Cross-talk response analysis on a piezoelectric

The study of the cross-talk and its effects in the performance of a matrix array of piezoelectric elements is an important issue. This corresponds to the study of the cross mode of vibration of each one of the piezoelectric elements that form the ultrasonic array. The aim is to detect and measure the cross-talk that is generated for the cross mode of vibration. In order to accomplish this task, an array of 2x3 elements was designed and developed. This was constructed using 8 MHz piezoelectric ceramics. A number of configurations have been experimented, considering the excitation of an increasing number of elements, in order to detect and measure the propagation of wave interference. Initial results show the way cross-talk interferes the beam generated by the array, this causing attenuation of the main beam and other negative effects.

Maximum likelihood estimation of new state space models for operational modal analysis

The modal analysis of a structural system consists on computing its vibrational modes. The experimental way to estimate these modes requires to excite the system with a measured or known input and then to measure the system output at different points using sensors. Finally, system inputs and outputs are used to compute the modes of vibration. When the system refers to large structures like buildings or bridges, the tests have to be performed in situ, so it is not possible to measure system inputs such as wind, traffic, . . .Even if a known input is applied, the procedure is usually difficult and expensive, and there are still uncontrolled disturbances acting at the time of the test. These facts led to the idea of computing the modes of vibration using only the measured vibrations and regardless of the inputs that originated them, whether they are ambient vibrations (wind, earthquakes, . . . ) or operational loads (traffic, human loading, . . . ). This procedure is usually called Operational Modal Analysis (OMA), and in general consists on to fit a mathematical model to the measured data assuming the unobserved excitations are realizations of a stationary stochastic process (usually white noise processes). Then, the modes of vibration are computed from the estimated model. The first issue investigated in this thesis is the performance of the Expectation- Maximization (EM) algorithm for the maximum likelihood estimation of the state space model in the field of OMA. The algorithm is described in detail and it is analysed how to apply it to vibration data. After that, it is compared to another well known method, the Stochastic Subspace Identification algorithm. The maximum likelihood estimate enjoys some optimal properties from a statistical point of view what makes it very attractive in practice, but the most remarkable property of the EM algorithm is that it can be used to address a wide range of situations in OMA. In this work, three additional state space models are proposed and estimated using the EM algorithm: • The first model is proposed to estimate the modes of vibration when several tests are performed in the same structural system. Instead of analyse record by record and then compute averages, the EM algorithm is extended for the joint estimation of the proposed state space model using all the available data. • The second state space model is used to estimate the modes of vibration when the number of available sensors is lower than the number of points to be tested. In these cases it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors). Here, the proposed state space model and the EM algorithm are used to estimate the modal parameters taking into account the data of all setups. • And last, a state space model is proposed to estimate the modes of vibration in the presence of unmeasured inputs that cannot be modelled as white noise processes. In these cases, the frequency components of the inputs cannot be separated from the eigenfrequencies of the system, and spurious modes are obtained in the identification process. The idea is to measure the response of the structure corresponding to different inputs; then, it is assumed that the parameters common to all the data correspond to the structure (modes of vibration), and the parameters found in a specific test correspond to the input in that test. The problem is solved using the proposed state space model and the EM algorithm. Resumen El análisis modal de un sistema estructural consiste en calcular sus modos de vibración. Para estimar estos modos experimentalmente es preciso excitar el sistema con entradas conocidas y registrar las salidas del sistema en diferentes puntos por medio de sensores. Finalmente, los modos de vibración se calculan utilizando las entradas y salidas registradas. Cuando el sistema es una gran estructura como un puente o un edificio, los experimentos tienen que realizarse in situ, por lo que no es posible registrar entradas al sistema tales como viento, tráfico, . . . Incluso si se aplica una entrada conocida, el procedimiento suele ser complicado y caro, y todavía están presentes perturbaciones no controladas que excitan el sistema durante el test. Estos hechos han llevado a la idea de calcular los modos de vibración utilizando sólo las vibraciones registradas en la estructura y sin tener en cuenta las cargas que las originan, ya sean cargas ambientales (viento, terremotos, . . . ) o cargas de explotación (tráfico, cargas humanas, . . . ). Este procedimiento se conoce en la literatura especializada como Análisis Modal Operacional, y en general consiste en ajustar un modelo matemático a los datos registrados adoptando la hipótesis de que las excitaciones no conocidas son realizaciones de un proceso estocástico estacionario (generalmente ruido blanco). Posteriormente, los modos de vibración se calculan a partir del modelo estimado. El primer problema que se ha investigado en esta tesis es la utilización de máxima verosimilitud y el algoritmo EM (Expectation-Maximization) para la estimación del modelo espacio de los estados en el ámbito del Análisis Modal Operacional. El algoritmo se describe en detalle y también se analiza como aplicarlo cuando se dispone de datos de vibraciones de una estructura. A continuación se compara con otro método muy conocido, el método de los Subespacios. Los estimadores máximo verosímiles presentan una serie de propiedades que los hacen óptimos desde un punto de vista estadístico, pero la propiedad más destacable del algoritmo EM es que puede utilizarse para resolver un amplio abanico de situaciones que se presentan en el Análisis Modal Operacional. En este trabajo se proponen y estiman tres modelos en el espacio de los estados: • El primer modelo se utiliza para estimar los modos de vibración cuando se dispone de datos correspondientes a varios experimentos realizados en la misma estructura. En lugar de analizar registro a registro y calcular promedios, se utiliza algoritmo EM para la estimación conjunta del modelo propuesto utilizando todos los datos disponibles. • El segundo modelo en el espacio de los estados propuesto se utiliza para estimar los modos de vibración cuando el número de sensores disponibles es menor que vi Resumen el número de puntos que se quieren analizar en la estructura. En estos casos es usual realizar varios ensayos cambiando la posición de los sensores de un ensayo a otro (múltiples configuraciones de sensores). En este trabajo se utiliza el algoritmo EM para estimar los parámetros modales teniendo en cuenta los datos de todas las configuraciones. • Por último, se propone otro modelo en el espacio de los estados para estimar los modos de vibración en la presencia de entradas al sistema que no pueden modelarse como procesos estocásticos de ruido blanco. En estos casos, las frecuencias de las entradas no se pueden separar de las frecuencias del sistema y se obtienen modos espurios en la fase de identificación. La idea es registrar la respuesta de la estructura correspondiente a diferentes entradas; entonces se adopta la hipótesis de que los parámetros comunes a todos los registros corresponden a la estructura (modos de vibración), y los parámetros encontrados en un registro específico corresponden a la entrada en dicho ensayo. El problema se resuelve utilizando el modelo propuesto y el algoritmo EM.

