Operational Modal Analysis: the CEME Skywalk at UBC, Vancouver

Slender and lighter footbridges are becoming more and more popular to meet the transportation demand and the aesthetical requirements of the modern society. The widespread presence of such particular structures has become possible thanks to the availability of new, lightweight and still capable of carrying heavy loads material . Therefore, these kind of structure, are particularly sensitive to vibration serviceability problems, especially induced by human activities. As a consequence, it has been imperative to study the dynamic behaviour of such slender pedestrian bridges in order to define their modal characteristics. As an alternative to a Finite Element Analysis to find natural frequencies, damping and mode shape, a so-called Operational Modal Analysis is a valid tool to obtain these parameters through an ambient vibration test. This work provides a useful insight into the Operational Modal Analysis technique and It reports the investigation of the CEME Skywalk, a pedestrian bridge located at the University of British Columbia, in Vancouver, Canada. Furthermore, human-induced vibration tests have been performed and the dynamic characteristics derived with these tests have been compared with the ones from the ambient vibration tests. The effect of the dynamic properties of the two buildings supporting the CEME Skywalk on the dynamic behaviour of the bridge has been also investigated.

Planetary Gear Modal Vibration Experiments and Correlation against Lumped-Parameter and Finite Element Models

Experimental modal analysis techniques are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Experimentally obtained natural frequencies, mode shapes, and dynamic response are compared to the results from lumped-parameter and finite element models. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures in the system to capture all of the natural frequencies and modes. The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures. The lumped-parameter and finite element models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. The number and types of modes in the low-frequency and high-frequency bands depend on the degrees of freedom in the central members and planet gears, respectively. The accuracy of natural frequency prediction is improved when the planet bearings have differing stiffnesses in the tangential and radial directions, consistent with the bearing load direction. (C) 2012 Elsevier Ltd. All rights reserved.

Investigation of Human-Structure Interaction Through Experimental and Analytical Studies

Vibration serviceability is a widely recognized design criterion for assembly-type structures, such as stadiums, that are likely subjected to rhythmic human-induced excitation. Human-induced excitation of a structure occurs from the movement of the occupants such as walking, running, jumping, or dancing. Vibration serviceability is based on the level of comfort that people have with the vibrations of a structure. Current design guidance uses the natural frequency of the structure to assess vibration serviceability. However, a phenomenon known as human-structure interaction suggests that there is a dynamic interaction between the structure and passive occupants, altering the natural frequency of the system. Human-structure interaction is dependent on many factors, including the dynamic properties of the structure, posture of the occupants, and relative size of the crowd. It is unknown if the shift in natural frequency due to humanstructure interaction is significant enough to warrant consideration in the design process. This study explores the interface of both structural and crowd characteristics through experimental testing to determine if human-structure interaction should be considered because of its potential impact on serviceability assessment. An experimental test structure that represents the dynamic properties of a cantilevered stadium structure was designed and constructed. Experimental modal analysis was implemented to determine the dynamic properties of the empty test structure and when occupied with up to seven people arranged in different locations and postures. Comparisons of the dynamic properties were made between the empty and occupied testing configurations and analytical results from the use of a dynamic crowd model recommended from the Joint Working Group of Europe. Data trends lead to the development of a refined dynamic crowd model. This dynamic model can be used in conjunction with a finite element model of the test structure to estimate the dynamic influence due to human-structure interaction due to occupants standing with straight knees. In the future, the crowd model will be refined and can aid in assessing the dynamic properties of in-service stadium structures.

Experimental Evaluation of the Influence of Human-Structure Interaction for Vibration Serviceability

The effects of human-structure interaction on the dynamic performance of occupied structures have long been observed. The inclusion of the effects of human-structure interaction is important to ensure that the dynamic response of a structure is not overestimated. Previous observations, both in service and in the laboratory, have yielded results indicating that the effects are dependent on the natural frequency of the structure, the posture of the occupants, and the mass ratio of the occupants to the structure. These results are noteworthy, but are limited in their application,because the data are sparse and are only pertinent to a specific set of characteristics identified in a given study. To examine these characteristics simultaneously and consistently, an experimental test structure was designed with variable properties to replicate a variety of configurations within a controlled setting focusing on the effects of passive occupants. Experimental modal analysis techniques were employed to both the empty and occupied conditions of the structure and the dynamic properties associated with each condition were compared. Results similar to previous investigations were observed, including both an increase and a decrease in natural frequency of the occupied structure with respect to the empty structure, as well as the identification of a second mode of vibration. The damping of the combined system was higher for all configurations. Overall, this study provides a broad data set representing a wide array of configurations. The experimental results of this study were used to assess current recommendations for the dynamic properties of a crowd to analytically predict the effects of human-structure interaction. The experimental results were used to select a set of properties for passive, standing occupants and develop a new model that can more accurately represent the behavior of the human-structure system as experimentally measured in this study.

