Caracterização dinâmica de um edifício existente de betão armado através de ensaios de vibração ambiental

Dissertação de natureza Científica para obtenção do grau de Mestre em Engenharia Civil

Observação do comportamento dinâmico de estruturas de engenharia civil

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização de Estruturas

Single side damage simulations and detection in beam-like structures

Beam-like structures are the most common components in real engineering, while single side damage is often encountered. In this study, a numerical analysis of single side damage in a free-free beam is analysed with three different finite element models; namely solid, shell and beam models for demonstrating their performance in simulating real structures. Similar to experiment, damage is introduced into one side of the beam, and natural frequencies are extracted from the simulations and compared with experimental and analytical results. Mode shapes are also analysed with modal assurance criterion. The results from simulations reveal a good performance of the three models in extracting natural frequencies, and solid model performs better than shell while shell model performs better than beam model under intact state. For damaged states, the natural frequencies captured from solid model show more sensitivity to damage severity than shell model and shell model performs similar to the beam model in distinguishing damage. The main contribution of this paper is to perform a comparison between three finite element models and experimental data as well as analytical solutions. The finite element results show a relatively well performance.

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Análise do comportamento dinâmico de uma plataforma sísmica e de um pórtico em betão armado e a sua evolução com o dano acumulado

Trabalho de Dissertação de Natureza Científica para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Estruturas

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Avaliação do comportamento de uma ponte metálica centenária sujeita à ação de tráfego ferroviário ligeiro

A presente dissertação tem como objetivo principal a análise numérica do comportamento dinâmico de uma ponte ferroviária, sob ação de tráfego ligeiro ferroviário. Neste contexto são apresentados alguns fundamentos teóricos a ter em conta nestes domínios, visando uma melhor compreensão dos fenómenos existentes no comportamento dinâmico de pontes ferroviárias quando sujeitas ao tráfego. O caso de estudo teve como foco a ponte Luiz I, uma ponte metálica situada sobre o rio Douro, que liga as cidades do Porto e Vila Nova de Gaia, sob ação de tráfego ligeiro ferroviário no seu tabuleiro superior para a condição anterior aos trabalhos de reabilitação e reforço realizados entre 2004 e 2005. Para o efeito foi desenvolvido um modelo numérico de elementos finitos da ponte realizado com recurso ao programa ANSYS, assim como um modelo numérico do veículo do Metro de Lisboa. Com base nestes modelos foram obtidos os parâmetros modais, nomeadamente as frequências naturais e os modos de vibração de toda a estrutura e do veículo. O estudo do comportamento dinâmico da ponte foi realizado por intermédio de uma metodologia de cargas móveis e de interação veículo-estrutura, através da ferramenta computacional Train-Bridge Interaction (TBI). As análises dinâmicas foram efetuadas para a passagem dos veículos de passageiros das redes de Metros do Porto e Lisboa. Nestas análises é estudada a resposta da estrutura em função da variabilidade ao nível da secção transversal, dependência do tramo, influência do veículo, da sua velocidade de circulação e impacto das frequências de vibração estimadas pelo modelo numérico.

Survey and dynamic behaviour of the Our Lady of Conception Church, Portugal

The Our Lady of Conception church is located in village of Monforte (Portugal) and is not in use nowadays. The church presents structural damage and, consequently, a study was carried out. The study involved the survey of the damage, dynamic identification tests under ambient vibration and the numerical analysis. The church is constituted by the central nave, the chancel, the sacristy and the corridor to access the pulpit. The masonry walls present different thickness, namely 0.65 m in the chancel, 0.70 m in the sacristy, 0.92 in the central nave and 0.65 m in the corridor. The masonry walls present 8 buttresses with different dimensions. The total longitudinal and transversal dimensions of the church are equal to 21.10 m and 14.26 m, respectively. The survey of the damage showed that, in general, the masonry walls are in good conditions, with exception of the transversal walls of the nave, which present severe cracks. The arches of the vault presents also severe cracks along the central nave. As consequence, the infiltrations have increased the degradation of the vault and paintings. Furthermore, the foundations present settlements in the Southwest direction. The dynamic identification test were carried out under the action of ambient excitation of the wind and using 12 piezoelectric accelerometers of high sensitivity. The dynamic identification tests allowed to estimate the dynamic properties of the church, namely frequencies, mode shapes and damping ratios. A FEM numerical model was prepared and calibrated, based on the first four experimental modes estimated in the dynamic identification tests. The average error between the experimental and numerical frequencies of the first four modes is equal to 5%. After calibration of the numerical model, pushover analyses with a load pattern proportional to the mass, in the transversal and longitudinal direction of the church, were performed. The results of the analysis numerical allow to conclude that the most vulnerable direction of the church is in the transversal one and the maximum load factor is equal to 0.35.