Trade-off aproaches for the vibroacoustic analysis of trains

Passengers’ comfort in terms of acoustic noise levels is a key design driver for train design. The problem is especially relevant for high speed trains, where the aerodynamic induced noise is dominant, but it is also important for medium speed trains where the mechanical sources of noise may have more influence. The numerical interior noise prediction inside the train is a very comp lex problem, involving many different parameters: complex geometries and materials, different noise sources, com- plex interactions among those sources, broad range of frequencies where the phenomenon is important, etc. In this paper, the main findings of this work developed at IDR/UPM (Instituto de Microgravedad “Ignacio Da Riva”, Universidad Politécnica de Madrid) are presented, concentrat ing on the different modelling methodologies used for the different frequency ranges of interest, from FEM-BEM models, hybrid FEM-SEA to pure SEA models. The advantages and disadvantages of the different approaches are summarized. Different modelling techniques have also been evaluated and compared, taking into account the various and specific geometrical configurations typical in this type of structures, and the material properties used in the models. The critical configuration of the train inside a tunnel is studied in order to evaluate the external loads due to noise sources of the train. In this work, a SEA-model composed by periodic characteristic sections of a high spee d train is analysed inside a tunnel.

Calibration of calculation models of wooden guardrails with Operational Modal Analysis

This study analyses the differences between two calculation models for guardrails on building sites that use wooden boards and tubular steel posts. Wood was considered an isotropic material in one model and an orthotropic material in a second model. The elastic constants of the wood were obtained with ultrasound. Frequencies and vibration modes were obtained for both models through linear analysis using the finite element method. The two models were experimentally calibrated through operational modal analysis. The results obtained show that for the three types of wood under analysis, the model which considered them as an orthotropic material fitted the experimental results better than the model which considered them as an isotropic material.

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.