Comparison of modal analysis results of laser vibrometry and nearfield acoustical holography measurements of an aluminum plate

Noise and vibration has long been sought to be reduced in major industries: automotive, aerospace and marine to name a few. Products must be tested and pass certain levels of federally regulated standards before entering the market. Vibration measurements are commonly acquired using accelerometers; however limitations of this method create a need for alternative solutions. Two methods for non-contact vibration measurements are compared: Laser Vibrometry, which directly measures the surface velocity of the aluminum plate, and Nearfield Acoustic Holography (NAH), which measures sound pressure in the nearfield, and using Green’s Functions, reconstructs the surface velocity at the plate. The surface velocity from each method is then used in modal analysis to determine the comparability of frequency, damping and mode shapes. Frequency and mode shapes are also compared to an FEA model. Laser Vibrometry is a proven, direct method for determining surface velocity and subsequently calculating modal analysis results. NAH is an effective method in locating noise sources, especially those that are not well separated spatially. Little work has been done in incorporating NAH into modal analysis.

Operational Modal Analysis on laminated glass beams

Laminated glass is a sandwich element consisting of two or more glass sheets, with one or more interlayers of polyvinyl butyral (PVB). The dynamic response of laminated glass beams and plates can be predicted using analytical or numerical models in which the glass and the PVB are usually modelled as linear-elastic and linear viscoelastic materials, respectively. In this work the dynamic behavior of laminated glass beams are predicted using a finite element model and the analytical model of Ross-Kerwin-Ungar. The numerical and analytical results are compared with those obtained by operational modal analysis performed at different temperatures.

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.

Operational Modal Analysis using Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on Maximum Likelihood Estimation and the Expectation Maximization algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated applying the proposed identification method to a set of 100 simulated cases. The numerical results show that the proposed method estimates all the modal parameters reasonably well in the presence of 30% measurement noise even. Finally, advantages and disadvantages of the method have been discussed.

Modal analysis of buildings : quantification of uncertainties and model updating

Una estructura vibra con la suma de sus infinitos modos de vibración, definidos por sus parámetros modales (frecuencias naturales, formas modales y coeficientes de amortiguamiento). Estos parámetros se pueden identificar a través del Análisis Modal Operacional (OMA). Así, un equipo de investigación de la Universidad Politécnica de Madrid ha identificado las propiedades modales de un edificio de hormigón armado en Madrid con el método Identificación de los sub-espacios estocásticos (SSI). Para completar el estudio dinámico de este edificio, se ha desarrollado un modelo de elementos finitos (FE) de este edificio de 19 plantas. Este modelo se ha calibrado a partir de su comportamiento dinámico obtenido experimentalmente a través del OMA. Los objetivos de esta tesis son; (i) identificar la estructura con varios métodos de SSI y el uso de diferentes ventanas de tiempo de tal manera que se cuantifican incertidumbres de los parámetros modales debidos al proceso de estimación, (ii) desarrollar FEM de este edificio y calibrar este modelo a partir de su comportamiento dinámico, y (iii) valorar la bondad del modelo. Los parámetros modales utilizados en esta calibración han sido; espesor de las losas, densidades de los materiales, módulos de elasticidad, dimensiones de las columnas y las condiciones de contorno de la cimentación. Se ha visto que el modelo actualizado representa el comportamiento dinámico de la estructura con una buena precisión. Por lo tanto, este modelo puede utilizarse dentro de un sistema de monitorización estructural (SHM) y para la detección de daños. En el futuro, podrá estudiar la influencia de los agentes medioambientales, tales como la temperatura o el viento, en los parámetros modales. A structure vibrates according to the sum of its vibration modes, defined by their modal parameters (natural frequencies, damping ratios and modal shapes). These parameters can be identified through Operational Modal Analysis (OMA). Thus, a research team of the Technical University of Madrid has identified the modal properties of a reinforced-concrete-frame building in Madrid using the Stochastic Subspace Identification (SSI) method and a time domain technique for the OMA. To complete the dynamic study of this building, a finite element model (FE) of this 19-floor building has been developed throughout this thesis. This model has been updated from its dynamic behavior identified by the OMA. The objectives of this thesis are to; (i) identify the structure with several SSI methods and using different time blocks in such a way that uncertainties due to the modal parameter estimation are quantified, (ii) develop a FEM of this building and tune this model from its dynamic behavior, and (iii) Assess the quality of the model, the modal parameters used in this updating process have been; thickness of slabs, material densities, modulus of elasticity, column dimensions and foundation boundary conditions. It has been shown that the final updated model represents the structure with a very good accuracy. Thus, this model might be used within a structural health monitoring framework (SHM). The study of the influence of changing environmental factors (such as temperature or wind) on the model parameters might be considered as a future work.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

The experimental stress analysis of the Firestone type R-5⁰, 20 x 75 truck rim.

Vols. 2-3 have title: The experimental stress analysis of truck rims.

Proceedings, of the Society for Experimental Stress Analysis.

Vol. 1, no. 1 contains Proceedings of the 17th (or the last) Eastern Photoelasticity Conference.