Dynamics of towers surrounded by water

The effects of interaction with surrounding water on the dynamic response behaviour of cantilever tower structures are studied. Expressions for response to harmonic ground motion in individual modes of vibration, including hydrodynamic interaction, are presented, the accuracy of responses obtained by ignoring surface waves and compressibility of water in the hydrodynamic solutions is evaluated, the effects of hydrodynamic interaction on the fundamental period of vibration are studied and the commonly used ‘added mass’ approach to account for effects of surrounding water is examined. The conclusions deduced from the results of this investigation include the following. Interaction with surrounding water increases the fundamental period of vibration of the tower and decreases the modal damping ratio. Compressibility of water has essentially no influence in the hydrodynamic effects on slender towers. The traditional definition of added mass is conceptually deficient, but is simple to employ; the errors in this simple added mass representation are negligible for the first mode of vibration of towers.     

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.     

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.     

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.     

Effects of reservoir bottom absorption on earthquake response of concrete gravity dams

A procedure is presented to analyse the response of concrete gravity dams due to horizontal and vertical earthquake ground motion components considering dam-water interaction and partial absorption of hydrodynamic pressure waves at the reservoir bottom into the foundation medium. The effects of reservoir bottom absorption on the hydrodynamic force on a rigid dam are examined first. The harmonic response of an idealized dam cross-section is presented for a wide range of parameters characterizing the properties of the dam, the impounded water and the foundation medium. Based on these frequency response functions the effects of dam-water interaction and of reservoir bottom absorption in the response of dams due to horizontal and vertical components of ground motion are investigated.     

Seismic response of offshore structures in random seas

A study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil-structure interaction effects and also on the evaluation of non-linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi-Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency-domain random vibration approach. It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil-structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.     

On tuned mass dampers for reducing the seismic response of structures

This paper presents an energy‐based theoretical model for a two degree‐of‐freedom mechanical system. After a general formulation in Appendix A, the model is specialized to study tuned mass dampers as a means to substantially increase modal damping in order to induce a consequential decrease of the seismic response of the structures thus provided. Although approximate since it neglects coupling due to damping, it is shown that the model yields a first‐order approximation to the exact frequencies, providing values of optimum damping that closely match exact results proposed by others. In view of this, it is proposed that the model be applied through an iterative numerical procedure that identifies the pertinent optimum parameters. It is also shown that for certain particular benchmark cases the model provides closed‐form equations for the parameters defining the dynamic states related to these special conditions. Despite its approximate nature the model presented in this paper is rational, and due to its explicit consideration of energy balance and overall simplicity, it provides a convenient platform for the study of tuned mass dampers, as well as for other methods of structural passive control. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

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.     

Spring tube braces for seismic isolation of buildings

A new low-cost seismic isolation system based on spring tube bracings has been proposed and studied at the Structural and Earthquake Engineering Laboratory of Istanbul Technical University. Multiple compression-type springs are positioned in a special cylindrical tube to obtain a symmetrical response in tension and compression-type axial loading. An isolation floor, which consists of pin-ended steel columns and spring tube bracings, is constructed at the foundation level or any intermediate level of the building. An experimental campaign with three stages was completed to evaluate the capability of the system. First, the behavior of the spring tubes subjected to axial displacement reversals with varying frequencies was determined. In the second phase, the isolation floor was assessed in the quasi-static tests. Finally, a ¼ scaled 3D steel frame was tested on the shake table using actual acceleration records. The transmitted acceleration to the floor levels is greatly diminished because of the isolation story, which effects longer period and higher damping. There are no stability and self-centering problems in the isolation floor.     

Modal decomposition method for stationary response of non-classically damped systems

The stationary response of multi-degree-of-freedom non-classically damped linear systems subjected to stationary input excitation is studied. A modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used to derive general expressions for the spectral moments of response. These expressions are in terms of cross-modal spectral moments and explicitly account for the correlation between modal responses; thus, they are applicable to structures characterized with significant non-classical damping as well as structures with closely spaced frequencies. Closed form solutions are presented for the important case of response to white-noise input. Various quantities of response of general engineering interest can be obtained in terms of these spectral moments. These include mean zero-crossing rate and mean, variance and distribution of peak response over a specified duration. Examples point out several instances where non-classical damping effects become significant and illustrate the marked improvement of the results of this study over conventional analysis based on classical damping approximations.     

Morison方程中动水阻力项对桥梁桩柱地震反应的影响

深水桥梁地震反应计算时,当采用Morison公式考虑水的作用时,增加了一个附加惯性项和一个附加阻尼项,其中附加阻尼项是非线性的。由于非线性附加阻尼项的存在,给采用反应谱方法求解桥梁的地震反应带来不便。讨论了非线性阻尼项对一般桥梁桩、墩结构地震反应的贡献,得到的结论是阻尼项的贡献很小,可以忽略。从而水中桥梁地震反应的计算就得到了很大的简化。     

Investigation of seismic behavior of fluid–rectangular tank–soil/foundation systems in frequency domain

Main purpose of this study is to evaluate the dynamic behavior of fluid–rectangular tank–soil/foundation system with a simple and fast seismic analysis procedure. In this procedure, interaction effects are presented by Housner's two mass approximations for fluid and the cone model for soil/foundation system. This approach can determine; displacement at the height of the impulsive mass, the sloshing displacement and base forces for the soil/foundation system conditions including embedment and incompressible soil cases. Models and equations for proposed method were briefly explained for different tank–soil/foundation system combinations. By means of changing soil/foundation conditions, some comparisons are made on base forces and sloshing responses for the cases of embedment and no embedment. The results showed that the displacements and base shear forces generally decreased, with decreasing soil stiffness. However, embedment, wall flexibility, and soil–structure interaction (SSI) did not considerably affect the sloshing displacement.     

