Seismic control of multi-degrees-of-freedom structures by vertical mass isolation method using MR dampers

Vertical mass isolation(VMI)is one of the novel methods for the seismic control of structures.In this method,the entire structure is assumed to consist of two mass and stiffness subsystems,and an isolated layer is located among them.In this study,the magnetorheological damper in three modes:passive-off,passive-on,and semi-active mode with variable voltage between zero and 9 volts was used as an isolated layer between two subsystems.Multi-degrees-of-freedom structures with 5,10,and 15 floors in two dimensions were examined under 11 pairs of near field earthquakes.On each level,the displacement of MR dampers was taken into account.The responses of maximum displacement,maximum inter-story drift,and maximum base shear in controlled and uncontrolled buildings were compared to assess the suggested approach for seismic control of the structures.According to the results,the semi-active control method can reduce the response by more than 12%compared to the uncontrolled mode in terms of maximum displacement of the mass subsystem of the structures.This method can reduce more than 16%and 20%of the responses compared to the uncontrolled mode in terms of maximum inter-story drift and base shear of the structure,respectively.

Theoretical and Experimental Study on the Performance of Hermetic Diaphragm Squeeze Film Dampers for Gas-Lubricated Bearings

Low damping characteristics have always been a key sticking points in the development of gas bearings.The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings.This paper proposed a novel hermetic diaphragm squeeze film damper(HDSFD)for oil-free turbomachinery supported by gas lubricated bearings.Several types of HDSFDs with symmetrical structure were proposed for good damping performance.By considering the compressibility of the damper fluid,based on hydraulic fluid mechanics theory,a dynamic model of HDSFDs under medium is proposed,which successfully reflects the frequency dependence of force coefficients.Based on the dynamic model,the effects of damper fluid viscosity,bulk modulus of damper fluid,thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed.An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted.The damper fluid transverse flow is added to the existing HDSFD concept,which aims to make the dynamic force coefficients independent of frequency.Although the force coefficient is still frequency dependent,the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply.The results serve as a benchmark for the calibration of analytical tools under development.

Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Variable stiffness tuned particle dampers for vibration control of cantilever boring bars

This research proposes a novel type of variable stiffness tuned particle damper(TPD)for reducing vibrations in boring bars.The TPD integrates the developments of particle damping and dynamical vibration absorber,whose frequency tuning principle is established through an equivalent theoretical model.Based on the multiphase flow theory of gas-solid,it is effective to obtain the equivalent damping and stiffness of the particle damping.The dynamic equations of the coupled system,consisting of a boring bar with the TPD,are built by Hamilton’s principle.The vibration suppression of the TPD is assessed by calculating the amplitude responses of the boring bar both with and without the TPD by the Newmark-beta algorithm.Moreover,an improvement is proposed to the existing gas-solid flow theory,and a comparative analysis of introducing the stiffness term on the damping effect is presented.The parameters of the TPD are optimized by the genetic algorithm,and the results indicate that the optimized TPD effectively reduces the peak response of the boring bar system.

Application of computational fluid dynamics in design of viscous dampers-CFD modeling and full-scale dynamic testing

Computational fluid dynamics(CFD)provides a powerful tool for investigating complicated fluid flows.This paper aims to study the applicability of CFD in the preliminary design of linear and nonlinear fluid viscous dampers.Two fluid viscous dampers were designed based on CFD models.The first device was a linear viscous damper with straight orifices.The second was a nonlinear viscous damper containing a one-way pressure-responsive valve inside its orifices.Both dampers were detailed based on CFD simulations,and their internal fluid flows were investigated.Full-scale specimens of both dampers were manufactured and tested under dynamic loads.According to the tests results,both dampers demonstrate stable cyclic behaviors,and as expected,the nonlinear damper generally tends to dissipate more energy compared to its linear counterpart.Good compatibility was achieved between the experimentally measured damper force-velocity curves and those estimated from CFD analyses.Using a thermography camera,a rise in temperature of the dampers was measured during the tests.It was found that output force of the manufactured devices was virtually independent of temperature even during long duration loadings.Accordingly,temperature dependence can be ignored in CFD models,because a reliable temperature compensator mechanism was used(or intended to be used)by the damper manufacturer.

Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers

Long-period pulses in near-field earthquakes lead to large displacements in the base of isolated structures.To dissipate energy in isolated structures using semi-active control,piezoelectric friction dampers（PFD） can be employed.The performance of a PFD is highly dependent on the strategy applied to adjust its contact force.In this paper,the seismic control of a benchmark isolated building equipped with PFD using PD/PID controllers is developed.Using genetic algorithms,these controllers are optimized to create a balance between the performance and robustness of the closed-loop structural system.One advantage of this technique is that the controller forces can easily be estimated.In addition,the structure is equipped with only a single sensor at the base floor to measure the base displacement.Considering seven pairs of earthquakes and nine performance indices,the performance of the closed-loop system is evaluated.Then,the results are compared with those given by two well-known methods：the maximum possive operation of piezoelectric friction dampers and LQG controllers.The simulation results show that the proposed controllers perform better than the others in terms of simultaneous reduction of floor acceleration and maximum displacement of the isolator.Moreover,they are able to reduce the displacement of the isolator systems for different earthquakes without losing the advantages of isolation.

Simplified design method for shear-valve magnetorheological dampers

Based on the Bingham parallel-plate model, a simplified design method of shear-valve magnetorheological （MR） dampers is proposed considering the magnetic circuit optimization. Correspondingly, a new MR damper with a full-length effective damping path is proposed. The prototype dampers are also fabricated and studied numerically and experimentally. According to the test results, the Bingham parallel-plate model is further modified to obtain a damping force prediction model of the proposed MR dampers. This prediction model considers the magnetic saturation phenomenon. The study indicates that the proposed simplified design method is simple, effective and reliable. The maximum damping force of the proposed MR dampers with a full-length effective damping path is at least twice as large as those of conventional MR dampers. The dynamic range of damping force increases by at least 70%. The proposed damping force prediction model considers the magnetic saturation phenomenon and it can realize the actual characteristic of MR fluids. The model is able to predict the actual damping force of MR dampers precisely.

Dynamic responses of two buildings connected by viscoelastic dampers under bidirectional earthquake excitations

In this study,dynamic responses of two buildings connected by viscoelastic dampers under bidirectional excitations are extensively investigated.The two buildings are a 10-story building and a 16-story building,with the shorter building on the left.Viscoelastic dampers are installed at all fl oors of the shorter building.Equations of motion are formulated using a fractional derivative model to represent the viscoelastic dampers.Three cases are considered with mass eccentricities at 0,10% and-10% with respect to the dimensions of the buildings.The responses of the buildings are numerically predicted at different damper properties.The simulation results indicated that the maximum horizontal responses of the buildings without eccentricities are signifi cantly mitigated.However,torsional effects are adversely increased.For asymmetric buildings,the effectiveness of the connecting dampers is affected by building eccentricities.As a result,mass eccentricities must be taken into account in damper selection.When compared with vibrations induced by unidirectional excitations,bidirectional excitations can increase the responses of coupled asymmetric buildings.In addition,installing dampers only at the top fl oor of the shorter building may cause a sudden change in lateral stiffness of the taller building.Consequently,the story shear envelopes of the taller building are changed.

Reduction of structural response to near fault earthquakes by seismic isolation columns and variable friction dampers

This paper focuses on the investigation of a hybrid seismic isolation system with passive variable friction dampers for protection of structures against near fault earthquakes. The seismic isolation can be implemented by replacing the conventional columns fixed to the foundations by seismic isolating ones. These columns allow horizontal displacement between the superstructure and the foundations and decouple the building from the damaging earthquake motion. As a result, the forces in the structural elements decrease and damage that may be caused to the building by the earthquake significantly decreases. However, this positive effect is achieved on account of displacements occurring in the isolating columns. These displacements become very large when the structure is subjected to a strong earthquake. In this case, impact may occur between the parts of the isolating column yielding their damage or collapse. In order to limit the displacements in the isolating columns, it is proposed to add variable friction dampers. A method for selecting the dampers＇ properties is proposed. It is carried out using an artificial ground motion record and optimal active control algorithm. Numerical simulation of a sevenstory structure shows that the proposed method allows efficient reduction in structural response and limits the displacements at the seismic isolating columns.

