse (PMI), which substitutes for resonant long‐duration ground motions. Finally, the influences of the passive viscous dampers, the redundancy of facility systems, and the uncertainty of manpower to repair the components on the building resilience are clarified through the results of numerical examples. [ABSTRACT FROM AUTHOR]

Summary: A new concept of a "lower‐bound transfer function (LBTF)" and a new frequency‐domain optimal damper design method are presented. LBTF expresses an ideal performance for response control in the frequency domain under a constant sum of added damping coefficients (or the total cost of dampers). The effectiveness of the damper design for each mode can be captured visually through plotting the transfer function amplitudes of the model and the LBTF. An efficient generation method of LBTFs is also proposed. The proposed design method provides designs with multimodal adaptability (effective for multimodes). It does not require much computational load to implement the method since the optimization is conducted in the frequency domain, and the first‐order or second‐order sensitivities of the objective function can be derived analytically. The proposed design and the fundamental mode optimal damper placement are compared for shear‐mass systems and moment‐resisting frames through the transfer functions and the incremental dynamic analysis (IDA). It is demonstrated that the proposed designs effectively reduce the floor acceleration responses and the elastic deformation responses. Moreover, it is shown that the proposed designs can effectively reduce the elastic–plastic responses although the optimization is conducted for linear elastic models. [ABSTRACT FROM AUTHOR]

In this study, a model for the evaluation of a building's resilience and recovery time is proposed, and a new method is developed for the optimal viscous damper placement for a targeted resilience. The features of this model are as follows: 1) building components are categorized into systems in view of their functionality, 2) recovery time is regarded as a function of the damage to building components and human resources for repairing the components, 3) the model is applicable to structural design. This design method uses a type of real‐coded genetic algorithm (GA). The effective use of a constraint on the sum of the added damper damping coefficients enables an efficient search for the solution. [ABSTRACT FROM AUTHOR]

A frequency-domain method is developed for evaluating the earthquake input energy to two building structures connected by viscous dampers. It is shown that the earthquake input energies to respective building structures and added viscous connecting dampers can be defined as works done by the boundary forces between the subsystems on their corresponding displacements. Fourier and inverse Fourier transformations enable one to transform the earthquake input energy in time domain to that in frequency domain. The earthquake input energy in frequency domain has an advantage that, while the input energy cannot be decomposed into the term for the structural parameters and that for the parameters of input ground motions in the conventional time-domain approach, it is possible in the proposed frequency-domain approach. It is demonstrated that the proposed energy transfer function is very useful for clearer understanding of dependence of energy consumption ratios in respective buildings and connecting viscous dampers on their properties. It is concluded that the total input energy to the overall system including both buildings and connecting viscous dampers is approximately constant regardless of the quantity and location of connecting viscous dampers. This property leads to an advantageous feature that, if the energy consumption in the connecting viscous dampers increases, the input energies to the buildings can be reduced drastically. DOI: 10.1061/(ASCE)0733-9445(2007)133:5(620) CE Database subject headings: Dynamic response; Structural control; Damping; Earthquake resistant structures; Energy methods; Frequency analysis; Structural design.

The input energy to a soil-structure interaction (SSI) system during earthquake shaking is taken as a structural performance measure and is formulated in the frequency domain. The purpose of this paper is to derive the closed-form expression of the sensitivity of the input energy to the SSI system with respect to uncertain parameters representing soil stiffness and damping. It is demonstrated first that the input energy expression can be of a compact form consisting of the product between the input motion component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the closed-form expressions of the sensitivity of the input energy to the SSI system with respect to uncertain parameters in contrast to the time-domain formulation including inevitable numerical error and instability. This formulation is then extended to a multidegree-of-freedom superstructure model. Numerical examples support the fact that the closed-form expressions enable one to find in a reliable and efficient way the most critical combination of the uncertain parameters that leads to the maximum energy input. DOI: 10.1061/(ASCE)0733-9399(2007)133:4(389) CE Database subject headings: Closed-form solutions; Earthquake resistant structures; Frequency analysis; Sensitivity analysis; Soil-structure interaction; Structural design; Energy methods.

Since earthquake ground motions and their input effects on structures are very uncertain even with the present state of knowledge, it is desirable to develop a 'robust' structural design method taking into account these uncertainties. Approaches based on critical excitation methods have been proven to be promising for such robust structural design. A new critical excitation method is developed here in which the mean earthquake energy input rate is chosen as a measure of criticality. The earthquake energy input rate is closely correlated with the story deformation and this supports the suitability of the energy input rate as a criticality measure in the case where the deformation is crucial in the design. The ground motion is described as a uniformly modulated nonstationary random process. The power [area of power spectral density (PSD) function] and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. The key for finding the new random critical excitation is the interchange of the order of the double maximization procedures with respect to time and to the PSD function. Examples for a specific envelope function of the ground motion are presented for demonstrating the validity of the proposed method. Extension of the proposed method will be discussed for a more general ground motion model, i.e., nonuniformly modulated nonstationary models, and for a more general problem for variable envelope functions and variable frequency contents. DOI: 10.1061/(ASCE)0733-9399(2006)132:9(990) CE Database subject headings: Dynamic response; Excitation; Ground motion; Vibration; Frequency analysis; Earthquakes; Probabilistic methods.