Development of a simulation tool for torsional vibration of branched power transmission system

In this master's thesis a mechanical model that is driven with variable speed synchronous machine was developed. The developed mechanical model simulates the mechanics of power transmission and its torsional vibrations. The mechanical model was developed for the need of the branched mechanics of a rolling mill and the propulsion system of a tanker. First, the scope of the thesis was to clarify the concepts connected to the mechanical model. The clarified concepts are the variable speed drive, the mechanics of power transmission and the vibrationsin the power transmission. Next, the mechanical model with straight shaft line and twelve moments of inertia that existed in the beginning was developed to be branched considering the case of parallel machines and the case of parallel rolls. Additionally, the model was expanded for the need of moreaccurate simulation to up to thirty moments of inertia. The model was also enhanced to enable three phase short circuit situation of the simulated machine. After that the mechanical model was validated by comparing the results of the developed simulation tool to results of other simulation tools. The compared results are the natural frequencies and mode shapes of torsional vibration, the response of the load torque step and the stress in the mechanical system occurred by the permutation of the magnetic field that is arisen from the three phase short circuit situation. The comparisons were accomplished well and the mechanical model was validated for the compared cases. Further development to be made is to develop the load torque to be time-dependent and to install two frequency converters and two FEM modeled machines to be simulated parallel.

Überwachung der Vorspannkraft Externer Spannglieder mit Hilfe der Modalanalyse

Aufgrund ihrer Vorteile hinsichtlich Dauerhaftigkeit und Bauwerkssicherheit ist in Deutschland seit 1998 die externe Vorspannung in Hohlkastenbrücken zur Regelbauweise geworden. Durch Verwendung der austauschbaren externen Vorspannung verspricht man sich im Brückenbau weitere Verbesserungen der Robustheit und damit eine Verlängerung der Lebensdauer. Trotz des besseren Korrosionsschutzes im Vergleich zur internen Vorspannung mit Verbund sind Schäden nicht völlig auszuschließen. Um die Vorteile der externen Vorspannung zu nutzen, ist daher eine periodische Überwachung der Spanngliedkräfte, z. B. während der Hauptprüfung des Bauwerks, durchzuführen. Für die Überwachung der Spanngliedkräfte bei Schrägseilbrücken haben sich die Schwingungsmessmethoden als wirtschaftlich und leistungsfähig erwiesen. Für die Übertragung der Methode auf den Fall der externen Vorspannung, wo kürzere Schwingungslängen vorliegen, waren zusätzliche Untersuchungen hinsichtlich der effektiven Schwingungslänge, der Randbedingungen sowie der effektiven Biegesteifigkeit erforderlich. Im Rahmen der vorliegenden Arbeit wurde das Modellkorrekturverfahren, basierend auf der iterativen Anpassung eines F.E.-Modells an die identifizierten Eigenfrequenzen und Eigenformen des Spanngliedes, für die Bestimmung der Spanngliedkräfte verwendet. Dieses Verfahren ermöglicht die Berücksichtigung der Parameter (Schwingungslänge, Randbedingungen und effektive Biegesteifigkeit) bei der Identifikation der effektiven Spanngliedkräfte. Weiterhin ist eine Modellierung jeder beliebigen Spanngliedausbildung, z. B. bei unterschiedlichen Querschnitten in den Verankerungs- bzw. Umlenkbereichen, gewährleistet. Zur Anwendung bei der Ermittlung der Spanngliedkräfte wurde eine spezielle Methode, basierend auf den besonderen dynamischen Eigenschaften der Spannglieder, entwickelt, bei der die zuvor genannten Parameter innerhalb jedes Iterationsschrittes unabhängig korrigiert werden, was zur Robustheit des Identifikationsverfahrens beiträgt. Das entwickelte Verfahren ist in einem benutzerfreundlichen Programmsystem implementiert worden. Die erzielten Ergebnisse wurden mit dem allgemeinen Identifikationsprogramm UPDATE_g2 verglichen; dabei ist eine sehr gute Übereinstimmung festgestellt worden. Beim selbst entwickelten Verfahren wird die benötigte Rechenzeit auf ca. 30 % reduziert [100 sec à 30 sec]. Es bietet sich daher für die unmittelbare Auswertung vor Ort an. Die Parameteridentifikationsverfahren wurden an den Spanngliedern von insgesamt sechs Brücken (vier unterschiedliche Spannverfahren) angewendet. Die Anzahl der getesteten Spannglieder beträgt insgesamt 340. Die Abweichung zwischen den durch Schwingungs-messungen identifizierten und gemessenen (bei einer Brücke durch eine Abhebekontrolle) bzw. aufgebrachten Spanngliedkräften war kleiner als 3 %. Ferner wurden die Auswirkungen äußerer Einflüsse infolge Temperaturschwankungen und Verkehr bei den durchgeführten Messungen untersucht. Bei der praktischen Anwendung sind Besonderheiten aufgetreten, die durch die Verwendung des Modellkorrekturverfahrens weitgehend erfasst werden konnten. Zusammenfassend lässt sich sagen, dass die Verwendung dieses Verfahrens die Genauigkeit im Vergleich mit den bisherigen Schwingungsmessmethoden beachtlich erhöht. Ferner wird eine Erweiterung des Anwendungsbereiches auch auf Spezialfälle (z. B. bei einem unplanmäßigen Anliegen) gewährleistet.

