The effect of axial inertia on the bending eigenfrequencies of a timoshenko two-bar frame

The equations of free lateral vibrations of a uniform Timoshenko two-bar frame including the effects of axial motion and joint mass with its rotational inertia are presented. The influence on the flexural eigenfrequencies of the axial motion alone or in combination with other parameters is fully assessed and thoroughly discussed. These parameters are: the translational and rotational inertia of the joint mass, the transverse shear deformation and rotatory inertia, the length, stiffness and slenderness ratios of the two bars of the frame. The variety of numerical results presented herein leads to the important finding that for framed structures the effect of axial inertia on the flexural eigenfrequencies alone or in combination with the foregoing parameters may be considerable. In particular, if the joint mass should be accounted for, the foregoing effect cannot be ignored, since it leads, in general, to considerable errors even for frames with relatively slender bars.     

钢筋混凝土空心桥墩的振动台试验研究

为研究空心桥墩的抗震性能及影响参数,对9个不同配筋率、配箍率和轴压比的试件进行振动台试验。研究了不同性能量化参数对破坏现象、加速度响应、动力放大系数、延性和耗能等的影响。结果表明:轴压比和配筋率较小时,裂缝开展较多且位置距墩底相对偏高。增大配筋率,加速度响应、动力放大系数和位移延性系数增大,耗能减小;轴压比的影响与配筋率相反。增大配箍率,加速度响应和动力放大系数减小,位移延性系数和试件耗能增大。可为矩形空心桥墩的抗震设计提供参考。     

Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system

With the aid of the analytical layer-element method, a comprehensive analytical derivation of the response of transversely isotropic multilayered half-space subjected to time-harmonic excitations is presented in a cylindrical coordinate system. Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the Fourier expansion, Hankel and Laplace integral transform, analytical layer-elements for a finite layer and a half-space are derived. Considering the continuity conditions on adjacent layers׳ interfaces and the boundary conditions, the global stiffness matrix equations for multilayered half-space are assembled and solved. Finally, some numerical examples are given to make a comparison with the existing solution and to demonstrate the influence of parameters on the dynamic response of the medium.     

Wave-induced dynamic response of saturated multi-layer porous media: Analytical solutions and validity regions of various formulations in non-dimensional parametric space

In this paper, dynamic response of saturated-layered porous media under harmonic waves is evaluated through a semi-analytical solution. The coupled differential equations governing the dynamics of saturated or nearly saturated porous media such as soils containing all the inertial terms of solid and fluid phases are presented for a multi-layer system. Possible simplifications of the equations which are called formulations are introduced based upon the presence of inertial terms associated with the phases. The semi-analytical solutions to the response of multiple layers for all the formulations are presented in terms of pore water pressure and stress variations considering a set of non-dimensional parameters and their respective ratios. Validity of the formulations is presented in a non-dimensional parametric space. The maximum discrepancies in the pore pressure response of the formulations leading to validity regions are illustrated for typical dynamic problems. Subsequently, the effects of layering and drainage conditions on these regions are also presented. The proposed semi-analytical solution may be served as a benchmark one for validating the coupled numerical solutions, which can be used to deal with real scientific and geo-engineering problems in the emerging field of computational geomechanics.     

土的动剪切模量、阻尼比和泊松比研究进展

介绍了现场测试与实验室测试土的最大动剪切模量的差别、动剪切模量和阻尼比与剪应变关系的表达式及其地区经验成果、固结比对最大动剪切模量影响、动泊松比研究、实验误差及其对地震动的影响等方面的主要成果。提出应加强动泊松比研究,加强共振柱和动三轴试验土动力学参数统一的数学模型研究,加强土动力学参数在均等固结与非均等固结条件下关系研究,加强土动力学参数与土的常规物理力学性质指标关系研究和土动力学参数实验误差研究。     

SLIDING SYSTEM PREDICTING LARGE PERMANENT CO-SEISMIC MOVEMENTS OF SLOPES

The sliding-block model is used widely for the prediction of permanent co-seismic displacements of slopes and earth structures. This model assumes motion in an inclined plane but does not consider the decrease in inclination of the sliding soil mass as a result of its downward motion, which is the usual state in the field. For the investigation of the above effect, this paper considers the dynamic motion of a variant sliding system; a perfectly flexible chain sliding along planes with gradually gentler inclinations. The governing equation of motion of the new model is approximately derived and solved for a number of earthquakes. The cases of ground slips where the permanent displacement of the new model differs considerably from that of the sliding-block model are detected and an improved method predicting permanent seismic deformations is proposed.     