Errors in response calculations for non-classically damped structures

The classical normal mode method of determining response is extremely useful for practical calculations, but depends upon the damping matrix being orthogonal with respect to the modal vectors. Approximations that allow the method to be used when this condition is not satisfied have been suggested; the simplest approach is to neglect off-diagonal terms in the triple matrix product formed from the damping and modal matrices. In this paper the errors in response caused by this approximation are determined for several simple structures for a wide range of damping parameters and different types of excitation. Based on these results a criterion, relating modal damping and natural frequencies, is formulated; if this is satisfied, the errors in response caused by this diagonalization procedure are within acceptable limits.     

Seismic response of intake towers including dam–tower interaction

The seismic response of the intake–outlet towers has been widely analyzed in recent years. The usual models consider the hydrodynamic effects produced by the surrounding water and the interior water, characterizing the dynamic response of the tower–water–foundation–soil system. As a result of these works, simplified added mass models have been developed. However, in all previous models, the surrounding water is assumed to be of uniform depth and to have infinite extension. Consequently, the considered added mass is associated with only the pressures created by the displacements of the tower itself. For a real system, the intake tower is usually located in proximity to the dam and the dam pressures may influence the equivalent added mass. The objective of this paper is to investigate how the response of the tower is affected by the presence of the dam. A coupled three‐dimensional boundary element‐finite element model in the frequency domain is employed to analyze the tower–dam–reservoir interaction problem. In all cases, the system response is assumed to be linear, and the effect of the internal fluid and the soil–structure interaction effects are not considered. The results suggest that unexpected resonance amplifications can occur due to changes in the added mass for the tower as a result of the tower–dam–reservoir interaction. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic design of yielding structures on flexible foundations

This paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.     

LARGE AMPLITUDE LIQUID SLOSHING IN SEISMICALLY EXCITED TANKS

An innovative method of analysis was developed to simulate the non-linear seismic finite-amplitude liquid sloshing in two-dimensional containers. In view of the irregular and time-varying liquid surface, the method employed a curvilinear mesh system to transform the non-linear sloshing problem from the physical domain with an irregular free-surface boundary into a computational domain in which rectangular grids can be analysed by the finite difference method. Non-linearities associated with both the unknown location of the free surface and the high-order differential terms were considered. The Crank–Nicolson time marching scheme was employed and the resulting finite difference algorithm is unconditionally stable and very lightly damped with respect to the temporal co-ordinate. In order to minimize numerical instability caused by the computational dispersion in spatially discretized surface wave, a second-order dissipation term was added to the system to filter out the spurious high-frequency waves. Sloshing effects and structural response were measured in terms of sloshing amplitude, base shear and overturning moment generated by the hydrodynamic pressure of the liquid exerted on the container walls. Simulation results of liquid sloshing induced by earthquake and harmonic base excitations were compared with those of the linear wave theory and the limitations of the latter in assessing the response of seismically excited liquids were addressed.     

Modal damping for torsionally coupled buildings on elastic foundation

A method to determine the approximate normal modes and the modal damping for torsionally coupled buildings on an elastic foundation is presented. The modal damping is determined by an iterative procedure which matches the approximate normal mode solution with the rigorous solution. The response quantity to be matched is selected in a consistent and logical manner. The normal modes and the damping ratios thus found are then used to determine the seismic response of the interaction system by the response spectrum technique.     

巨型框筒部分悬挂结构控制体系地震反应特性及阻尼控制研究

本文提出巨型框筒部分悬挂结构新体系，研究这种结构体系对地震反应特性，提出用阻尼器进行巨型框筒部分悬挂体系地震反应的控制方法，采用结构动力学有限元方法，建立空间分析模型，对结构体系进行地震随机振动分析、时程分析和地震反应谱分析。分析结果表明，这种结构体系能有效地减小结构的地震响应，最后研究了影响控制效果的主要因素及控制器参数的影响规律。     

Seismic design and evaluation of steel moment‐resisting frames with compressed elastomer dampers

This paper evaluates the hysteretic behavior of an innovative compressed elastomer structural damper and its applicability to seismic‐resistant design of steel moment‐resisting frames (MRFs). The damper is constructed by precompressing a high‐damping elastomeric material into steel tubes. This innovative construction results in viscous‐like damping under small strains and friction‐like damping under large strains. A rate‐dependent hysteretic model for the compressed elastomer damper, formed from a parallel combination of a modified Bouc–Wen model and a non‐linear dashpot is presented. The model is calibrated using test data obtained under sinusoidal loading at different amplitudes and frequencies. This model is incorporated in the OpenSees [17] computer program for use in seismic response analyses of steel MRF buildings with compressed elastomer dampers. A simplified design procedure was used to design seven different systems of steel MRFs combined with compressed elastomer dampers in which the properties of the MRFs and dampers were varied. The combined systems are designed to achieve performance, which is similar to or better than the performance of conventional steel MRFs designed according to current seismic codes. Based on the results of nonlinear seismic response analyses, under both the design basis earthquake and the maximum considered earthquake, target properties for a new generation of compressed elastomer dampers are defined. Copyright © 2011 John Wiley & Sons, Ltd.