Numerical technique for dynamic analysis of structures with friction devices

In recent years a number of studies on employing friction elements for the seismic protection of buildings has demonstrated conclusively that such devices can markedly reduce earthquake-induced vibrations. Any numerical estimate of the effectiveness of such isolation systems implies a correct solution of the pertinent nonlinear equations of motion. In direct integration algorithms, the phase transitions between adherence and sliding, or the sliding phase may be accompanied by marked high-frequency oscillation of the relative velocity difference. The paper presents a numerical technique for overcoming these problems, thus leading to increased accuracy of the solutions of equations of motions with Coulomb damping. Since only the damping matrix and the loading vector are involved, the procedure is also computationally efficient. In order to validate the proposed numerical technique, an experimental study of a friction system has been carried out. The dynamic response of a four-storey braced frame with friction devices is presented as an example for the practical application of the proposed numerical technique.     

Seismic response of simple structures using spring-assisted sliding slabs with coulomb damping

Coulomb damping can be utilized effectively to reduce the dynamic response of structures subjected to seismic ground motions. To activate this damping, some parts of a vibrating structure are allowed to slide at rough interfaces. The dynamic response of structures provided with sliding interfaces at the base, between a floor slab and frame and in the cross bracings of a frame has been examined recently. In this paper, a simple slab sliding system provided with a spring to introduce a recovery mechanism and to reduce the sliding displacement requirement for low frequency structures has been examined. The equations of motion for this system are developed. An approach is presented to solve these coupled equations for earthquake induced ground motions. Structures with varying frequency and friction characterisics are considered and the numerical results are presented in response spectrum form. It is observed that, in low frequency structures, provision of a rather weak spring can reduce the sliding displacement requirements without significantly increasing the forces in the supporting frame and the acceleration input to supported secondary systems.     

Seismic response of light internal equipment in base-isolated structures

The seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system. The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base-isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment-structure interaction need not be considered and multiple support response analysis is rendered unnecessary. Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead-rubber hysteretic bearings, having a force-displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead-rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment. The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.     

Controlling seismic response of eccentric structures by friction dampers

Previous studies have demonstrated the good performance of friction dampers in symmetric frame structures subjected to earthquake excitation. This paper examines their effectiveness in asymmetric structures where lateral-torsional coupling characterizes the behaviour. A parametric study is first performed employing an idealized single-storey structure; this is followed by the example of a three-dimensional 5-storey prototype structure equipped with friction dampers. The parametric results show that it is necessary to tune the friction damped braces with respect to both the stiffness of the braces and the slip load of the devices. For properly tuned structures, maximum response for all magnitudes of eccentricity between the centres of stiffness and mass is reduced to levels equal to or less than that of the corresponding symmetric structure. Compared to this prediction, the prototype structure with friction damped bracing exhibits the desired improvement in performance; namely, the devices slip at all storey levels while the frames remain elastic.     

Non-classical damping in dynamic analysis of base-isolated structures with internal equipment

It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response.     

完整锚杆低应变动力响应问题的半解析解及分析

建立完整锚杆低应变瞬态动力响应的数学力学模型并推导出相应的半解析解，研究分析了不同参数对锚杆顶端瞬态动力响应的影响，并将瞬态激振条件下得到的理论曲线与反射波法测得的实际曲线进行了拟合对比，结果表明两者吻合很好。     

单向张弦梁结构风振响应的时域分析

张弦梁屋盖结构自重轻,地震作用下的动力问题不是结构设计的控制因素,但是在风荷载作用下结构的动力响应较为显著,在设计中应给予足够重视。本文首先利用Matlab编程工具,模拟结构的风速时程曲线,然后利用有限元软件中的瞬态动力学分析模块对这种结构进行动力时程分析,讨论其在脉动风荷载作用下的动力响应,并将结果和频域法脉动风荷载的分析结果进行对比,验证了计算结构的可靠性。得到一些有意义的结论,供张弦梁结构的工程应用参考。     

On the dynamic response of regular structures exhibiting tilt

The mechanical characteristics of earthquake‐resistant structures and the ground motion properties that have an important influence on the seismic performance of structures with asymmetric load–deformation behaviour, are identified from the results obtained from a parametric study of the dynamic response of single‐degree‐of‐freedom systems. The dynamic response of tilted single and multi‐degree‐of‐freedom systems, designed according to Mexican requirements for the design of asymmetric structures is studied. After a general understanding of this phenomenon is offered, shortcomings in current design requirements for tilted structures are discussed. Research needs to establish a rational design approach of this type of structures are identified. Copyright © 2000 John Wiley & Sons, Ltd.     

