Evaluation of the Lateral Vibration Response of Footbridges under Uncertainty Conditions

<p>The evaluation of the vibration performance of footbridges due to walking pedestrians is an issue of increasing importance in current footbridge design practice. The growing trend of slender footbridges with long spans and light materials has led to serviceability problems in lateral vibrations, which occur when the number of pedestrians reaches a “critical number”. Considering the mode of vibration in which the lateral instability is more likely to develop, the structural response depends on the modal characteristics of the footbridge; in particular, the natural frequency and the damping ratio. These modal parameters are stochastic variables, as it is not possible to determine them without a level of uncertainty. Thus, the purpose of this paper is to obtain the value of the lateral dynamic response of slender footbridges with a certain confidence level under uncertainty conditions. The uncertainties of those modal parameters are considered using a probabilistic approach. Both the natural frequency and the damping ratio are modelled as uncorrelated random variables that follow a predetermined probabilistic distribution function. Consequently, the structural response will also be described by a probabilistic distribution function, which can be estimated through Monte Carlo numerical simulations. As a result, the study allows the footbridge lateral response and the critical number of pedestrians to be calculated for different confidence levels and load scenarios, especially for crowd densities above the “critical number”.</p>

Prediction of System Parameters of Carbon-Based Composite Structure for Different Carbon Fiber Orientations with Mode Information at Reference Angle Only

The prediction of system parameters is important for understanding the dynamic behavior of composite structures or selecting the configuration of laminated carbon in carbon-based composite (CBC) structures. The dynamic nature of CBC structures allows the representation of system parameters as modal parameters in the frequency domain, where all modal parameters depend on the carbon fiber orientations. In this study, the variation in the system parameters of a carbon fiber was derived from equivalent modal parameters, and the system parameters at a certain carbon fiber orientation were predicted using the modal information at the reference carbon fiber orientation only and a representative curve-fitted function. The target CBC structure was selected as a simple rectangular structure with five different carbon fiber orientations, and the modal parameters were formulated based on a previous study for all modes. Second-order curve-fitted polynomial functions were derived for all possible cases, and representative curve-fitting functions were derived by averaging the polynomial coefficients. The two system parameters were successfully predicted using the representative curve-fitting function and the modal information at only the reference carbon fiber orientation, and the feasibility of parameter prediction was discussed based on an analysis of the error between the measured and predicted parameters.

Modal Parameter Identification of Structures Using Reconstructed Displacements and Stochastic Subspace Identification

A method of modal parameter identification of structures using reconstructed displacements was proposed in the present research. The proposed method was developed based on the stochastic subspace identification (SSI) approach and used reconstructed displacements of measured accelerations as inputs. These reconstructed displacements suppressed the high-frequency component of measured acceleration data. Therefore, in comparison to the acceleration-based modal analysis, the operational modal analysis obtained more reliable and stable identification parameters from displacements regardless of the model order. However, due to the difficulty of displacement measurement, different types of noise interferences occurred when an acceleration sensor was used, causing a trend term drift error in the integral displacement. A moving average low-frequency attenuation frequency-domain integral was used to reconstruct displacements, and the moving time window was used in combination with the SSI method to identify the structural modal parameters. First, measured accelerations were used to estimate displacements. Due to the interference of noise and the influence of initial conditions, the integral displacement inevitably had a drift term. The moving average method was then used in combination with a filter to effectively eliminate the random fluctuation interference in measurement data and reduce the influence of random errors. Real displacement results of a structure were obtained through multiple smoothing, filtering, and integration. Finally, using reconstructed displacements as inputs, the improved SSI method was employed to identify the modal parameters of the structure.

