Ambient vibration test of an anchorage of South Bisan-seto suspension bridge

Dynamical properties of an anchorage of South Bisan-seto Suspension Bridge are determined by means of in situ measurement of the ambient vibrations. This anchorage, being located in the sea, is tall and slender; its natural frequencies are expected to be low. On the other hand, the elasticity of the ground estimated from the conventional geological data is highly dispersed. It even suggests the possibility of resonance between the towers and this anchorage. It is therefore necessary to know its natural frequencies precisely. Seismic motions and microtremors are acquired and used properly. The observation is repeated every year during the period of construction of the anchorage so that its inertial properties change significantly. First modes of the longitudinal and the transversal vibrations of the anchorage are identified and their frequencies determined. The elasticity modulus estimated from these natural frequencies is about five times as large as that of the geological survey while it is consistent with that obtained from the velocity of the elastic waves of the ground.     

含软弱夹层岩质边坡的模态分析及其对边坡地震动力响应影响的初步研究

本文以含软弱夹层岩质边坡作为研究对象,基于数值软件ANSYS的模态分析给出了含不同倾角与厚度软弱夹层边坡的前5阶固有频率与振型,并分析了夹层倾角和厚度对边坡固有模态的影响。接着,结合已有的大型振动台模型试验结果,在小应变范围内讨论了边坡的固有模态与其动力响应特性之间的关系。结果表明:(1)在夹层倾角相同时,含较厚软弱夹层边坡固有频率低于含较薄软弱夹层边坡;(2)在夹层厚度相同时,随着倾角增加,夹层从反倾变化到顺倾,低阶(1、2)固有频率也逐渐增加,而高阶(3、4、5)固有频率则呈下降趋势;(3)从第3、4阶开始,边坡变形受夹层影响增强;(4)基于加速度傅里叶谱比分析得出的边坡响应放大频率与边坡前5阶固有频率范围接近,加速度和位移响应在夹层及以上部位响应强烈,与边坡前5阶振型较为一致,预示了边坡的共振响应。需要指出的是,本文得出的结论尚且不能用于准确解释边坡在大变形及破坏阶段的动力响应特征,但可为边坡动力特性及共振响应的深入研究提供思路。     

Vibration tests and analysis of a model arch dam

Vibration tests were conducted on a 1/24-scale model of the North Fork Dam, a double-curvature arch dam, to determine natural frequencies, mode shapes and hydrodynamic pressures. The mode shapes and natural frequencies were determined from tests using two vibrators mounted on the crest of the dam. Hydrodynamic pressures at the dam/reservoir interface were determined from tests in which the vibrator was attached to the downstream foundation of the dam. The hydrodynamic pressures calculated using Westergaard's theory and a theory for arch dams developed by Perumalswami and Kar accurately predicted the measured pressure at frequencies below the first mode frequency of the dam. The differences in the two theories were insignificant. The Structural Analysis Program (SAP), a linear three-dimensional (3-D) finite element code, was used to compute mode shapes and frequencies for the dam with its base fixed and with a foundation. Numerical solution schemes used in the finite element analysis consisted of a Ritz analysis and a subspace iteration method. Calculations were conducted for both full and empty reservoir conditions. The accuracy of the Ritz analysis improved considerably as more nodes in flexible regions of the dam were loaded. However, the lowest eigenvalues were computed using the subspace iteration method. For the full reservoir, the natural frequencies decreased by 20-30 per cent when the foundation was included in the finite element model. The difference was less when the reservoir was empty. The calculations using the subspace iteration scheme and including the foundation agreed closely with experimental mode shapes and corresponding natural frequencies.     