三维地震波速结构约束下的变黏度地幔对流及其动力学意义

建立了三维黏度扰动下的变黏度地幔对流模型,并提供了在引入地幔的三维地震波速度结构下相应的求解方法. 依此反演了瑞利数Ra = 106时,两种不同边界条件下的极、环型场对流图像,这有助于深化对地幔物质流动和大地构造运动的深部动力学过程的认识和理解. 研究结果表明,不但地幔浅部的极型场对流图像显示出了与大地构造运动的相关性并揭示了其深部动力学过程,更重要的是,地幔浅部的环型场对流图像首次为我们认识和理解板块构造的水平与旋转运动提供了重要的信息：环型场速度剖面中在赤道附近存在一条大致南东东—北西西向的强对流条带,可能与环赤道附近大型剪切带的形成相关,进而表明可能是该带强震发生的深部动力学背景;在南北半球存在的旋转方向相反的对流环表明它们整体上可能存在差异旋转.     

Parametric analysis of liquid storage tanks base isolated by curved surface sliding bearings

Curved surface sliding bearings, which are usually called as friction pendulum system (FPS) are commonly used for base isolation of liquid storage tanks since the period of the isolation system is independent of the storage level. However the restoring force and the damping at the isolation system are functions of axial load which changes during an earthquake excitation. This change might be in appreciable amounts especially for the tanks with high aspect ratios. The present paper focuses on earthquake performances of both broad and slender tanks base isolated by FPS bearings. The effects of overturning moment and vertical acceleration on axial load variation at the bearings are considered. The efficiency of the isolation system is investigated by analyzing the effects of various parameters such as; (i) isolation period, (ii) tank aspect ratio and (iii) coefficient of friction. The Haroun and Housner's three-degrees-of-freedom lumped mass model was used to solve the governing equations of motion in which convective, impulsive and rigid masses were included. A number of selected ground motions were considered and the results were compared to those of non-isolated cases.As a result, base isolation was found to be effective in reducing the base shear values for both broad and slender tanks without significantly affecting the sloshing displacements of the broad ones. The efficiency was even more pronounced for slender tanks subjected to near fault ground motions for isolation periods above 3 s. This specific value of isolation period also eliminated possible design problems arising from under-estimation of base shear values (up to 40%) due to ignoring the effects of axial load variation in lower isolation periods. Overturning effects should not be ignored especially for tanks with high aspect ratios (S) and being subjected to near fault ground motion.     

Modelling hysteretic behaviour of coupled walls for dynamic analysis

Modelling techniques for dynamic inelastic response analysis of coupled wall structures are investigated. Emphasis is placed on effects of parameters defining the force-displacement hysteresis loop. Specifically, effects of axial force-moment interaction, strength reduction, shear yielding, pinching, reloading and unloading branches of hysteresis loops are considered. Effects of modelling parameters on selected response quantities are investigated and discussed in detail. A 20-storey coupled wall structure was selected for dynamic analysis. Ranges of parameters characterizing force-displacement hysteresis loops were obtained from laboratory tests under slowly reversed static loading. Previously recorded strong motion accelerograms were used as input motions. Results indicate that wall axial forces and beam strength reduction can have significant effects on response envelopes. Moderate variations in unloading and reloading branches of hysteresis loops and pinching appear to have little effect on dynamic response.     

凸起地形对地震动特性的影响

采用基于ABAQUS平台的显式有限元动力学分析方法,结合人工黏弹性边界理论,研究了局部凸起地形对地震动特性(包括反应谱、峰值加速度、峰值速度和峰值位移等)的影响,分析了台地宽度对地形放大效应的影响.结果表明:凸起地形平台段空间点地震动受地形效应影响较大,在零阻尼条件下,其谱比曲线呈双峰特点,.8—0.9s的中长周期段谱比达到一个较大值1.6,在0.08—0.09s的高频段谱比超过2.0,且最大值出现在平台中点;对于凸起地形斜坡段,在大部分周期点处,顶点的谱比高于其它斜坡点,而且在周期超过0.4s的频段,斜坡段观测点的谱比表现出较明显的规律性,即越靠近顶点的观测点,其谱比值越大;坡底段地表不同观测点的谱比基本在脚点与计算边界点(人工边界点)对应的谱比值之间变化,在不同的频段均表现出较明显的规律性.凸起地形平台段宽度对地震动高频成分的放大效应具有较大影响,但只局限在一定的宽度范围内,随着宽度的增大,其对地形放大效应的影响逐渐减弱. 此外,台地宽度的变化对地震动峰值加速度的放大效应有一定的影响,而对峰值速度、峰值位移的放大效应的影响则不明显.      

Vertical dynamic response of a disk on a saturated poroelastic half-space

This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform.     

Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space

Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the global stiffness matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the global stiffness matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.     

