Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control.To evaluate the performance of structures installed with viscoelastic dampers,different analytical models have been used to characterize their dynamic force deformation characteristics.The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well.However,accurate analytical procedures are needed to calculate the response of structures with such damper models.This paper presents a modal analysis approach,similar to that used for the analysis of linear systems,for solving the equations of inotion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions.The uncoupled modal equations still have fractional derivatives,but can be solved by numerical or analytical procedures.Both numerical and analytical procedures are formulated.These procedures are then used to calculate the dynamic response of a multi-degree of fleedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.

Simplified analysis of frame structures with viscoelastic dampers considering the effect of soil-structure interaction

In this study, simplified numerical models are developed to analyze the soil-structure interaction （SSI） effect on frame structures equipped with viscoelastic dampers （VEDs） based on pile group foundation. First, a single degree-of- freedom （SDOF） oscillator is successfully utilized to replace the SDOF energy dissipated structure considering the SSI effect. The equivalent period and damping ratio of the system are obtained through analogical analysis using the frequency transfer function with adoption of the modal strain energy （MSE） technique. Aparametric analysis is carried out to study the SSI effect on the performance of VEDs. Then the equilibrium equations of the multi degree-of-freedom （MDOF） structure with VEDs considering SSI effect are established in the frequency domain. Based on the assumption that the superstructure of the coupled system possesses the classical normal mode, the MDOF superstructure is decoupled to a set of individual SDOF systems resting on a rigid foundation with adoption of the MSE technique through formula derivation. Numerical results demonstrate that the proposed methods have the advantage of reducing computational cost, however, retaining the satisfactory accuracy. The numerical method proposed herein can provide a fast evaluation of the efficiency of VEDs considering the SSI effect.

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

Viscoelastic dampers,as spplementary energy dissipation devices,have been used in building structures un- der seismic excitation or wind loads.Different analytical models have been proposed to describe their dynamic force deform- ation characteristics.Among these analytieal 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 foree-detormation relationship is described by a fractional derivative mod- el.Then,a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamie system subjected to deterministic or random excitation.Through numerical verification,it is shown that viscoelastic dampers are ef- fective in reducing structural responses over a wide frequency range,and the proposed schmnes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model wills frac- tional derivative.

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.

Experimental and analytical study on design performance of full-scale viscoelastic dampers

Viscoelastic（VE） dampers, with their stiffness and energy dissipation capabilities, have been widely used in civil engineering for mitigating wind-induced vibration and seismic responses of structures, thus enhancing the comfort of residents and serviceability of equipment inside. In past relevant research, most analytical models for characterizing the mechanical behavior of VE dampers were verified by comparing their predictions with performance test results from small-scale specimens, which might not adequately or conservatively represent the actual behavior of full-scale dampers, especially with regard to the ambient temperature, temperature rise, and heat convection effects. Thus, in this study, by using a high-performance testing facility with a temperature control system, full-scale VE dampers were dynamically tested with different displacement amplitudes, excitation frequencies, and ambient temperatures. By comparing the analytical predictions with the experimental results, it is demonstrated that adopting the fractional derivative method together with considering the effects of excitation frequencies, ambient temperatures, temperature rises, softening, and hardening, can reproduce the design performance of full-scale VE dampers very well.

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.

Application of Lead Viscoelastic Dampers to Wind Vibration Control on Big-Span Power Transmission Tower

To study the wind vibration response of power transmission tower, the lead viscoelastic dampers （LVDs） were applied to a cup tower. With time history analysis method, the displacement, velocity, acceleration and force response of the tower was calculated and analyzed. The results show that the control effect of lead viscoelastic dampers is very good, and the damping ratio can reach 20% or more when they are applied to the tower head.

Optimal Vibration Control of Adjacent Building Structures Interconnected by Viscoelastic Dampers

The objective of this paper is to investigate the dynamic characteristics of two adjacent building structures interconnected by viscoelastic dampers under seismic excitations. The computational procedure for an analytical model including the system model formulation, complex modal analysis and seismic time history analysis is presented for this purpose. A numerical example is also provided to illustrate the analytical model. The complex modal analysis is conducted to determine the optimal damping ratio, the optimal damper stiffness and the optimal damper damping of the viscoelastic dampers for each mode of the system. For the damper stiffness and damping with optimal values, the responses can be categorized into underdamped and critically damped vibrations. Furthermore, compared to the viscous dampers with only the energy dissipation mechanism, the viscoelastic dampers with both the energy dissipation and redistribution mechanisms are more effective for increasing the damping ratio of the system. The seismic time history analysis is conducted to assess the effectiveness of the viscoelastic dampers for vibration control. Based on the optimal damping ratio, the optimal damper stiffness, the optimal damper damping of the viscoelastic dampers for a certain mode of the system, and the viscoelastic dampers can be used to effectively suppress the root-mean-square responses as well as the peak responses of the two adjacent buildings.

