Response prediction,experimental characterization and P‐spectra design of frames with viscoelastic–plastic dampers

Viscoelastic–plastic (VEP) dampers are hybrid passive damping devices that combine the advantages of viscoelastic and hysteretic damping. This paper first formulates a semi‐analytical procedure for predicting the peak response of nonlinear SDOF systems equipped with VEP dampers, which forms the basis for the generation of Performance Spectra that can then be used for direct performance assessment and optimization of VEP damped structures. This procedure is first verified against extensive nonlinear time‐history analyses based on a Kelvin viscoelastic model of the dampers, and then against a more advanced evolutionary model that is calibrated to characterization tests of VEP damper specimens built from commercially available viscoelastic damping devices, and an adjustable friction device. The results show that the proposed procedure is sufficiently accurate for predicting the response of VEP systems without iterative dynamic analysis for preliminary design purposes. A design method based on the Performance Spectra framework is then proposed for systems equipped with passive VEP dampers and is applied to enhance the seismic response of a six‐storey steel moment frame. The numerical simulation results on the damped structure confirm the use of the Performance Spectra as a convenient and accurate platform for the optimization of VEP systems, particularly during the initial design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response of steel frame structures with added viscoelastic dampers

The feasibility of using viscoelastic (VE) dampers to mitigate earthquake-induced structural response is studied in this paper. The properties of VE dampers are briefly described. A procedure for evaluating the VE damping effect when added to a structure is proposed in which the damping effect of VE dampers is incorporated into modal damping ratios through an energy approach. Computer simulation of the damped response of a multi-storey steel frame structure shows significant reduction in floor displacement levels.     

Simplified design procedure for frame buildings with viscoelastic or elastomeric structural dampers

A simplified design procedure (SDP) for preliminary seismic design of frame buildings with structural dampers is presented. The SDP uses elastic‐static analysis and is applicable to structural dampers made from viscoelastic (VE) or high‐damping elastomeric materials. The behaviour of typical VE materials and high‐damping elastomeric materials is often non‐linear, and the SDP idealizes these materials as linear VE materials. With this idealization, structures with VE or high‐damping elastomeric dampers can be designed and analysed using methods based on linear VE theory. As an example, a retrofit design for a typical non‐ductile reinforced concrete (RC) frame building using high‐damping elastomeric dampers is developed using the SDP. To validate the SDP, results from non‐linear dynamic time history analyses (NDTHA) are presented. Results from NDTHA demonstrate that the SDP estimates the seismic response with sufficient accuracy for design. It is shown that a non‐ductile RC frame building can be retrofit with high‐damping elastomeric dampers to remain essentially elastic under the design basis earthquake (DBE). Copyright © 2005 John Wiley & Sons, Ltd.     

Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

Simplified seismic design approach for steel portal frame piers with hysteretic dampers

A simplified seismic design procedure for steel portal frame piers installed with hysteretic dampers is proposed, which falls into the scope of performance‐based design philosophy. The fundamental goal of this approach is to design a suite of hysteretic damping devices for existing and new bridge piers, which will assure a pre‐defined target performance against future severe earthquakes. The proposed procedure is applicable to multi‐degree‐of‐freedom systems, utilizing an equivalent single‐degree‐of‐freedom methodology with nonlinear response spectra (referred to as strength‐demanded spectra) and a set of formulae of close‐form expressions for the distribution of strength and stiffness produced in the structure by the designed hysteretic damping devices. As an illustrative example, the proposed procedure is applied to a design of a simple steel bridge pier of portal frame type with buckling‐restrained braces (one of several types of hysteretic dampers). For the steel portal frame piers, an attempt is made to utilize not only the displacement‐based index but also the strain‐based index as pre‐determined target performance at the beginning of design. To validate this procedure, dynamic inelastic time‐history analyses are performed using the general‐purpose finite element program ABAQUS. The results confirm that the proposed simplified design procedure attains the expected performance level as specified by both displacement‐based and strain‐based indices with sufficient accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Damper placement optimization in a shear building model with discrete design variables: a mixed‐integer second‐order cone programming approach