Intelligent technology-based control of motion and vibration using MR dampers

Due to their intrinsically nonlinear characteristics,development of control strategies that are implementable and can fully utilize the capabilities of semiactive control devices is an important and challenging task.In this study,two control strategies are proposed for protecting buildings against dynamic hazards,such as severe earthquakes and strong winds,using one of the most promising semiactive control devices,the magnetorheological (MR) damper.The first control strategy is implemented by introducing an inverse neural network (NN) model of the MR damper.These NN models provide direct estimation of the voltage that is required to produce a target control force calculated from some optimal control algorithms.The major objective of this research is to provide an effective means for implementation of the MR damper with existing control algorithms.The second control strategy involves the design of a fuzzy controller and an adaptation law.The control objective is to minimize the difference between some desirable responses and the response of the combined system by adaptively adjusting the MR damper.The use of the adaptation law eliminates the need to acquire characteristics of the combined system in advance. Because the control strategy based on the combination of the fuzzy controller and the adaptation law doesn't require a prior knowledge of the combined building-damper system,this approach provides a robust control strategy that can be used to protect nonlinear or uncertain structures subjected to random loads.

Improving the seismic performance of base-isolated liquid storage tanks with supplemental linear viscous dampers

Large tanks are extensively used for storing water,petrochemicals and fuels.Since they are often cited in earthquake-prone areas,the safe and continuous operation of these important structures must be ensured even when severe earthquakes occur,since their failure could have devastating financial and socio-environmental consequences.Base-isolation has been widely adopted for the efficient seismic protection of such critical facilities.However,base-isolated tanks can be located relatively close to active faults that generate strong excitations with special characteristics.Consequently,viscous dampers can be incorporated into the isolation system to reduce excessive displacement demands and to avoid overconservative isolator design.Nonetheless,only a few studies have focused on the investigation of seismic response of base-isolated liquid storage tanks in conjunction with supplemental viscous dampers.Therefore,the impact of the addition of supplemental linear viscous dampers on the seismic performance of tanks isolated by single friction pendulum devices is investigated herein.Four levels of supplemental damping are assessed and compared with respect to isolators′displacement capacity and accelerations that are transferred to the tanks.

An alternative practical design method for structures with viscoelastic dampers

Viscoelastic dampers（VEDs） are one of the most common passive control devices used in new and retrofit building projects which reduce the structure responses and dissipate seismic energy during an earthquake.Various methods to design this kind of dampers have been proposed based on the desired level of additional damping,eigenvalue assignment,modal strain energy,linear quadratic regulator control theories,and other approaches.In the current engineering practice,the popular method is the one based on the modal strain energy that uses the inter-story lateral stiffness as one of the main variables for damper design.However,depending on the configuration of the structure,in some cases the resulting interstory lateral stiffness can be very large.Consequently,the dampers size would also be large producing much more damping than that effectively necessary,resulting in an increase of the overall cost of the supplemental damping system and causing excessive stress on the structural elements connected to the dampers.In this paper an alternative practical design method for structures with VEDs is proposed.This method uses the inter-story shear forces as one of the main variables to accomplish the damper design compared to what was done in previous studies.Nonlinear time-history analyses were conducted on a 7-story reinforced concrete（RC） structure to check the reliability and effectiveness of the proposed method.Comparisons on the seismic performance between the structure without dampers and that equipped with VEDs were carried out.It is concluded that the proposed method results in a very suitable size of dampers,which are able to improve the performance of the structure at all levels of earthquake ground motions and satisfying the drift requirement prescribed in the codes.

An Experimental and Analytical Study on Cross-Laminated Bamboo Rocking Walls with Friction Dampers

Cross-laminated bamboo(CLB)have a high strength to weight ratio and stable bidirectional mechanical properties.Inspired by the investigation on cross-laminated timber(CLT)rocking walls,CLB rocking walls with conventional friction dampers(CFDs)are studied in this paper.To investigate the mechanical properties of the CLB rocking wall,seven tests are conducted under a cyclic loading scheme,and different test parameters,including the existence of the CFDs,the moment ratio,and the loading times,are discussed.The test results show a bilinear behavior of the CLB rocking wall.The small residual displacements of the CLB rocking wall demonstrate an idealized self-centering capacity.The cumulative energy dissipation curves indicate that the energy dissipation capacity of the CLB rocking wall can be greatly improved with CFDs.The limit states of the CLB rocking wall under a lateral force are proposed based on the strains,stress,and damage level of the CLB material and posttensioned rebar.In addition,an analytical model of the CLB rocking wall is developed based on the proposed limit states of the CLB rocking wall to evaluate the hysteretic response of the CLB rocking wall,and the model is validated by the experimental data.The comparison results show the potential value of the analytical model for engineering design.

