Modal Contribution Coefficients in Bridge Condition Evaluation

Impact modal testing combined with finite element (FE) analyses is currently being used to evaluate the condition of steel bridges in the state of Ohio. Using modal testing techniques, it is relatively easy to measure the dynamic response of bridges, including mode shapes, frequencies, and modal scaling factors. These responses are compared to the results of the FE analyses and the model is iteratively updated until a good agreement is obtained. After a good agreement between experimental and analytical results has been achieved, the FE model is used to obtain stresses that are used to load rate the bridge. During the iterative calibration process, several quantities, including the fundamental mode shapes and frequencies, are used to evaluate the accuracy of the FE model. Since each mode shape plays a different role in the dynamic behavior of the structure, a more efficient calibration routine can be achieved if more emphasis is placed on obtaining good matches for the modes that are most influential. The aim of this paper is to develop a quantitative measure of the contribution of different modes to the overall dynamic response of a structure. The proposed measure, a series of contribution coefficients, is used to identify which modes are most critical in the process of modal testing and FE model calibration. Several applications of the contribution coefficients are identified.     

Experimental and Numerical Study of Damaged Cantilever

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.     

Finite-Element Model Tuning of Global Modes of a Grandstand Structure Using Ambient Vibration Testing

This paper describes the experimental and analytical modal analysis of a full-scale cantilevered grandstand. A 3D finite-element model was successfully updated manually based on the global modes identified from ambient vibration measurements. The ambient vibration testing was effective in capturing the global modes of the large grandstand. A number of global vibration modes of the entire grandstand were reliably identified in the frequency range 0–3.1 Hz, in addition to modes in the same frequency range that engaged primarily the cantilever roof structure. Following a two-stage manual FE model updating process, the correlation between the experimental and analytical results showed good agreement, with physically meaningful updated parameters. It was clearly illustrated that both the roof system and the nonstructural elements contributed significantly to the stiffness and mass of the global modes. Useful and novel lessons are highlighted for efficient and reliable future finite-element modeling of global modes of similar grandstand structures.     

连铸板坯在结晶器内凝固行为的研究

在考虑结晶器铜板水槽结构尺寸和分布的基础上，建立了连铸板坯在结晶器内温度场和应力场之间耦合过程的有限元分析模型。通过耦合计算，发现板坯在连铸结晶器中宽窄面方向上的坯壳表面温度、坯壳生长及其受力变形等行为沿拉坯方向上的变化规律，为分析和解决铸坯在结晶器中产生的质量问题、设计或优化有关结晶器工艺和结构参数提供了理论依据。     

液化气储罐受热引爆机理分析

沸腾液体膨胀蒸气爆炸(boiling liquid expanding vapor explosion,BLEVE)是过热液体整体沸腾迅速膨胀引发的爆作.液化气罐在储运中时有BLEVE在发生.基于英国健康与安全署的关于液化气罐在火焰包围环境下的实验结果,分析了储罐受热后其内部压力、罐壁温度变化及储罐介质排放等一系列热物理过程及各相关因变量之间的相互关系.据此介绍了可以模拟储罐受热引发BLEVE现象的压力液化气仿真软件PLGS99的物理模型与数学模型,并在此基础上详举实例讨论了储罐受热引发BLEVE爆炸的机理.     

Overview of a Modal-Based Condition Assessment Procedure

Condition assessment is a term that is used to describe the process of characterizing the physical condition of constructed systems. This paper summarizes a condition assessment (CA) procedure based on a complete system of field-testing, finite element (FE) modeling, and load rating. Experimental techniques, including both modal testing and truckload testing, are used to collect measurements of the constructed systems. The basic mechanism and procedure of the FE modeling and calibration are presented. Different physical parameters of FE models are adjusted during the calibration process using both static and dynamic responses as criteria to achieve convergence between experimental measurements and analytical results using carefully developed objective functions. Finally, a bridge load rating is completed on the basis of the calibrated model. These developments are described and illustrated using a representative bridge as an example.     

Research on mode localization of reticulated shell structures

Reticulated shell structures (RSSs) are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features: some modal vectors of the structure change remarkably when the values of its physical parameters (mass or stiffness) have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS,and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.     

Determination of the shortest interatomic distance in a liquid metal using its structure factor

The structure factor (SF) and atomic radial distribution function (RDF) of liquid lead simulated at a temperature of 613 K are compared. The shortest interatomic distance obtained from SF is found to be smaller than that determined as the abscissa of the first RDF coordination peak. It is shown that a satisfactory agreement between the experimental and calculated curves in the high-angle portion of SF can only be obtained when at least two most probable shortest interatomic distances r ₁ and r ₂, which indicate a complex structure of the first coordination shell of the liquid metal, are taken into account.     