Asymptotic and computational analysis of mistuning effects on the dynamics of bladed disks

Es bien conocido que las pequeñas imperfecciones existentes en los álabes de un rótor de turbomaquinaria (conocidas como “mistuning”) pueden causar un aumento considerable de la amplitud de vibración de la respuesta forzada y, por el contrario, tienen típicamente un efecto beneficioso en el flameo del rótor. Para entender estos efectos se pueden llevar a cabo estudios numéricos del problema aeroelástico completo. Sin embargo, el cálculo de “mistuning” usando modelos de alta resolución es una tarea difícil de realizar, ya que los modelos necesarios para describir de manera precisa el componente de turbomáquina (por ejemplo rotor) tienen, necesariamente, un número muy elevado de grados de libertad, y, además, es necesario hacer un estudio estadístico para poder explorar apropiadamente las distribuciones posibles de “mistuning”, que tienen una naturaleza aleatoria. Diferentes modelos de orden reducido han sido desarrollados en los últimos años para superar este inconveniente. Uno de estos modelos, llamado “Asymptotic Mistuning Model (AMM)”, se deriva de la formulación completa usando técnicas de perturbaciones que se basan en que el “mistuning” es pequeño. El AMM retiene sólo los modos relevantes para describir el efecto del mistuning, y permite identificar los mecanismos clave involucrados en la amplificación de la respuesta forzada y en la estabilización del flameo. En este trabajo, el AMM se usa para estudiar el efecto del “mistuning” de la estructura y de la amortiguación sobre la amplitud de la respuesta forzada. Los resultados obtenidos son validados usando modelos simplificados del rotor y también otros de alta definición. Además, en el marco del proyecto europeo FP7 "Flutter-Free Turbomachinery Blades (FUTURE)", el AMM se aplica para diseñar distribuciones de “mistuning” intencional: (i) una que anula y (ii) otra que reduce a la mitad la amplitud del flameo de un rotor inestable; y las distribuciones obtenidas se validan experimentalmente. Por último, la capacidad de AMM para predecir el comportamiento de flameo de rotores con “mistuning” se comprueba usando resultados de CFD detallados. Abstract It is well known that the small imperfections of the individual blades in a turbomachinery rotor (known as “mistuning”) can cause a substantial increase of the forced response vibration amplitude, and it also typically results in an improvement of the flutter vibration characteristics of the rotor. The understanding of these phenomena can be attempted just by performing numerical simulations of the complete aeroelastic problem. However, the computation of mistuning cases using high fidelity models is a formidable task, because a detailed model of the whole rotor has to be considered, and a statistical study has to be carried out in order to properly explore the effect of the random mistuning distributions. Many reduced order models have been developed in recent years to overcome this barrier. One of these models, called the Asymptotic Mistuning Model (AMM), is systematically derived from the complete bladed disk formulation using a consistent perturbative procedure that exploits the smallness of mistuning to simplify the problem. The AMM retains only the essential system modes that are involved in the mistuning effect, and it allows to identify the key mechanisms of the amplification of the forced response amplitude and the flutter stabilization. In this work, AMM methodolgy is used to study the effect of structural and damping mistuning on the forced response vibration amplitude. The obtained results are verified using a one degree of freedom model of a rotor, and also high fidelity models of the complete rotor. The AMM is also applied, in the frame of the European FP7 project “Flutter-Free Turbomachinery Blades (FUTURE)”, to design two intentional mistuning patterns: (i) one to complete stabilize an unstable rotor, and (ii) other to approximately reduce by half its flutter amplitude. The designed patterns are validated experimentally. Finally, the ability of AMM to predict the flutter behavior of mistuned rotors is checked against numerical, high fidelity CFD results.

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.

Improved damage detectability in a wind turbine blade by optimal selection of vibration signal correlation coefficients

Piotr Omenzetter and Simon Hoell’s work within the Lloyd’s Register Foundation Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research.