Supplemental damping is known as an efficient and practical means to improve seismic response of building structures. Presented in this paper is a mixed‐integer programming approach to find the optimal placement of supplemental dampers in a given shear building model. The damping coefficients of dampers are treated as discrete design variables. It is shown that a minimization problem of the sum of the transfer function amplitudes of the interstory drifts can be formulated as a mixed‐integer second‐order cone programming problem. The global optimal solution of the optimization problem is then found by using a solver based on a branch‐and‐cut algorithm. Two numerical examples in literature are solved with discrete design variables. In one of these examples, the proposed method finds a better solution than an existing method in literature developed for the continuous optimal damper placement problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic design and evaluation of steel moment‐resisting frames with compressed elastomer dampers

This paper evaluates the hysteretic behavior of an innovative compressed elastomer structural damper and its applicability to seismic‐resistant design of steel moment‐resisting frames (MRFs). The damper is constructed by precompressing a high‐damping elastomeric material into steel tubes. This innovative construction results in viscous‐like damping under small strains and friction‐like damping under large strains. A rate‐dependent hysteretic model for the compressed elastomer damper, formed from a parallel combination of a modified Bouc–Wen model and a non‐linear dashpot is presented. The model is calibrated using test data obtained under sinusoidal loading at different amplitudes and frequencies. This model is incorporated in the OpenSees [17] computer program for use in seismic response analyses of steel MRF buildings with compressed elastomer dampers. A simplified design procedure was used to design seven different systems of steel MRFs combined with compressed elastomer dampers in which the properties of the MRFs and dampers were varied. The combined systems are designed to achieve performance, which is similar to or better than the performance of conventional steel MRFs designed according to current seismic codes. Based on the results of nonlinear seismic response analyses, under both the design basis earthquake and the maximum considered earthquake, target properties for a new generation of compressed elastomer dampers are defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

On tuned mass dampers for reducing the seismic response of structures

This paper presents an energy‐based theoretical model for a two degree‐of‐freedom mechanical system. After a general formulation in Appendix A, the model is specialized to study tuned mass dampers as a means to substantially increase modal damping in order to induce a consequential decrease of the seismic response of the structures thus provided. Although approximate since it neglects coupling due to damping, it is shown that the model yields a first‐order approximation to the exact frequencies, providing values of optimum damping that closely match exact results proposed by others. In view of this, it is proposed that the model be applied through an iterative numerical procedure that identifies the pertinent optimum parameters. It is also shown that for certain particular benchmark cases the model provides closed‐form equations for the parameters defining the dynamic states related to these special conditions. Despite its approximate nature the model presented in this paper is rational, and due to its explicit consideration of energy balance and overall simplicity, it provides a convenient platform for the study of tuned mass dampers, as well as for other methods of structural passive control. Copyright © 2005 John Wiley & Sons, Ltd.     

Design of dampers for structures based on optimal control theory

The aim of this paper was to propose a design guideline for using visco‐elastic dampers for the control of building structures subjected to earthquake loading as well as suspension roof structures subjected to wind loading. The active control algorithm was used to calculate the control forces. Based on the single‐mode approach the control forces were transformed to the forces which visco‐elastic dampers can provide. Application of the method to the design of the building structure with passive damping devices in the bracing system and to the suspension roof with dampers was studied. Through the application of optimal control theory a systematic design procedure to implement dampers in structures is proposed. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal placement of dampers for passive response control

The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake‐induced ground excitations. Frequency‐dependent and ‐independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of friction damped structures using lateral force procedure

A trilinear model is used to simulate the seismic resisting mechanism of a single‐degree‐of‐freedom friction‐damped system to reflect the situation in which both dampers and frame members lose their elastic resistance. The seismic response of the friction‐damped system is normalized with respect to the response of its corresponding linear system by an approach that incorporates a credible equivalent linearization method, a damping reduction rule and the algebraic specification of the design spectrum. The resulting closed‐form solutions obtained for the normalized response are then used to define a force modification factor for friction‐damped systems. This force modification factor, together with the condensation procedure for multi‐degree‐of‐freedom structures, enables the establishment of a quasi‐static design procedure for friction‐damped structures, which is intended for the benefit and use of structural practitioners. A curve‐fitting technique is employed to develop an explicit expression for the force modification factor used with the proposed design procedure; it is shown that this simplification results in satisfactory accuracy. Finally, a design example is given to illustrate the validation of the proposed design procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