A more reliable and stable method, compared to the previous one developed by the present writers, of stiffness-damping simultaneous identification of shear-type building structures is proposed using stationary random records under limited observation. It is shown that when stationary random horizontal accelerations are recorded at the floors just above and below a specific story in a shear building model, the story stiffness and the damping ratio can be identified uniquely. The viscous damping coefficient and the material damping ratio can also be identified simultaneously in a numerical model structure. It is also shown that unfavorable effects by extraneous noises, including measurement noises, due to wind excitation, building facilities, and the motion of the occupants can be eliminated partially by using the present method. The accuracy of the present identification method is investigated through the actual records under limited observation in a base-isolated building. DOI: 10.1061/(ASCE)0733-9399(2005)131:10(1027) CE Database subject headings: Stiffness; Damping; Noise; Base isolation; Buildings.

A new general critical excitation method is developed for a damped linear elastic single-degree-of-freedom structure. In contrast to previous studies considering amplitude nonstationarity only, no special constraint of input motions is needed on nonstationarity. The input energy to the structure during an earthquake is introduced as a new measure of criticality. It is shown that the formulation of earthquake input energy in the frequency domain is essential for solving the critical excitation problem and deriving a bound on the earthquake input energy for a class of ground motions. It is remarkable that no mathematical programming technique is required in the solution procedure. This enables structural engineers to use the method in their structural design practice without difficulty. The constancy of earthquake input energy for various natural periods and damping ratios is discussed based on an original sophisticated mathematical treatment. Through numerical examinations for four classes of recorded ground motions, the bounds under acceleration and velocity constraints (time integral of the squared base acceleration and time integral of the squared base velocity) are clarified to be meaningful in the short and intermediate/long natural period ranges, respectively. CE Database subject headings: Excitation; Earthquakes; Velocity; Damping.

An input velocity adjustment method of the critical double impulse (DI) is presented for efficient design of viscous dampers for elastic‐plastic moment frames. The input velocity is adjusted so that the input energy to the lowest eigenmode under the critical DI is equal to those under the selected recorded ground motions. This adjustment makes the critical DI work as the active earthquake. The response bounding property of the critical DI is supported by, (1) the multi‐modal property of the critical DI, (2) the usual excitation of the lowest mode response under recorded ground motions, (3) the large proportion of the instantaneous input energy to the total input energy in the critical DI. The proposed method can treat not only pulse‐like near‐fault ground motions but also ground motions of random nature. To validate the proposed method, the input energies and the maximum interstory drifts under the recorded ground motions and the critical DI with the adjusted input velocity are investigated for elastic single‐degree‐of‐freedom (SDOF) models, elastic proportionally damped MDOF models, and elastic‐plastic proportionally damped MDOF models. The optimization method presented in the previous paper is extended so that the critical DI can be treated for the design of viscous dampers for elastic‐plastic moment frames. [ABSTRACT FROM AUTHOR]

Since earthquake ground motions involve various intrinsic and epistemic uncertainties, it is difficult even with the present knowledge to predict forthcoming events at a specific site in a reasonably accurate way. It is therefore desirable to develop a robust structural design method taking into account these uncertainties even partially. Critical excitation or worst-case analysis approaches are making remarkable progress recently and seem to be promising as a candidate to overcome such difficulties. In this paper, the power (area of power spectral density function) and the intensity (magnitude of power spectral density function) are fixed and the critical excitation is found under these restrictions. A design problem for restricted variable design earthquakes is formulated as a minimum-maximum problem which is expected to lead to the maximum global performance design for variable critical excitations. The elastic-plastic response characteristics of the building models designed by the present method are revealed for a broader class of excitations and code-specified design earthquakes. DOI: 10.1061/(ASCE)0733-9445(2002)128:12(1565) CE Database keywords: Earthquake excitation; Stiffness; Sensitivity analysis; Elastoplasticity; Building design.

A critical review of methods for critical excitation (worst-case input) is presented to enhance the robustness of structural design of aerospace, mechanical, and civil engineering structures. These structures are often subjected to disturbances including inherent uncertainties due mainly to their occurrence scarcity and worst-case analysis is expected to play an important role in avoiding difficulties induced by such uncertainties. During the last three decades, various critical excitation methods have been proposed extensively and applied to some structural design problems, mainly for important structures of which the failure or collapse must be absolutely avoided. Comparison of the critical responses with the corresponding structural responses to recorded ground motions, deterministic or stochastic treatment, elastic or elastic-plastic responses, system-dependent critical excitations are major subjects of discussion. DOI: 10.1061/(ASCE)0733-9445(2002)128:5(665) CE Database keywords: Robust design; Excitation; Random vibration; Ground motion; Uncertainty; Structural design.

For a simplified model of a structure-pile-soil system, semiexplicit forms of the responses to random earthquake inputs are derived together with sensitivity expressions of the random responses with respect to a certain model parameter. Originally this model has a non-tridiagonal stiffness and damping matrices with single earthquake input. It is shown for the first time that independent treatment of the free-field ground and multiple imposition of the free-field ground response into the structure-pile system allow for a transformation of the governing equations so that the final form has tridiagonal stiffness and damping matrices. Closed-form expressions of the inverse of the tridiagonal matrix lead to semiexplicit expressions of the random responses and their sensitivities with respect to a certain model parameter.