Parameter identification of structural dynamic models by inverse statistical analysis

Auf dem Gebiet der Strukturdynamik sind computergestützte Modellvalidierungstechniken inzwischen weit verbreitet. Dabei werden experimentelle Modaldaten, um ein numerisches Modell für weitere Analysen zu korrigieren. Gleichwohl repräsentiert das validierte Modell nur das dynamische Verhalten der getesteten Struktur. In der Realität gibt es wiederum viele Faktoren, die zwangsläufig zu variierenden Ergebnissen von Modaltests führen werden: Sich verändernde Umgebungsbedingungen während eines Tests, leicht unterschiedliche Testaufbauten, ein Test an einer nominell gleichen aber anderen Struktur (z.B. aus der Serienfertigung), etc. Damit eine stochastische Simulation durchgeführt werden kann, muss eine Reihe von Annahmen für die verwendeten Zufallsvariablengetroffen werden. Folglich bedarf es einer inversen Methode, die es ermöglicht ein stochastisches Modell aus experimentellen Modaldaten zu identifizieren. Die Arbeit beschreibt die Entwicklung eines parameter-basierten Ansatzes, um stochastische Simulationsmodelle auf dem Gebiet der Strukturdynamik zu identifizieren. Die entwickelte Methode beruht auf Sensitivitäten erster Ordnung, mit denen Parametermittelwerte und Kovarianzen des numerischen Modells aus stochastischen experimentellen Modaldaten bestimmt werden können.

Structural Dynamics Model of a Cartesian Robot

Methods are developed for predicting vibration response characteristics of systems which change configuration during operation. A cartesian robot, an example of such a position-dependent system, served as a test case for these methods and was studied in detail. The chosen system model was formulated using the technique of Component Mode Synthesis (CMS). The model assumes that he system is slowly varying, and connects the carriages to each other and to the robot structure at the slowly varying connection points. The modal data required for each component is obtained experimentally in order to get a realistic model. The analysis results in prediction of vibrations that are produced by the inertia forces as well as gravity and friction forces which arise when the robot carriages move with some prescribed motion. Computer simulations and experimental determinations are conducted in order to calculate the vibrations at the robot end-effector. Comparisons are shown to validate the model in two ways: for fixed configuration the mode shapes and natural frequencies are examined, and then for changing configuration the residual vibration at the end of the mode is evaluated. A preliminary study was done on a geometrically nonlinear system which also has position-dependency. The system consisted of a flexible four-bar linkage with elastic input and output shafts. The behavior of the rocker-beam is analyzed for different boundary conditions to show how some limiting cases are obtained. A dimensional analysis leads to an evaluation of the consequences of dynamic similarity on the resulting vibration.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

On the control of vibrations using synchrophasing

This paper describes the application of a technique, known as synchrophasing, to the control of machinery vibration. It is applicable to machinery installations, in which several synchronous machines, such as those driven by electrical motors, are fitted to an isolated common structure known as a machinery raft. To reduce the vibration transmitted to the host structure to which the machinery raft is attached, the phase of the electrical supply to the motors is adjusted so that the net transmitted force to the host structure is minimised. It is shown that while this is relatively simple for an installation consisting of two machines, it is more complicated for installations in which there are more than two machines, because of the interaction between the forces generated by each machine. The development of a synchrophasing scheme, which has been applied to propeller aircraft, and is known as Propeller Signature Theory (PST) is discussed. It is shown both theoretically and experimentally, that this is an efficient way of controlling the phase of multiple machines. It is also shown that synchrophasing is a worthwhile vibration control technique, which has the potential to suppress vibration transmitted to the host structure by up to 20 dB at certain frequencies. Although the principle of synchronisation has been demonstrated on a one-dimensional structure, it is believed that this captures the key features of the approach. However, it should be realised that the mode-shapes of a machinery raft may be more complex than that of a one-dimensional structure and this may need to be taken into account in a real application. © 2013 Elsevier Ltd.

Estudo da influência da flexibilidade dos discos nas rotações críticas de rotores

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)