An investigation of tuned liquid dampers equipped with damping screens under 2D excitation

This paper reports on the results of a study conducted on tanks partially filled with water, representing tuned liquid dampers (TLD), subjected to both 1D and 2D horizontal excitations. The sloshing response of the water in the tank is characterized by the free surface motion, the resulting base shear force, and evaluation of the energy dissipated by the sloshing water. A 1D non‐linear flow model capable of simulating a TLD equipped with damping screens is employed to model a 2D TLD. Application of this particular model requires the assumption that the response is decoupled and can be treated as the summation of two independent 1D TLDs. Results from the non‐linear flow model are compared with the 2D experimental shake table test results leading to a validation of the decoupled response assumption. This attractive decoupled response property allows square and rectangular tanks to be used as 2D TLDs, which can simultaneously reduce the dynamic response of a structure in two perpendicular modes of vibration. Copyright © 2005 John Wiley & Sons, Ltd.     

Tuned liquid dampers for controlling earthquake response of structures

Numerical simulations of a single‐degree‐of‐freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structure's response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure's natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water‐depth to tank‐length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water‐mass to structure‐mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure's natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical evaluation of hydrodynamic damping due to the Upper Mounted Baffles in real scale tanks

In this study, the hydrodynamic damping effects of Upper Mounted Baffles (UMB) used in the real scale liquid tanks are numerically investigated. In this regard, the paper follows three main purposes. First, the accuracy of the analytical model developed by the author is examined for full scale applications. In this regard, the tanks equipped by UMB with various dimensions and locations are numerically analyzed in free vibration mode. Then, the numerical results are compared with an analytical solution results, and the validity of the analytical formulation for using in real applications is discussed. Second, the seismic efficiency of UMB is considered, and the reduction of the sloshing wave height due to the presence of the UMB is examined under several earthquake excitations. Finally, a seismic design procedure is proposed to evaluate the effect of UMB on the suppression of sloshing in a liquid tank, and its predictions are compared with the results of numerical analysis.     

核电结构PCS水箱液动压力分析等效模型

中国核电厂抗震设计规范推荐采用的Housner模型不适用于复杂形状核电储液结构的流固耦合分析。对于AP1000和CAP1400核电站屏蔽厂房顶部非能动安全壳冷却系统重力水箱(简称PCS水箱),基于圆柱形水箱的Housner等效质量-弹簧模型,通过引入水箱体积修正参数,提出PCS水箱的三维等效质量-弹簧模型。采用有限元软件ADINA建立水箱结构流固耦合整体有限元模型以进行模态分析,计算分析PCS水箱和对应环形水箱在不同尺寸和液体深度条件下的液体晃动自振特性。对比整体有限元模型与三维等效质量-弹簧模型计算结果发现,提出的PCS水箱三维等效质量-弹簧模型能给出其内液体晃动各阶振型的液动压力合理估计值,适用于具有复杂形状的PCS水箱液动压力分析。本文的等效模型方法可推广应用于其他复杂形状水箱的液动压力分析。     

Investigation of sloshing damping in baffled rectangular tanks subjected to the dynamic excitation

In this research, an analytical model is developed to estimate the hydrodynamic damping ratio of liquid sloshing for wall bounded baffles using the velocity potential formulation and linear wave theory. Here, an analytical solution approach and experimental investigations are conducted for describing the hydrodynamic damping which is provided by vertical and horizontal baffles in partially filled rectangular liquid tanks. In order to evaluate the accuracy of the analytical solution which is developed in present work, a series of experiments are carried out with a rectangular liquid tank excited by harmonic oscillation. The parametric study is conducted on the damping efficiencies of both vertical and horizontal baffles with various dimensions and locations. According to the results of the present investigations, the hydrodynamic damping is significantly affected by the size and location of baffles. Furthermore, the validity of the developed analytical approach as well as the effectiveness of various baffle configurations are discussed. Finally, a simple approach is proposed for estimating the damping ratios of the baffles during earthquake motions.     

Investigation of nonlinear sloshing effects in seismically excited tanks

Nonlinear behavior of liquid sloshing inside a partially filled rectangular tank is investigated. The nonlinearity in the numerical modeling of the liquid sloshing originates from the nonlinear terms of the governing equations of the fluid flow and the liquid free surface motion as a not known boundary condition. The numerical simulations are performed for both linear and nonlinear conditions. The computed results using linear conditions are compared with readily available exact solution. In order to verify the results of the nonlinear numerical solution, a series of the shaking table tests on rectangular tank were conducted. Having verified linear and nonlinear numerical models, they are used for computation of near wall sloshing height at a series of real scale tanks (with various dimensions) under the both harmonic and earthquake base excitation. Finally, the nonlinear effects on liquid sloshing modeling are discussed and the practical limitations of the linear solution in evaluating the response of seismically excited liquids are also addressed.     

Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion

In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd.     

TLD控制的钢结构振动台模型试验研究

本文通过钢结构的振动台模型试验,研究了在刚性地基条件下矩形调谐流体阻尼器(TLD)对结构地震反应的减震机理和减震效果,为进一步研究土-结构相互作用对结构TLD减震控制效率影响的振动台模型试验提供对比数据。试验结果表明,在水箱中设置铁丝网有助于提高TLD的减震效率,地震动的频谱特性和峰值加速度大小对TLD的减震效率有重要影响。     

大型储液罐摩擦摆基底隔震控制分析

针对弹性钢制圆柱储液罐,基于Haroun-Housner模型,将连续流体质量等效为3种集中质量,分别为:对流质量、脉冲质量和刚性质量,与这些集中质量连接的相应刚度取值依赖于储罐壁和流体质量.在水平地震激励下,在储罐底部加摩擦单摆支座,给出了简化的液体 - 储罐-隔震支座的力学分析模型,建立了摩擦摆支座基底隔震体系的振动控制方程,并利用Newmark逐步积分法对控制方程进行了数值求解,研究了摩擦摆支座基底隔震的储液罐地震反应,验证了FPB隔震的有效性.     

The properties of tuned liquid dampers using a TMD analogy

Liquid motions in shallow Tuned Liquid Dampers (TLDs) with rectangular, circular, and annular tanks, subject to harmonic base excitation, are measured experimentally. Using a Single-Degree-of-Freedom (SDOF) Tuned Mass Damper (TMD) analogy, equivalent mass, stiffness and damping of the TLD are calibrated from the experimental results. These parameters are functions of the TLD base amplitude. Some important properties of the TLD are discussed on the basis of these results.     

Fluid–structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM–FEM and comparison with test results

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.     

TLD结构减震体系的简化计算

本文提出了ＴＬＤ结构减体系的简化计算方法,并与数值计算方法进行了比较,通过对ＴＤＬＤ结构系振动控制仿真计算结果的分析, 结论;两种计算方法的结果比较吻合。     

大连国贸大厦高层水箱风振控制研究及应用

本文针对一实际工程结构———大连国贸大厦,研究了风荷载作用下调液阻尼器的减振控制作用。首先建立了该结构的简化计算模型,利用Davenport谱给出了模拟风荷载。在大厦所处位置进行多次测量,得到实际风速样本。选取其中风速较大、过程平稳的样本,对实测样本和模拟样本的频谱进行比较,验证了模拟风荷载的合理性。文中将大厦顶层的生活水箱设计成可减小结构位移及加速度反应的控制装置TLD(tuned liqu id damper),根据不同工况进行数值计算,选出最佳方案,设计出可实际应用、并达到一定减振效果的减振水箱,以提高大厦在风荷载作用下的舒适度。     

Tuned liquid dampers simulation for earthquake response control of buildings

This paper is focused on the study of an earthquake protection system, the tuned liquid damper (TLD), which can, if adequately designed, reduce earthquake demands on buildings. This positive effect is accomplished taking into account the oscillation of the free surface of a fluid inside a tank (sloshing). The behaviour of an isolated TLD, subjected to a sinusoidal excitation at its base, with different displacement amplitudes, was studied by finite element analysis. The efficiency of the TLD in improving the seismic response of an existing building, representative of modern architecture buildings in southern European countries was also evaluated based on linear dynamic analyses.     

大跨度斜拉桥钢塔施工阶段制振用TMD、TLD装置及其性能试验

本文以南京长江第三大桥为例,研制了用于钢塔施工阶段涡激振动响应制振的制振器TMD和TLD。对制振装置以及其所采用的一些关键技术进行了说明。通过振动台试验测试了制振器的动力特性。根据试验结果,对TMD的工作性能,即装置的频率特性、阻尼特性、起动时所需的外激励水平及装置的框架刚度等,进行了评价分析;对TLD实现了其阻尼方案的优化,并确定了其工作时的阻尼隔栅状态。确认了制作完成的制振器具有良好的工作性能。     

Sloshing analysis of rectangular tanks with a submerged structure by using small-amplitude water wave theory

