Designing tuned mass dampers via static output feedback: a numerical approach

The paper presents a numerical approach to the problem of determining the design parameters of a vibration absorber to minimize the effect of disturbing forces. The approach is also applicable to multi‐input systems such as civil engineering structures. The resulting devices are appealing since they can be implemented passively and are more economic and reliable than active control devices. Copyright © 2000 John Wiley & Sons, Ltd.     

Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.     

强震记录对三个土层地震反应分析程序的检验

为了对国内外广泛使用的3个一维土层地震反应分析程序（DENSOR98、SHAKE91和LSSRLI-1）的计算精度进行检验,本文以4次地震中唐山响瞠井下三维台阵的基岩强震记录为输入地震动,利用这3个程序对此测井剖面分别进行计算,计算结果分别与同次地震中相应的台阵地表强震记录相比较,可得如下结论：在地震动不大的情况下,3个程序都可满足工程要求,其差别为SHAKE91算得的峰值偏大,DENSOR98算得的峰值偏小,LSSRLI-1得到的反应谱更接近实际,DENSOR98得到的反应谱偏低,从安全角度和经济角度综合来看,LSSRLI-1程序较好。     

On the seismic performances of rigid block‐like structures coupled with an oscillating mass working as a TMD

In this paper, the effects of a mass damper on the rocking motion of a non‐symmetric rigid block‐like structure, subject to different seismic excitation, are investigated. The damper is modelled as a single degree of freedom oscillating mass, running at the top of the block and connected to it by a linear visco‐elastic device. The equations of rocking motion, the uplift and the impact conditions are derived. A nondimensionalisation of the governing equations is performed with the aim to obtain an extensive parametric analysis. The results are achieved by numerical integration of these equations. The slenderness and the base of the rigid block, and the eccentricity of the centre of mass are taken as variable parameters in the analyses. The main objective of the study is to check the performance of the damper versus the spectral characteristics of the seismic input. Three earthquake registrations with different frequency contents are used in the analyses. The results show that the presence of the mass damper leads to different levels of improvement of the response of the system, depending on the spectral characteristics of the seismic input. Curves providing the overturning slenderness of blocks of specific sizes versus the characteristics of the TMD are obtained. Copyright © 2017 John Wiley & Sons, Ltd.     

黄土高填方场地地震动参数特性分析

削山造地后形成的黄土高填方场地对地震动参数特性影响较大。以实际工程项目为研究对象,构造不同填土高度的计算剖面,采用一维等效线性化方法计算土层地震动参数,分析基岩地震动输入参数和填土高度对场地地表放大效应的影响。研究表明:场地地震放大系数随填土层的高度增加呈递减趋势。在多遇地震动和基本地震动作用下,场地地震放大系数递减速度比罕遇地震动和极罕遇地震动作用下要大。当填土高度达到一定程度后放大效应趋于平稳;填土高度的变化,会改变地表加速度反应谱的形状。填土高度越大,地表反应谱长周期的频谱成分越显著,反应谱曲线向后移,反应谱峰值点均明显向长周期移动,并出现多个峰值点,反应谱特征周期值变大;下伏基岩的刚度越大,地表峰值加速度的放大效应越大。地表加速度反应谱特征值相比变小。当填土高度增大到一定程度时,下伏基岩的种类对地表地震动特性影响则不明显。该研究成果对高填方场地的地震安全评价和结构抗震设计提供参考。     

Lifecycle cost optimization of tuned mass dampers for the seismic improvement of inelastic structures

The seismic performance of tuned mass dampers (TMDs) on structures undergoing inelastic deformations may largely depend on the ground motion intensity. By estimating the impact of each seismic intensity on the overall cost of future seismic damages, lifecycle cost (LCC) proves a rational metric for evaluating the benefits of TMDs on inelastic structures. However, no incorporation of this metric into an optimization framework is reported yet. This paper presents a methodology for the LCC‐optimal design of TMDs on inelastic structures, which minimizes the total seismic LCC of the combined building‐TMD system. Its distinctive features are the assumption of a mass‐proportional TMD cost model, the adoption of an iterative suboptimization procedure, and the initialization of the TMD frequency and damping ratios according to a conventional linear TMD design technique. The methodology is applied to the seismic improvement of the SAC‐LA benchmark buildings, taken as representative of standard steel moment‐resisting frame office buildings in LA, California. Results show that, despite their limited performance at the highest intensity levels, LCC‐optimal TMDs considerably reduce the total LCC, to an extent that depends on both the building vulnerability and the TMD unit cost. They systematically present large mass ratios (around 10%) and frequency and damping ratios close to their respective linearly designed optima. Simulations reveal the effectiveness of the proposed design methodology and the importance of adopting a nonlinear model to correctly evaluate the cost‐effectiveness of TMDs on ordinary structures in highly seismic areas.     

Coordinative similitude law considering fluid‐structure interaction for underwater shaking table tests

Generally, when a model is made of the same material as the prototype in shaking table tests, the equivalent material density of the scaled model is greater than that of the prototype because mass is added to the model to satisfy similitude criteria. When the water environment is modeled in underwater shaking table tests, however, it is difficult to change the density of water. The differences in the density similitude ratios of specimen materials and water can affect the similitude ratios of the hydrodynamic and wave forces with those of other forces. To solve this problem, a coordinative similitude law is proposed for underwater shaking table tests by adjusting the width of the upstream face of the model or the wave height in the model test to match the similitude ratios of hydrodynamic and wave forces with those of other forces. The designs of the similitude relations were investigated for earthquake excitation, wave excitation, and combined earthquake and wave excitation conditions. Series of numerical simulations and underwater shaking table tests were performed to validate the proposed coordinative similitude law through a comparison of coordinative model and conventional model designed based on the coordinative similitude law and traditional artificial mass simulation, respectively. The results show that the relative error was less than 10% for the coordinative model, whereas it reached 80% for the conventional model. The coordinative similitude law can better reproduce the dynamic responses of the prototype, and thus, this similitude law can be used in underwater shaking table tests.     

A simple strategy for dynamic substructuring: I. Concept and development

Dynamic substructuring refers to physical testing with computational models in the loop. This paper presents a new strategy for such testing. The key feature of this strategy is that it decouples the substructuring controller from the physical subsystem. Unlike conventional approaches, it does not explicitly include a tracking controller. Consequently, the design and implementation of the substructuring controls are greatly simplified. This paper motivates the strategy and discusses the main concept along with details of the substructuring control design. The focus is on configurations that use shake tables and active mass drivers. An extensive experimental assessment of the new strategy is presented in a companion paper, where the influence of various factors such as virtual subsystem dynamics, control gains, and nonlinearities is investigated, and it is shown that robustly stable and accurate substructuring is achieved.     

Variation in soil saturated hydraulic conductivity along the hillslope of collapsing granite gullies

Saturated hydraulic conductivity (K_s) affects the soil hydrological process and is influenced by many factors that exhibit strong spatial variations. To accurately measure K_s and its scale, spatial variability and relationship with collapsing gullies, we analysed four double-ring infiltrometer diameters in three soil layers during in situ experiments designed to measure K_s in two typical collapsing gullies (three slope sites) in Tongcheng County of China. The results showed that K_s increased with increasing inner ring diameter, but no significant difference existed between inner diameters of 30 and 40 cm. The K_s in red soil layers was higher than that in sandy soil layers, the transition layers had the lowest values. K_s also varied with slope position, gradually decreasing with distance from the gully head. The suggestion is that the spatial variation in K_s is affected not only by the intrinsic soil properties but also by the interaction with the collapsing gully.