Vibration analysis of steel structures including the effect of panel zone flexibility based on the energy method

New approximate formulas are proposed to determine the natural frequencies of structures considering the effects of panel zone flexibility and soil-structure interaction. Several structures with various earthquake resisting systems are idealized as prismatic cantilever flexural-shear beams. Floor masses are considered as lumped masses at each story level and masses of columns are evenly distributed along the cantilever beam. Soil-structure interaction is considered as axial and rotational springs, whose potential energy are formulated and incorporated into overall potential energy of the structure. Subsequently, natural frequency equations are derived on the basis of energy conservation principle. The effect of axial forces on natural frequency is also considered in the proposed formulas. Using the method presented in this study, natural frequencies are computed using a simplified method with no complex numerical modeling. The proposed formulas are verified via experimental and numerical methods. Close agreement between the results from these three approaches are observed. Furthermore, the effects of panel zone flexibility, continuity plates and doubler plates on the natural frequencies of buildings are investigated.     

Vibration studies and tests of a suspension bridge

The natural frequencies of the San Pedro-Terminal Island Suspension Bridge were fairly accurately determined by measuring traffic-excited vertical vibrations with sensitive seismometers mounted at various locations on the bridge. The Fourier amplitude spectrum of the recorded vertical movements was computed and plotted. The measurements revealed a wide band of natural frequencies. The results for the vertical and torsional natural frequencies were correlated with the computed frequencies. The results of the field measurements showed reasonable agreement with the computed values. Finally, further recommendations toward obtaining better results were also indicated.     

功能梯度复合材料圆柱壳固有频率解

本文建立了功能梯度复合材料圆柱壳的基本动力方程，给出了各类功能梯度复合材料圆柱壳固有频率的一般解析解法，并具体导出了两端简支功能梯度圆柱壳各阶固有频率解的解析表达式，十分简明、实用。     

Asymptotic formulae for correcting finite element predicted natural frequencies of gravity and embankment dams

Extraction of natural frequencies of a gravity dam or an embankment dam plays an important role in the seismic design of the dam because the seismic response of a dam is dependent largely on the dynamic characteristics of the dam. Owing to the lack of exact solutions and the geometry of a dam, numerical methods such as finite element methods have been often used to extract the natural frequencies of the dam. Since the finite element method is an approximate one, the resulting finite element solution to the natural frequency of a dam cannot be safely used unless its accuracy is evaluated within the acceptable range for the seismic design of the dam. To solve this problem, some asymptotic formulae for correcting the finite element predicted natural frequencies of a gravity dam and an embankment dam have been developed in this paper. Since the present asymptotic formulae are derived from the fact that the finite element solution tends to the exact one if the finite element size used approaches zero, they provide a corrected solution of higher accuracy for the natural frequency of a dam so that the accuracy of a finite element solution can be evaluated against this corrected solution. After the correctness and usefulness of the present formulae are assessed, two practical examples have been given to show how the asymptotic formulae can be used to correct and evaluate the discretization error for the finite element predicted natural frequencies of gravity dams and embankment dams.     

Determination of scoured bridge natural frequencies with soil–structure interaction

This study developed a finite element method with the effect of soil–fluid–structure interaction to calculate bridge natural frequencies. The finite element model includes bridge girders, piers, foundations, soil, and water. The effective mass above the soil surface was then used to find the first natural frequency in each direction. A field experiment was performed to validate that the natural frequencies calculated using the proposed finite element method had acceptable accuracy. The calculated natural frequencies with the fluid–structure interaction effect are always smaller than those without this effect. However, the frequency change due to the fluid effect is not obvious, so using the soil–structure interaction model is accurate enough in the bridge natural frequency analysis. The trend of the frequency decreases with the increase of the scour depth, but the curve is not smooth because of non-uniform foundation sections and layered soils. However, when the scour depth is such that pile cap is exposed, the changes in natural frequency with the scour depth are more obvious, and this is useful for measurement of the depth using bridge natural frequencies.     

In-plane free vibration of supported/free parabolic cables

The free-vibration analysis of parabolic cables fixed at the lower end and free to move in the horizontal direction at the upper end is performed. The dynamic stiffness of such cables is zero at the natural frequencies and this property is used to obtain the governing frequency equation. Double-frequency points at which two consecutive natural frequencies are identical occur for specific values of stiffness parameters. Expressions for the natural modes of vibration and for the contribution of the extensional and inextensional cable resistances to the modal potential energy are given.     