Simplified lateral free field boundary based on a lumped mass system

After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions, the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms. First, the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary. Second, typical examples were implemented using the finite element software ABAQUS. The incident shear wave was taken to be perpendicular to the bottom to verify the effectiven...     

Optimization of the seismic response of bridges using variable-width joints

An aspect of seismic design of bridges that has hardly received proper attention so far is the appropriate selection of joint gaps. End gaps define the boundary conditions of the bridge and affect its dynamic response; their proper design can lead to an improved structural performance under dynamic actions. The idea of the ‘Dynamic Intelligent Bridge’ is explored here, wherein current bridge joints that have a fixed width are substituted by variable-width joints and, under seismic loading, the joint gap is optimised either with a one-off adjustment, or continuously (in real time) through semi-active control. In all cases, a novel device is used that permits this improved behaviour of the joints, the moveable shear key (MSK), a device for blocking the movement of the bridge deck, which has the possibility to slide, hence varying the size of the existing joint gap. In this context, the effect of gap size on the seismic response of bridges is assessed herein and a methodology is put forward for optimising this size, using a number of criteria such as maintaining the functionality of the bridge for moderate earthquakes, and ensuring the safety of the bridge and its users under earthquakes stronger than that used for design.     

A simplified seismic analysis of rigid base liquid storage tanks under vertical exicitation with soil-structure interaction

A study is carried out to evaluate dynamic response of an elastic circular cylindrical tank having a rigid base under a vertical excitation taking into consideration the interaction with the foundation soil. At first, the soil is represented by frequency-independent parameters. Two coupled differential equations, governing the motion of the shell and the base, are solved using a step by step integration technique. The hydrodynamic pressures, acting on the shell and on the base, are derived from a velocity potential function which satisfies the Laplace equation and the appropriate boundary conditions. The response of the simplified model of a tank having a rigid base on a stiff foundation soil is compated to that obtained elsewhere to check the accuracy of the present model. Reasonable agreement is found between the maximum wall displacement and the associated stresses with those found by a more elaborate model. The interaction of the tank and the soil reduces the response than that calculated under the assumption of a rigid foundation soil. A parametric study to examine the effects of the height-to-radius ratio of the tank, and the effects of the shear wave velocity of the soil on the response is conducted. Varieties of foundation models are used to assess the sensitivity of the response to the variation in the soil parameters. Finally, a more representative solution for the problem in the frequency domain is obtained where the soil is appropriately modelled by frequency-dependent parameters. The transfer functions of the response of the tank wall and of the relative base motion are evaluated, and a comparison between the frequency-dependent and the frequency-independent solutions is made.     

考虑流固耦合的桥墩地震反应方法

跨海桥梁地震反应中,作用于桥墩上的动水压力具有明显的流固耦合特征。依据张量理论,推导时变区域散度变换关系及微分形式的几何守恒律;基于任意拉格朗日一欧拉描述,从采用欧拉描述的流体运动Navier—Stokes方程出发,推导时变区域的流体运动控制方程;给出流固耦合问题中的结构计算模型、耦合面接触条件、耦合场计算方法以及流场网格运动控制方法。以某跨海大桥为例说明桥墩地震反应方法,重点突出地震动输入、流场初始条件模拟等问题。计算结果表明：流固耦合理论能够模拟桥梁墩台地震反应中的流场和结构特性;流场初始条件的正确模拟可保证计算稳定性,并减少运算量;横向地震动激励下,桥墩基底剪力较大,纵向地震动激励下,结构运动剧烈;流固耦合系统中的线弹性结构在地震反应中具有明显的非线性特征。     

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study, the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated. The boundary conditions and properties of each beam vary, and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations. By examining a high-speed railway (HSR) with mixed boundary conditions, the rationality for the newly proposed method is verified, the difference in simulated multiple-beam models with different beam numbers is explored, and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined. Results suggest that the number of beams in the model should be as close to the actual beam number as possible. Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure. Neglecting the track-structure can overestimate the resonant speed of a high-speed railway, simply-supported beam bridge. The effective interval of foundation stiffness (EIFS) can provide a reference for future engineering designs.

     

Simple formulations of ground impedance functions for rigid surface foundations

A differential equation is formulated for the dynamic response of ground medium by using a simplified ground model. Applying Galerkin's procedure for weighted residual, this equation leads to a governing equation only at the ground surface. The equation indicates that the ground surface behavior can be computed even further by a simplified model. By solving the governing equation for the boundary conditions along the surface, expressions in simple closed forms are developed for the dynamic response analysis of a massless rigid foundation that rests on the ground surface. Despite their significant simplicity, the developed expressions compute the values very close to those computed by far more complex rigorous solutions. They are found to be capable of capturing the important characteristics of the dynamic ground behavior well.     

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.     

Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion

This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.