Automatic modal parameters identification and uncertainty quantification based on block-bootstrap and multi-stage clustering under ambient excitation

This study proposes an algorithm for autonomous modal estimation to automatically eliminate false modes and quantify the uncertainty caused by the clustering algorithm and ambient factors. This algorithm belongs to the stochastic subspace identification (SSI) techniques and is based on the Block-Bootstrap and multi-stage clustering analysis. First, the Block-Bootstrap is introduced to decompose the response signal of the structure into M blocks of data. The covariance-driven stochastic subspace identification (SSI-Cov) method is used to process a random sample of data and obtain the corresponding M stabilization diagrams. In addition, the hierarchical clustering method is adopted to carry out the secondary clustering of the picked stable axis according to the defined distance threshold. Then, false modes are eliminated according to the proposed true and false modal discrimination index ( MDI). Finally, the above steps are repeated B times, and MDI is used to modify the initial modal parameters of group B. The mean value of elements in the cluster is taken as the recognition result of modal parameters, and the standard deviation is used to measure the accuracy of the recognition result. The numerical simulation results and the modal parameter identification of the Jing-yuan Yellow River Bridge show that, for identifying true and false modals, the proposed modal discrimination index is more effective than the threshold value of the traditional index. Also, it was found that the proposed method can eliminate the uncertainty introduced in the clustering process. In addition, this method can remove the influence of ambient noises, and it can improve the identification accuracy. It will be shown that this method has better anti-noise performance.

Finite Element Analysis and Preliminary Dynamic Tests of Laboratory Bridge Model

A preliminary dynamic test of a two-span continuous girder bridge is reported in this paper, including the design specifications, the numerical model, and the modal identification result. This laboratory bridge is made of aluminum plates and connected via bolts. The finite element method is applied to build a numerical model of the bridge to aid the design and test plan. Several ambient vibration tests are conducted to extract the modal parameters, e.g., modal frequencies, damping ratios, and mode shapes, of the constructed bridge, and the Bayesian FFT algorithm is used for modal identification. We compare the identified results with those predicted by the finite element model and vary the magnitude of load to investigate its potential influence on the modal parameters. Damage cases by loosening structure members are also considered, and significant changes are observed in modal frequencies. The constructed model will be used as a benchmark for damage identification, model updating, and condition assessment, etc.

Identification of Modal Parameters for Reinforcement of Walls in Earthen Ruins

The protection of earthen sites plays an important role in the context of preservation of cultural heritage, especially in the inheritance and promotion of history and culture. The aim of the paper is to present the essential results of an ongoing research on a reinforced rammed earthen wall in Suoyang City (Guazhou, China). The wall vibrations caused by ambient actions were analyzed using the stochastic subspace algorithm to estimate the modal parameters of the wall. The frequencies of the first three orders are 3.566 Hz, 5.003 Hz, and 6.250 Hz, and the corresponding modes are first-order transverse bending, second-order left and right torsion, and third-order vertical bending, respectively. Then, according to the data of elastic modulus obtained in the lab, the finite element calculation is carried out, and referring to the results of field measurement, the revised elastic modulus value is 205.90 MPa. It is worth mentioning that the revised value is significantly improved from the original laboratory value, and it is also indicated that the seismic performance of the reinforced wall has been significantly improved. The present work is expected to provide a theoretical basis for reinforcement, protection, and seismic control of earthen ruins.

Fatigue damage in bending of reinforced concrete frames using non-destructive tests for dynamic strength of the cylinder

PurposeThe purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.Design/methodology/approachThe problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.FindingsThe modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.Originality/valueThe paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

Quality Assessment of Installed Rock Bolts

The chapter presents a method for non-destructive identification of discontinuity of a resin layer (grout) surrounding rock bolts. The method uses modal analysis procedures and is based on an impact excitation where a response transducer is positioned at a visible part of a rock bolt. Since the installed rock bolt acts as an oscillator, its modal parameters are changed by different lengths and positions of grouting discontinuity. Thanks to proper extraction of these parameters, with a resonant frequency seen as the most valuable, the intended identification is possible. The measurements and analyses were performed in laboratory conditions and subsequently at experimental and working coal mines where the measurement system was verified. The developed finite element model of the system under test, rock bolt - resin - rock mass, may be used as reference data base for investigated rock bolts. The advantages of the method include plausibility of grouting discontinuity assessment at any time after its installation, a non-destructive character of the method and the fact that it is not necessary to install any additional equipment into a roof section. It enables a localization of a grout discontinuity, whether it is the back part or the front part of a rock bolt.