A new sloshing analysis method for rectangular tank systems with a submerged structure are proposed by using the velocity potential and the linear water wave theory. The velocity potential functions are obtained by decomposing the surface wave into a wall-induced wave, reflected and transmitted waves, and a scattered wave. A simplified method using a response spectrum for zero damping is also proposed. The results of the simplified method are in good agreement with those of the analytical method. The sloshing response of the fluid-structure system is found to be very sensitive to the characteristics of the ground motion and the configuration of the system. Under typical earthquakes, the submerged structure shows a tendency to decrease sloshing amplitude, hydrodynamic pressure, and base shear, while it shows a tendency to increase the overturning moment. For the ground excitation dominated by low-frequency contents, the sloshing response increases significantly and the contribution of the higher sloshing modes increases. Copyright © 1999 John Wiley & Sons, Ltd.     

Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations

A numerical and experimental study on the sloshing behaviours of cylindrical and rectangular liquid tanks is addressed. A three‐dimensional boundary element method for space with the second‐order Taylor series expansion in time is established to simulate the sloshing phenomenon and its related physical quantities inside a liquid tank subjected to horizontal harmonic oscillations or recorded earthquake excitations. The small‐scale model experiments are carried out to verify some results of numerical methods in this study. The comparisons between numerical and experimental results show that the numerical method is reliable for both kinds of ground excitations. Finally, the water wave and the base shear force of a rectangular tank due to harmonic excitation are also presented at different frequencies. A huge cylindrical water tank subjected to a recorded earthquake excitation is used for application and discussion. Copyright © 2007 John Wiley & Sons, Ltd.     

水平地震激励下储罐液体晃动与提离分析

在考虑地基与储罐相互作用的情况下,采用有限元法对储罐在水平地震荷载作用下的液面晃动及储罐提离反应进行了分析。结果表明:罐内液体的晃动是长周期运动,其周期受地震动影响。无论是小体积罐还是大体积罐,在一定的地震烈度下均可以发生提离,而且储罐发生提离的时刻大多数是在地震动的峰值过后的一段时间内。大体积的储罐的提离明显小于小体积的罐。底板提离区域为月牙形。     

Sloshing response of layered liquids in rigid tanks

The sloshing action of layered liquids in rigid cylindrical and long rectangular tanks is investigated, considering both their free vibrational characteristics and their response to a horizontal component of base shaking. Special attention is given to the maximum surface displacement induced by the base motion. The analysis is formulated for systems with N superimposed layers of different thicknesses and densities, and is illustrated by a numerical example. In addition, comprehensive numerical data are presented for two-layered and some three-layered systems which elucidate the underlying response mechanisms and the effects and relative importance of the numerous parameters involved. It is shown that for each horizontal natural mode of vibration, there are N distinct vertical modes, the frequencies of which are lower than the natural frequency of a homogeneous liquid of the same total depth. It is further shown that the maximum surface sloshing displacement of the base-excited layered system is typically larger than that of the corresponding homogeneous system, and that the results for the long rectangular and cylindrical tanks are quite similar.     

On the seismic behavior of cylindrical base-isolated liquid storage tanks excited by long-period ground motions

A common effective method to reduce the seismic response of liquid storage tanks is to isolate them at base using base-isolation systems. It has been observed that in many earthquakes, the foregoing systems significantly affect on the whole system response reduction. However, in exceptional cases of excitation by long-period shaking, the base-isolation systems could have adverse effects. Such earthquakes could cause tank damage due to excessive liquid sloshing. Therefore, the numerical seismic response of liquid storage tanks isolated by bilinear hysteretic bearing elements is investigated under long-period ground motions in this research. For this purpose, finite shell elements for the tank structure and boundary elements for the liquid region are employed. Subsequently, fluid–structure equations of motion are coupled with governing equation of base-isolation system, to represent the whole system behavior. The governing equations of motion of the whole system are solved by an iterative and step-by-step algorithm to evaluate the response of the whole system to the horizontal component of three ground motions. The variations of seismic shear forces, liquid sloshing heights, and tank wall radial displacements are plotted under various system parameters such as the tank geometry aspect ratio (height to radius), and the flexibility of the isolation system, to critically examine the effects of various system parameters on the effectiveness of the base-isolation systems against long-period ground motions. From these analyses, it may be concluded that with the installation of this type of base-isolation system in liquid tanks, the dynamic response of tanks during seismic ground motions can be considerably reduced. Moreover, in the special case of long-period ground motions, the seismic response of base-isolated tanks may be controlled by the isolation system only at particular conditions of slender and broad tanks. For the case of medium tanks, remarkable attentions would be required to be devoted to the design of base-isolation systems expected to experience long-period ground motions.