Torsionally Coupled Response Control of Offshore Platform Structures Using Circular Tuned Liquid Column Dampers

In this paper, the control performance is investigated of Circular Tuned Liquid Column Dampers (CTLCD) over torsional response of offshore platform structures excited by ground motions. Based on the equation of motion for the CTLCD-structure system, the optimal control parameters of CTLCD are given through some derivations on the supposition that the ground motion is a stochastic process. The influence of systematic parameters on the equivalent damping ratio of the structures is analyzed with purely torsional vibration and translational-torsional coupled vibration, respectively. The results show that the Circular Tuned Liquid Column Damper (CTLCD) is an effective torsional response control device.

Dynamic Analysis for Structures Isolated with Dampers

In this paper, mathematical models and dynamic analyses for both SDOF and MDOF structures isolated with dampers are established and performed, and a comprehensive computation method is provided. The shock absorbing effect is illustrated through an example of a two DOF damper-isolated system excited by sinusoidal waves and actual ground acceleration input recorded in earthquakes. It is shown that most of the responses of the structure with dampers reduce greatly near the resonant zone, but acceleration is enlarged in the lower or higher frequency zone; among various parameters, the influence of frictional coefficient n is the most significant, that of damping ratio of the dampers , is the second, and that of stiffness coefficient of the dampers k, is the slightest.

Real-time hybrid simulation of structures equipped with viscoelastic-plastic dampers using a user-programmable computational platform

A user-programmable computational/control platform was developed at the University of Toronto that offers real-time hybrid simulation （RTHS） capabilities. The platform was verified previously using several linear physical substructures. The study presented in this paper is focused on further validating the RTHS platform using a nonlinear viscoelastic-plastic damper that has displacement, frequency and temperature-dependent properties. The validation study includes damper component characterization tests, as well as RTHS of a series of single-degree-of-freedom （SDOF） systems equipped with viscoelastic-plastic dampers that represent different structural designs. From the component characterization tests, it was found that for a wide range of excitation frequencies and friction slip loads, the tracking errors are comparable to the errors in RTHS of linear spring systems. The hybrid SDOF results are compared to an independently validated thermal- mechanical viscoelastic model to further validate the ability for the platform to test nonlinear systems. After the validation, as an application study, nonlinear SDOF hybrid tests were used to develop performance spectra to predict the response of structures equipped with damping systems that are more challenging to model analytically. The use of the experimental performance spectra is illustrated by comparing the predicted response to the hybrid test response of 2DOF systems equipped with viscoelastic-plastic dampers.

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.

Closure to“Discussion on‘Optimum placement and characteristics of velocity-dependent dampers under seismic excitation' by SA Mousavi and AK Ghorbani-Tanha”by Izuru Takewaki

The authors would like to thank the discusser for his considerations and comments. The discusser believes that some of the derived formulations need to be referred to his previously published works and also some related studies have not been cited.

Optimal placement of dampers and actuators based on stochastic approach

A general method is developed for optimal application of dampers and actuators by installing them at optimal location on seismic-resistant structures.The study includes development of a statistical criterion,formulation of a general optimization problem and establishment of a solution procedure.Numerical analysis of the seismic response in time-history of controlled structures is used to verify the proposed method for optimal device application and to demonstrate the effectiveness of seismic response control with optimal device location.This study shows that the proposed method for the optimal device application is simple and general,and that the optimally applied dampers and actuators are very efficient for seismic response reduction.

Impact of seismic excitation characteristics on the efficiency of tuned liquid column dampers

Various types of passive control systems have been used to suppress the seismic response of structures in recent years. Among these systems, Tuned Liquid Column Dampers （TLCDs） dissipate the input earthquake energy by combining the effects of the movement of the liquid mass in the container, the restoring force on the liquid due to the gravity loads and the damping due to the liquid movement through orifices. In this study, the effects of seismic excitation characteristics such as frequency content and soil condition on the seismic performance of TLCDs are investigated using nonlinear time-history analyses. In this regard, among the past earthquake ground motion records of Iran, 16 records with different parameters were selected. In the structural model developed, the attached TLCD is simulated as a Tuned Mass Damper （TMD） having the same vibration period and damping ratio as the original TLCD. The numerical results show that the seismic excitation characteristics have a substantial role on the displacement reduction capability of TLCDs and they should be considered accordingly in the design of TLCDs.