Reduction of Mixing in Jet-Fed Water Storage Tanks

Contrary to usual mains-water practice, mixing in water storage tanks used in rainwater harvesting systems is undesirable because pathogen die-off can occur in the unmixed water prior to its extraction for use. The principal cause of mixing in these tanks is the momentum of the inflow during a rainfall event. We investigate the effect of inflow-jet configuration on the proportion of stored water in a tank which mixes with the slightly cooler inflow of rooftop water. Scale experiments are conducted which show that the nondimensional height of the mixing front above the jet inlet is proportional to the inflow-jet densimetric Froude number for both single and multijet arrangements of various geometries. For each arrangement a coefficient of mixing is found. The results are then used to assess the level of mixing in full-scale rooftop rainwater harvesting storage tanks and determine whether residence time in such tanks is a viable strategy for pathogen reduction. For such applications, a radial manifold of jets outwardly directed from the tank center is found to be the most promising.     

Pressure Waves in Porous Medium Saturated with Liquid Containing Gas Bubbles

Theoretical analyses on nonlinear pressure waves evolution in porous medium saturated with a liquid containing gas bubbles is carried out. The evolution equations for fast and slow longitudinal modes are derived for slightly nonlinear, disperse, and dissipation processes. The pressure wave distribution in gas bubble liquid-saturated porous media was investigated experimentally. It was revealed that both modes might have oscillating structure induced by bubble oscillation in the wave. It is shown that the wave damping is determined by a combined impact of heat losses due to gas cooling in the bubbles and dissipation due to longitudinal displacement of liquid and porous skeleton, both influenced by the wave. Experimental data on the velocity and structure of fast and slow modes are compared with results of theoretical modeling.     

Development of Dynamic-Response-Based Objective Functions for Finite-Element Modeling of Bridges

The basic mechanism and procedures of finite-element (FE) bridge modeling and calibration are briefly presented. Different physical parameters of FE models are adjusted during the calibration process. Dynamic-response-based objective functions are carefully developed based on two powerful indices: the modal assurance criterion and frequency correlation trend line. The nominal bridge models are calibrated by minimizing the quantified difference between analytical results and experimental measurements. Using an existing calibration strategy, a nominal FE bridge model is optimized by minimizing this global dynamic-response-based objective function. The value of the objective function is reduced from 10.70 to 4.61%. The minimization of the objective function indicates the convergence of calibration and it is shown that the automated calibration becomes practical due to the formulation of the dynamic-response-based objective function.     

Response of Curved Sandwich Panels Subjected to Blast Loading

Curved sandwich panels with two aluminium face sheets and an aluminium foam core under air blast loadings were investigated experimentally and numerically. Specimens with two values of radius of curvature and different core/face sheet configurations with the same projected area were tested for three blast intensities. All four edges of the panels were fully clamped. The experiments were carried out by a four-cable ballistic pendulum with corresponding sensors. The impulse acting on the front face of the assembly, the deflection history at the center of the back face sheet, and the strain history at some characteristic points on the back face were obtained. Then the deformation/failure modes of specimens were classified and analyzed systematically. The commercial software LS-DYNA was employed to simulate those physical processes. The finite-element (FE) model was validated by the data from experiments. Detailed deformation and energy dissipation mechanisms were further revealed by the FE models. The valuable experimental data and results from FE models show that the initial curvature of a curved sandwich panel changes the deformation/collapse mode with an extended range for bending-dominated deformation mode, which suggests that the performance of the sandwich shell structures slightly exceeds that of both their equivalent solid counterpart and a flat sandwich plate in certain blast intensity ranges.     

Research on Finite Element Determinant of Orthotropic Plate in Steamlined Steel Box Girder

A new type of streamlined girder bridge with orthotropic plates steel box girder is evaluated via testing and analysis. Although the use of finite element modeling has become indispensable for the detailed calculation of certain details and connections, an analytical approach remains a very effective method to determine the internal forces and moments in the box girder. Two new theoretical analysis models are undertaken to study the behavior of aimed bridge. The FE determinants of the two models are built. The validity of the proposed methods is checked by full finite element calculation using shell elements. In addition, a total experimental model is set up to verify the reliability of computational models. The computation results compare well with the experimental results. It is illustrated that it is an effective method to predict properties of this kind of bridges.     