Accuracy and improvement of natural frequency prediction using component mode synthesis

This paper is concerned with establishing error bounds on natural frequencies of a discrete structural model using the MacNeal–Rubin Component Mode Synthesis (CMS) method. A method is proposed whereby lower bounds to natural frequencies of a finite element model with compatible elements can be obtained after upper bounds have been calculated with the CMS technique. This method uses the idea that the inertial contribution from the neglected high frequency component modes can be expressed as a function of a residual approximation frequency. Increasing the residual approximation frequency raises the effective inertia added to the system, which in turn decreases the system natural frequencies. The technique is formulated for discrete, undamped systems, and is applied to finite element models of a beam and a container ship. It is also shown that for a particular mode of the system, estimates of the residual approximation frequency can be improved using Newton's method. Thus, a frequency determined with CMS can be steadily improved until it converges to the frequency of the model. Numerical results for the finite element models indicate that convergence is fast, even when the initial error is large.     

Vibration of beams on partial elastic foundations

The natural response of a beam or pile having only a portion of its span supported by an elastic foundation is investigated for the two cases when both ends are either simply supported or free. The derivation of the shape functions and the computed natural frequencies are compared with the extreme cases where the element is either completely supported by, or fully detached from, the elastic foundation.     

Approximate natural frequencies for coupled shear walls

An approximate yet accurate formula is proposed for the natural frequencies of coupled shear walls under continuous medium assumptions. First the deflected shape of the structure is represented as the sum of two components: one due to flexural cantilever action and one due to shear-flexure cantilever action. The natural frequencies of the latter two systems are then combined in Dunkerley's formula to yield the approximate frequency of the structure.     

Dynamic response of a staggered wall-beam structure

A method for the dynamic analysis of staggered wall-beam frames is developed using consistent mass terms which are derived and given in simple terms. The method uses effective stiffnesses for wall-beam elements developed in an earlier paper. Experiments using a nine storey 1 : 15 scale perspex model are described. The first three natural frequencies of the model were obtained using two methods: sinusoidal external excitation of the structure with the base fixed and white noise excitation employing a single degree-of-freedom shake table, in the latter method with and without the addition of mass throughout the model. Agreement between analytical predictions of the first three natural frequencies and mode shapes and experimentally determined values is considered satisfactory, particularly for the first two modes. The lumped mass assumption gave reasonable results for these two cases, whereas the consistent mass theory gave reasonable results for the first three natural frequencies.     

电流变体-砂浆复合梁结构的振动特性研究

利用电流变体作为驱动元件与基体砂浆材料结合制成智能悬臂梁结构,调节施加在电流变体上的电压,用锤击法瞬态击振测定其在不同电场强度下的自振频率,对频率随电场强度的变化规律进行了研究。实验结果表明电流变片埋置位置对复合梁的整体振动特性的影响比较大。     

半刚性连接钢管混凝土框架剪力墙结构的动力特性分析

将钢管混凝土框架剪力墙结构作为连续弹性无限自由度结构，建立自由振动方程，分析了半刚性连接对结构自振周期和频率的影响，推导出半刚性连接框剪结构自振周期系数的计算公式。使用通用有限元程序ANSYS进行结构的模态分析，有限元分析结果和公式计算结果吻合良好。结果表明，半刚性连接使得结构自振周期增大，半刚性连接对高阶振型自振周期的影响很小。提出了地震区钢管混凝土框剪结构体系的设计建议，可供工程设计人员参考使用。     