Dynamic investigation of an ancient masonry bell tower with operational modal analysis: a non-destructive experimental technique to obtain the dynamic characteristics of a structure

This paper shows the results of an experimental analysis on the bell tower of “Chiesa della Maddalena” (Mola di Bari, Italy), to better understand the structural behavior of slender masonry structures. The research aims to calibrate a numerical model by means of the Operational Modal Analysis (OMA) method. In this way realistic conclusions about the dynamic behavior of the structure are obtained. The choice of using an OMA derives from the necessity to know the modal parameters of a structure with a non-destructive testing, especially in case of cultural-historical value structures. Therefore by means of an easy and accurate process, it is possible to acquire in-situ environmental vibrations. The data collected are very important to estimate the mode shapes, the natural frequencies and the damping ratios of the structure. To analyze the data obtained from the monitoring, the Peak Picking method has been applied to the Fast Fourier Transforms (FFT) of the signals in order to identify the values of the effective natural frequencies and damping factors of the structure. The main frequencies and the damping ratios have been determined from measurements at some relevant locations. The responses have been then extrapolated and extended to the entire tower through a 3-D Finite Element Model. In this way, knowing the modes of vibration, it has been possible to understand the overall dynamic behavior of the structure.

Analysis of a metallic pedestrian bridge under dynamic human loads in pre and post reinforcement phases

The purpose of this work is to study the dynamic behavior of a pedestrian bridge in Alicante, Spain. It is a very slender footbridge with vertical and horizontal vibration problems during the passage of pedestrians. Accelerations have been recorded by accelerometers installed at various locations of the bridge. Two scenarios, in free vibration (after the passage of a certain number of pedestrians on the bridge) and forced vibration produced by a fixed number of pedestrians walking on the bridge at a certain speed and frequency. In each test, the effect on the comfort of the pedestrians, the natural frequencies of vibration, the mode shapes and damping factors have been estimated. It has been found that the acceleration levels are much higher than the allowable by the Spanish standards and this should be considered in the restoration of the footbridge.

Numerical evaluation of the vibration reduction index for structural joints

The present paper addresses the analysis of structural vibration transmission in the presence of structural joints. The problem is tackled from a numerical point of view, analyzing some scenarios by using finite element models. The numerical results obtained making use of this process are then compared with those evaluated using the EN 12354 standard vibration reduction index concept. It is shown that, even for the simplest cases, the behavior of a structural joint is complex and evidences the frequency dependence. Comparison with results obtained by empirical formulas reveals that those of the standards cannot accurately reproduce the expected behavior, and thus indicate that alternative complementary calculation procedures are required. A simple methodology to estimate the difference between numerical and standard predictions is here proposed allowing the calculation of an adaptation term that makes both approaches converge. This term was found to be solution-dependent, and thus should be evaluated for each structure.

Effects of whole body vibration on strength and jumping performance in volleyball and beach volleyball players

The primary aim of this study was to examine the effects of 6-week strength training with whole body vibration (WBV) on leg strength and jumping performance in volleyball and beach volleyball players. Twenty-three sub-elite male volleyball (VB; n=12) and beach volleyball players (BVB; n=11) aged 21.2±3.0 years were divided into two groups and subjected to 6 weeks of strength training (three one-hour sessions per week): (I) 12 players (6 VB and 6 BVB players) underwent training with WBV (30-40 Hz, 1.7-2.5 mm, 3.0-5.7 g), and (II) 11 players (6 VB and 5 BVB players) underwent traditional strength training. Squat jump (SJ) and countermovement squat jump (CMJ) measurements by the Ergo Tester contact platform and maximum leg press test (1RM) were conducted. Three-factor (2 time x 2 WBV use x 2 discipline) analysis of variance for SJ, CMJ and 1RM revealed a significant time main effect (p<0.001), a WBV use effect (p<0.001) and a discipline effect (p<0.001). Significantly greater improvements in the SJ (p<0.001) and CMJ (p<0.001) and in 1RM (p<0.001) were found in the WBV training groups than in traditional training groups. Significant 3-way interaction effects (training, WBV use, discipline kind) were also found for SJ, CMJ and 1RM (p=0.001, p<0.001, p=0.001, respectively). It can be concluded that implementation of 6-week WBV training in routine practice in volleyball and beach volleyball players increases leg strength more and leads to greater improvement in jump performance than traditional strength training, but greater improvements can be expected in beach volleyball players than in volleyball players.

Data analysis of tractor-trailer drivers to access drivers' perception of heavy duty truck ride quality. Final report.

National Highway Traffic Safety Administration, Office of Driver and Pedestrian Research, Washington, D.C.

46th Shock and Vibration Symposium, Royal Inn at the Wharf, San Diego, California, 21-23 October 1975 /

Called Symposium on Shock and Vibration in vols. 2-5.

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoclasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. (C) 2003 Elsevier Science Ltd. All rights reserved.