Key parameters governing the dynamic response of long-period structures

The present study describes the important factors (period, duration, and intensity) involved in evaluating input ground motion and structural response for the design of long-period structures such as high-rise buildings and base-isolated buildings. First, the fundamental dynamic properties of high-rise buildings are explained based on the results of newly introduced vibration observations programs. Next, the distribution of the predominant period and duration of seismic ground motion within the Nobi Plain, one of the largest sedimentary plains in Japan, is discussed with respect to the possibility of resonance of long-period structures. Finally, we introduce a recently developed long-stroke shaking table that is intended to convince structural engineers and building owners to take adequate countermeasures against large floor response in high-rise buildings because of resonance. Presented at the International Workshop on Long-Period Ground Motion Simulation and Velocity Structures Earthquake Research Institute, University of Tokyo, Tokyo, November 14–15, 2006.     

Effect of viscous,viscoplastic and friction damping on the response of seismic isolated structures

In this paper the efficiency of various dissipative mechanisms to protect structures from pulse‐type and near‐source ground motions is examined. Physically realizable cycloidal pulses are introduced, and their resemblance to recorded near‐source ground motions is illustrated. The study uncovers the coherent component of some near‐source acceleration records, and the shaking potential of these records is examined. It is found that the response of structures with relatively low isolation periods is substantially affected by the high‐frequency fluctuations that override the long duration pulse. Therefore, the concept of seismic isolation is beneficial even for motions that contain a long duration pulse which generates most of the unusually large recorded displacements and velocities. Dissipation forces of the plastic (friction) type are very efficient in reducing displacement demands although occasionally they are responsible for substantial permanent displacements. It is found that the benefits by hysteretic dissipation are nearly indifferent to the level of the yield displacement of the hysteretic mechanism and that they depend primarily on the level of the plastic (friction) force. The study concludes that a combination of relatively low friction and viscous forces is attractive since base displacements are substantially reduced without appreciably increasing base shears and superstructure accelerations. Copyright © 2000 John Wiley & Sons, Ltd.     

Investigation of dynamic response of masonry minaret structures

Almost all historical minarets in Turkey were constructed using cut stone, masonry blocks or combination of these two materials. The structural and geometrical properties of each masonry minaret, or slender tower structure, depend on many factors including the structural knowledge and applications at the time of construction, experience of the architect or engineer, seismicity of the region, and availability of construction materials in that area. Recent earthquakes in Turkey have shown that most masonry minarets in high seismic regions are vulnerable to structural damage and collapse. In this study, in order to investigate the dynamic behavior of historical unreinforced masonry minarets, three representative minarets with 20, 25, and 30 m height were modeled and analyzed using two ground motions recorded during the 1999 Kocaeli and Duzce, Turkey earthquakes. The modal analyses of the models have shown that the structural periods and the overall structural response are influenced by the minaret height and spectral characteristics of the input motion. The dynamic displacement and axial stress time histories are computed at the critical points on the minarets. During recent earthquakes, most minaret failures occurred above the base of the structure. Consistent with the observed response, the largest stresses were calculated at the same location.     

A study of seismic response characteristics of structures with friction damping

The effectiveness of introducing Coulomb damping in structures to reduce seismic response is evaluated. Response characteristics of simple one-degree-of-freedom structures with sliding interfaces between the top slab and supporting frame and between the base and foundation are studied and compared. It is shown that, analytically, the top slab sliding system is a special case of the base sliding system. The slab sliding system is seen to offer certain advantages over the base sliding system inasmuch as it provides a more effective reduction in the lateral forces in the supporting frame as well as a better isolation of supported secondary systems, as depicted by a significantly reduced level of floor spectrum response. The analytical ease of predicting the response of the slab sliding system is also demonstrated. The required unobstructed sliding displacements seem to be reasonable except, may be, for flexible systems. The similarities and differences between the hysteretic and slab sliding systems are also highlighted by comparison of their response results.     