Optimal arrangement of viscoelastic dampers for seismic control of adjacent shear-type structures

The optimal arrangement of viscoelastic dampers (VEDs) used to link two adjacent shear-type structures under seismic excitation was investigated. A two-step optimal design method is proposed. First, optimal parameter expressions of the Kelvin model are used to calculate the optimal stiffness and damping coefficient of the VEDs. Then, using the two-step optimal design method, taking the quadratic performance index as the optimization objective, the optimal arrangement of the dampers is determined. General rules about the optimal arrangement of the VEDs were obtained. The results show that the placement of only one damper between two adjacent shear-type structures should be avoided; if more than one damper is used, they should be distributed on the top and lower floors of the structures. Optimization of the number of dampers had little effect on response reduction. The most important factor was the optimization of the placement of the dampers. Through comparative study, for buildings of equal and unequal heights, the optimal parameters of dampers from parametric studies were shown to match the theoretical results for different numbers and placements of dampers. The level of response reduction was shown to be sensitive to the damping coefficient of the dampers.

The role of viscoelastic damping on retrofitting seismic performance of asymmetric reinforced concrete structures

The primary purpose of this research is to improve the seismic response of a complex asymmetric tall structure using viscoelastic(VE) dampers. Asymmetric structures have detrimental effects on the seismic performance because such structures create abrupt changes in the stiffness or strength that may lead to undesirable stress concentrations at weak locations. Structural control devices are one of the effective ways to reduce seismic impacts, particularly in asymmetric structures. For passive vibration control of structures, VE dampers are considered among the most preferred devices for energy dissipation. Therefore, in this research, VE dampers are implemented at strategic locations in a realistic case study structure to increase the level of distributed damping without occupying significant architectural space and reducing earthquake vibrations in terms of story displacements(drifts) and other design forces. It has been concluded that the seismic response of the considered structure retrofitted with supplemental VE dampers corresponded well in controlling the displacement demands. Moreover, it has been demonstrated that seismic response in terms of interstory drifts was effectively mitigated with supplemental damping when added up to a certain level. Exceeding the supplemental damping from this level did not contribute to additional mitigation of the seismic response of the considered structure. In addition, it was found that the supplemental damping increased the total acceleration of the considered structure at all floor levels, which indicates that for irregular tall structures of this type, VE dampers were only a good retrofitting measure for earthquake induced interstory deformations and their use may not be suitable for acceleration sensitive structures. Overall, the research findings demonstrate how seismic hazards to these types of structures can be reduced by introducing additional damping into the structure.

Dynamic properties of structures with dampers modelled using fractional order derivatives

The focus of this paper is on determination of the dynamic parameters of structural systems with viscoelastic (VE) dampers described by Maxwell rheological models. Such parameters could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frames with VE dampers. The solution to the nonlinear eigenvalue problem is obtained by equating to zero the determinant of the considered system of equations. Apart from complex conjugate eigenvalues, the real ones occurred when dampers that are described by the classic Maxwell model, are also determined.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

Full-scale dynamic testing of response-controlled buildings and their components:concepts,methods,and findings

A series of shake-table tests was conducted by inserting and replacing 4 different types of dampers,or by removing them in a full-scale 5-story steel frame building. The objective is to validate response-control technologies that are increasingly adopted for major Japanese buildings without being attested to-date by a major earthquake. Test results are briefly described,and good performance of the dampers and frame demonstrated. The concepts of the full-scale building tests and various contributions are discussed. The difficulty associated with full-scale dynamic testing is explained.

Relation of the infrasound characteristics and the continuous steel bridge vibration modes generated by the vibration of moving heavy trucks

As heavy trucks pass over highway bridges, bridge vibration occurs and generates infrasound. General trucks in Japan with rear leaf suspension have whole body vibration （suspension spring vibration） frequencies of about 3 Hz. Also, the frequencies of the wheel vibration （tire spring vibration） are about 10-20 Hz. The continuous steel highway bridges with middle span length have vibration modes with the same phase in each span at the frequencies of about 3 Hz and also have those with the secondary mode shape at the frequencies of about 10-20 Hz. Truck vibrations and bridge vibrations are closely related. In this work, vibration tests are conducted using a heavy test truck for two cases of infrasound complaints in order to investigate the relation between the continuous steel bridge vibration modes generated by the vibration of moving heavy trucks and its infrasound characteristics. As a result of the examination, two types of bridge vibration modes are caused by the vibrations of a moving heavy truck. Moreover, the bending vi- bration modes with the same phase in each span have the most powerful infrasound pressure, since each span vibrates with the same phase. Two countermeasures, including viscoelastic damper at the end of the girders and extended deck method, are proposed to reduce the amplitude of bridge vibration and its infrasound.

Passive vibration control of truss-cored sandwich plate with planar Kagome truss as one face plane

Kagome based high authority shape morphing structure is a kind of truss-cored sandwich metal plate with a planar Kagome truss as one of its face plane. The planar Kagome truss can achieve arbitrary in-plane nodal displacements with minimal internal resistance when its rods are deformed. Moreover, the in-plane deflection of the planar Kagome truss may induce the lateral deflection of the whole sandwich plate. In this paper, the feasibility to enhance the damping of the truss-cored sandwich plate through the replacement of a very small portion of rods in the planar Kagome truss by cylindrical viscoelastic dampers is exploited. The Biot model is chosen to simulate the behavior of the viscoelastic material in the dampers, and the fraction of axial modal strain energy of the rods in the planar Kagome truss is adopted as the index to decide the positions of the dampers. Through complex modal analysis and time-domain simulation, it is shown that the passive vibration control approach is very effective for the vibration reduction of this kind of truss-cored sandwich plates.