Experimental validation of soil–structure interaction of offshore wind turbines

Estimating the natural frequencies of a wind turbine system consisting rotor, nacelle, tower, foundation and surrounding soil is one of the important design considerations. This paper experimentally investigates the behaviour of a model wind turbine supported on a particular type of foundation called a monopile. Monopile is a single large diameter (2.5–4 m) long slender column inserted deep into the ground. This can be thought of as an extension of the wind turbine tower. In particular, the role of soil/foundation in the dynamics of wind turbines has been investigated. Analytical methods are developed incorporating the rotational and translation flexibility of the foundation. Novel experimental techniques have been developed to obtain the parameters necessary for the analytical model. The analytical model is validated using a finite element approach and experimental measurements. In total, results from 17 test cases is reported in the paper. Experimental results show that the natural frequencies and the damping factors of the wind turbine tower change significantly with the type of soil/foundation. Analytical results for the natural frequencies agree reasonably well to the experimental results and finite element results.     

Tuned mass dampers for structures with closely spaced natural frequencies

Analytical results are developed for vibration control of structures with one or more Tuned Mass Dampers (TMDs). The input is a harmonic load with a range of possible frequencies. The control objective is to reduce the maximum amplitude of the structural response. Perturbation theory is used with three sets of small parameters: the ratio of TMD and structural modal masses, the damping of the system, and the differences between the structural and loading frequencies. It is shown analytically that for structures with widely spaced natural frequencies, the response can be approximated accurately by the response of the well-known single-mode structure/TMD system. For structures with p closely spaced natural frequencies, more general analytical results are developed to describe the coupling between the motions of the p modes of the structure and the multiple TMDs. The results show that at least p TMDs with properly placed attachments to the structure are necessary to control the response. If fewer TMDs are used, the maximum frequency response has a lower bound which is independent of the properties of the TMDs. The TMD placement is shown to be always important, regardless of the spacing of the structure's natural frequencies. The results are illustrated for both lumped-mass and continuous structures.     

Peak response of 2-DOF uncoupled oscillator under two-directional base motion

This paper investigates the peak response of a 2-DOF uncoupled linear oscillator under arbitrarily oriented two-component horizontal earthquake motion. Input data consist of 22 two-component acceleration records from the magnitude 6.6, October 15, 1979 Imperial Valley earthquake. One-directional response spectra for each principal direction of the oscillator, and two-directional response spectra (amplitude of the peak resultant response and its direction with respect to principal directions) are calculated by considering all angles of incidence of the excitation. The results indicate that, for oscillators that are not too flexible (i.e. with natural frequencies greater than 0.8 Hz), the two-directional peak response is controlled by the weaker direction of the oscillator. For flexible oscillators the two-directional peak response is controlled by the direction whose natural frequency is closer to dominant ground motion frequencies. The results also show that when the two-directional peak response is expressed as a weighted sum of one-directional peak responses, the weighting factors are not constants, but functions of oscillator and dominant ground motion frequencies.     

大型火力发电厂框排架混合结构主厂房动力特性试验与分析

选取1 000MW大型火力发电厂新型混合结构主厂房体系的三跨三榀进行缩尺比为1/7的空间模型试验研究.采用锤击法测试模型结构的动力特性,得到其自振频率和振型,并根据相似关系换算到原型结构.使用SAP2000软件建立混合结构主厂房模型和原型结构的有限元模型,进行模态分析,得到模型和原型结构的频率和振型,并与试验结果进行对比分析.可为大型火力发电厂新型混合结构主厂房体系的抗震性能研究提供依据.     

Validation of new equations for dynamic analyses of tall frame-type structures

The accuracy of the new equations for long frame-type structures, derived by Kerr and Zarembski, and extended recently by Kerr and Accorsi also to dynamic analyses, is investigated. At first, the natural frequencies of a tall frame-type structure, with twenty floors, are determined using the new equations, and then they are compared with the corresponding results calculated using the finite element method and the common shear-building analysis. The found agreement with the finite element analysis is close. To check further the accuracy of the new equations, small scale models are tested on a shake table. The natural frequencies recorded in the tests are then compared with those determined from the new equations, for a wide range of geometrical parameters. The agreement with the test data is good. The presented study indicates that the new equations are well suited for analyzing the dynamic response of tall frame-type structures.