The effect of coulomb damping on multidegree of freedom elastic structures

This paper is based on the premise that the damping mechanism of a multidegree of freedom structure can be represented by viscous and coulomb dampers. A closed form solution for the structure subjected to a sinusoidal forcing function is presented. The solution is used as the basis of a method for determining relative amounts of viscous and coulomb damping from vibration tests. The method was applied to the results of a series of vibration tests on a five storey reinforced concrete structure and approximate values of viscous and coulomb damping obtained. A comparison of the effect of various combined damping values on the earthquake response of the structure was made. It was concluded that the use of the equivalent viscous damping concept to approximate the combined effect of viscous and coulomb damping results in a low estimate of the elastic response of the structure.     

A comparative study of bounding techniques in dynamic shakedown of elasto-plastic structures

Two conceptually different procedures to obtain upper bounds to displacements and deformations developed in the dynamic evolution of elasto-plastic structures are considered. Computationally, both methods require the dynamic analysis of a linear system and a sequence of constrained optimization problems, each roughly analogous to a limit analysis procedure in the quasi-static range, with a substantial saving in effort when compared to an incremental analysis of the plasto-dynamic response. A discrete model for frames is proposed and the two approaches are reformulated in a convenient matrix form. The approaches are then compared on the basis of the information needed (total or plastic displacements, deformations, dissipated energy), of the usefulness of results obtained and of the computational effort involved. The results seem to indicate the practical usefulness of these techniques and encourage the extension of the study to broader classes of structures.     

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.     

Seismic response of multi‐supported structures by proper orthogonal decomposition

The seismic analysis of structures is usually carried out considering the ground motion as fully‐correlated in space and determining the structural response by pseudo‐deterministic methods such as the response spectrum technique. Actually, the partial correlation of the seismic acceleration may influence heavily the behaviour of spatially extended structures, such as bridges, viaducts or pipelines. In order to take its partial correlation into account, the seismic ground motion is schematized as a stochastic process dependent on time and on space; the hypotheses of stationarity and homogeneity are used to obtain simple and general results. The influence of the partial correlation of the seismic ground motion on the structural response is investigated by introducing suitable Equivalent Spectra. The acceleration of the support‐points of the structure is represented by the Proper Orthogonal Decomposition (POD), defining the modes of the earthquake. The method is formulated for any kind of multi‐degree‐of‐freedom system and is applied, as a case study, to an ideal single‐storey multi‐supported frame with an axially rigid beam. In the case of two supports, the POD decouples the pseudo‐static and the dynamic contributions to the structural response. This property is preserved for structural systems with many supports, where only the lower modes of the earthquake, usually the first two POD modes, are responsible for the structural response. Copyright © 2003 John Wiley & Sons, Ltd.     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.     

Variations in the dynamic response of structures founded on piles induced by obliquely incident SV waves

Although the seismic actions generally consist of a combination of waves, which propagates with an angle of incidence not necessarily vertical, the common practice when analyzing the dynamic behavior of pile groups is based on the assumption of vertically incident wave fields. The aim of this paper is to analyze how the angle of incidence of SV waves affects the dynamic response of pile foundations and piled structures. A three-dimensional boundary element-finite element coupling formulation is used to compute impedances and kinematic interaction factors corresponding to several configurations of vertical pile groups embedded in an isotropic homogeneous linear viscoelastic half-space. These results, which are provided in ready-to-use dimensionless graphs, are used to determine the effective dynamic properties of an equivalent single-degree-of-freedom oscillator that reproduces, within the range where the peak response occurs, the response of slender and nonslender superstructures through a procedure based on a substructuring model. Results are expressed in terms of effective flexible-base period and damping as well as maximum shear force at the base of the structure. The relevance and main trends observed in the influence of the wavefront angle of incidence on the dynamic behavior of the superstructure are inferred from the presented results. It is found that effective damping is significantly affected by the variations of the wave angle of incidence. Furthermore, it comes out that the vertical incidence is not always the worst-case scenario.     

摩擦消能支撑钢框架结构的弹塑性地震反应时程分析

本文分析了摩擦消能支撑及框架主体结构弹塑性本构关系，并给出了动力时程分析的计算方法。同时，对六层钢框架模型做了各种工况下的地震反应时程分析。结果表明，摩擦消能支撑钢框架（FEDBF）比抗弯钢框架（MRF）的地震作用明显降低，尤其在强震作用下效果更加明显。