Real‐time hybrid testing of a smart base isolation system

Real‐time hybrid testing is a very effective technique for evaluating the dynamic responses of rate‐dependent structural systems subjected to earthquake excitation. A smart base isolation system has been proposed by others using conventional low‐damping isolators and controllable damping devices such as magnetorheological (MR) dampers to achieve specified control target performance. In this paper, real‐time hybrid tests of a smart base isolation system are conducted. The simulation is for a base‐isolated two‐degrees‐of‐freedom building model where the superstructure and the low‐damping base isolator are numerically simulated, and the MR damper is physically tested. The target displacement obtained from the step‐by‐step integration of the numerical substructure is imposed on the MR damper, which is driven by three different control algorithms in real‐time. To compensate the actuator delay and improve the accuracy of the test, an adaptive phase‐lead compensator is implemented. The accuracy of each test is investigated by using the root mean square error and the tracking indicator. Experimental results demonstrate that the hybrid testing procedure using the proposed actuator compensation techniques is effective for investigating the control performance of the MR damper in a smart base isolation system. Copyright © 2013 John Wiley & Sons, Ltd.     

A seismic retrofit method by connecting viscous dampers for microelectronics factories

The implementation of viscous dampers to microelectronics factories has been previously proved not to affect the micro‐vibration of the factories in operation so that the vibration‐sensitive manufacturing process will not be interfered. Therefore, a seismic retrofit strategy which employs the viscous dampers installed in between the exterior and interior structures of the ‘fab’ structure is proposed in the study. The design formulas corresponding to the proposed retrofit method are derived using the non‐proportional damping theory. Based on the study, it is found that the added damping ratio to the fab structure depends greatly on the frequency ratio of the two structures in addition to the damping coefficients of the added dampers. Outside the bandwidth of the frequency ratio in which the added damping ratio is very sensitive to the variation of the frequency ratio, the added damping ratio can be well captured using the classical damping theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Concept and performance testing of a high‐capacity oil damper comprising multiple damper units

There has been a significant increase in the size of building structures in recent years. Huge structures such as high‐rise buildings and large‐domed stadiums require high‐performance structural control, including the use of high‐capacity dampers, especially in an earthquake‐prone country like Japan. The objective of the present study was the enhancement of both human and structural safety in such structures through the development of a rate‐dependent type of damper with a high damping capacity. Among the various available types of rate‐dependent dampers, the authors focused on the oil damper owing to its stable performance against long‐duration vibrations. The target maximum damping force was 6000 kN, which is higher than that of any existing oil damper utilized in building structures. The authors developed a novel concept for achieving this high capacity while maintaining the size of the damper within acceptable dimensions from an architectural point of view. The concept involves the use of multiple damper units that produce mechanically parallel damping forces spatially arranged in series. As a prototype, a 1500‐kN oil damper was fabricated by combining three 500‐kN dampers. The 1500‐kN prototype damper was conceived as a full‐scale prototype of a damper that is more slender than comparable commercially available dampers in Japan, and as a scaled model of the proposed 6000‐kN damper. Sinusoidal loading tests were conducted on the prototype damper using a frequency range of 0.1–1.5 Hz and a velocity range of 0.4–300 mm/s. The results confirmed that the damper produced the design damping forces. The results of earthquake loading tests also revealed that the damper exerted a stable damping force against a large earthquake and maintained its performance after the earthquake. The damper is particularly effective against earthquakes with long‐period components that could increase the temperature of a damper. This is afforded by its high heat capacity compared to conventional dampers. Considering that the proposed 6000‐kN damper will generate a damping force that is about 2–3 times that of the strongest conventional oil damper, existing manufacturer test machines would be inadequate for evaluating its full performance characteristics. To address this issue, the authors also propose a test method for evaluating the overall damping force. The method is premised on the fact that the characteristic feature of the proposed damper is its combination of multiple damper units. The overall performance is thus evaluated using the test results for the individual damper units while the other dampers are bypassed. This method was verified by the results of the abovementioned sinusoidal loading tests, with the error for the 1500‐kN prototype damper found to be less than 5%. Copyright © 2016 John Wiley & Sons, Ltd.