Modeling superheat removal during continuous casting of steel slabs

To investigate superheat dissipation in a continuous slab casting machine, mathematical models have been developed to compute fluid flow velocities, temperature distribution within the liquid pool, heat transfer to the inside of the solidifying shell, and its effect on growth of the shell. Three-dimensional (3-D) velocity and heat-transfer predictions compare reasonably with pre-vious experimental measurements and two-dimensional (2-D) calculations. The results indicate that the maximum heat input to the shell occurs near the impingement point on the narrow face and confirm that most of the superheat is dissipated in or just below the mold. Superheat tem-perature and casting speed have the most important and direct influence on heat flux. The effects of other variables, including mold width, nozzle jet angle, and submergence depth, are also investigated. Calculated heat flux profiles are then input to a one-dimensional (1-D) solidifi-cation model to calculate growth of the shell. Shell thickness profiles down the wide and narrow faces are compared with the predictions of conventional heat conduction models and available measurements.     

Mixing theories for gas-stirred melts

Initially, the paper gives a survey on known theoretical models of mixing in gas-stirred melts. A new model that combines the concepts of the circulating concentration cloud and the two-tank model is presented. In this model, the combined effect of recirculation flow and turbulent mixing is expressed by a number of ideally mixed tanks in series. The tanks in series are additionally connected with a dead volume according to the two-tank model. In total, the model contains four characteristic parameters. The results of numerical calculations using the model are compared with experimental data of mixing in a water model and in a 40 t steel ladle both with centric gas-stirring.     

Compression Tests on Cylinders with Circumferential Weld Depressions

The behavior of thin cylindrical shells under axial compression is very sensitive to imperfections in the initial geometry. Local axisymmetric imperfections are among the most detrimental and have been shown to be a regular feature of circumferentially welded joints in civil engineering shell structures such as steel silos and tanks. Many of the experiments on which current design rules are based were performed on elastic Mylar, copper, or aluminum specimens, which have some very different characteristics to those of steel shells. Furthermore, very few laboratory tests have ever examined the consequences of fabrication processes on shell buckling strength, although these strongly influence the amplitudes and forms of geometric imperfections. This paper presents the findings of a careful experimental program on large steel cylinders fabricated with a fully welded circumferential joint. Thorough measurements were made of the initial imperfections and their transformation into a buckling mode. The results are compared with elastic-plastic finite-element predictions and the most recent design standard.     

Bayesian Modal Updating using Complete Input and Incomplete Response Noisy Measurements

The problem of identification of the modal parameters of a structural model using complete input and incomplete response time histories is addressed. It is assumed that there exist both input error (due to input measurement noise) and output error (due to output measurement noise and modeling error). These errors are modeled by independent white noise processes, and contribute towards uncertainty in the identification of the modal parameters of the model. To explicitly treat these uncertainties, a Bayesian framework is adopted and a Bayesian time-domain methodology for modal updating based on an approximate conditional probability expansion is presented. The methodology allows one to obtain not only the optimal (most probable) values of the updated modal parameters but also their uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite-element model based on these modal estimates. The proposed approach requires only one set of excitation and corresponding response data. It is found that the updated probability density function (PDF) can be well approximated by a Gaussian distribution centered at the optimal parameters at which the posterior PDF is maximized. Numerical examples using noisy simulated data are presented to illustrate the proposed method.     

Effect of Installation Method on External Shaft Friction of Caissons in Soft Clay

The influence of the installation method on the soil flow pattern, resulting external radial total stress changes, and final external shaft friction after consolidation has been investigated for caissons in soft clay by means of centrifuge model tests, large deformation finite-element (FE) analysis, and a simple cavity expansion approach. Both the centrifuge measurements and the FE results show that more soil is forced into the caisson under suction than under jacking. However, the difference in the resulting external radial total stress changes or penetration-induced excess pore-water pressure is much less significant, since the expansion-induced excess pore pressure is smaller for thin-walled caissons than for driven piles. After subsequent consolidation, the influence of the installation method reduces further, and the final shaft friction ratios are close for the two installation methods. Based on the magnitude of heave ratios derived from the centrifuge measurements and the FE analysis, a simple form of cavity expansion approach can reasonably estimate external radial stress changes during installation and after consolidation, and final shaft friction ratios for the caissons. An approach for estimating the external shaft friction ratios for vertical pullout of sealed caissons is proposed.     

Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes

Previously a Bayesian theory for modal identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the modal identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to modal identification of two field buildings. Using the proposed algorithm, Bayesian modal identification can now be performed in a few seconds even for a moderate to large number of measurement channels.