Thesis (MEng) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: Full scale measurements were conducted on the polar supply and research vessel the S.A. Agulhas II during a 78 day voyage from Cape Town to Antarctica in 2013/2014. Investigations were conducted into the effect of vibration on human comfort and the structural dynamic response of the vessel. Vibration measured in the bridge of the vessel is found to have little effect on human comfort for a standing person and is classified as not uncomfortable according to BS ISO 2631-1. Structural fatigue as a result of vibration is found to reach levels where damage is possible in the stern and where damage is probable in the bow during open water navigation, according to ship vibration guidelines by Germanischer Lloyd. Multivariate statistical analyses are performed to investigate the relationships between multiple predictor variables and vibration response. Factor analysis revealed data structure from which specific physical phenomena could be identified. Multivariable linear regression models are developed to predict vibration response and are found to provide more accurate predictions in open water than in ice. The 2-node, 3-node and 4-node normal bending modes of the structure are identified using operational modal analysis while the vessel was moored in the harbour. The natural frequencies, damping ratios and mode shapes are estimated and compared using LMS Operational PolyMAX and ARTeMIS CCSSI. A comparison of operational modal analysis results to the STX Finland finite element model show that the vessel’s modes occur at lower frequencies than numerically predicted. Clear potential is identified to further investigate structural vibration and operational modal analysis algorithm development in future research. / AFRIKAANSE OPSOMMING: Volskaal metings was op die poolvoorsienings en navorsingskip die S.A. Agulhas II uitgevoer tydens ’n 78 dae reis van Kaapstad tot Antarktika in 2013/2014. Ondersoeke is uitgevoer met betrekking tot die effek van vibrasie op menslike gemak en die strukturele dinamiese reaksie van die vaartuig. Vibrasie wat in die brug van die skip gemeet is, het min invloed op menslike gemak vir ’n staande persoon en word geklassifiseer as nie ongemaklik volgens BS ISO 2631-1. Strukturele vermoeidheid as gevolg van vibrasie bereik vlakke waar skade moontlik is in die spieël en waar skade waarskynlik is in die boog tydens navigasie in oop water, volgens skip vibrasie riglyne deur Germanischer Lloyd. Meerveranderlike statistiese ontledings is uitgevoer om die verhoudings tussen verskeie voorspellerveranderlikes en vibrasieterugvoer te ondersoek. Faktorontleding het data struktuur openbaar waaruit spesifieke fisiese verskynsels geïdentifiseer kan word. Multi-veranderlike lineêre regressiemodelle was ontwikkel om vibrasie reaksie te voorspel en lewer meer akkurate voorspellings in oop water as in ys. Die 2-nodus, 3-nodus en 4-nodus normale buig modes van die struktuur is geïdentifiseer met behulp van operasionele modale analise terwyl die skip vasgemeer in die hawe is. Die natuurlike frekwensie, demping verhoudings en mode vorms is beraam en vergelyk met behulp van LMS operasionele Polymax en ARTeMIS CCSSI. ’n vergelyking van operasionele modale analise resultate en ’n STX Finland eindige element model toon dat die vaartuig se modusse voorkom by laer frekwensies as wat numeries voorspel word. Duidelike potensiaal is geïdentifiseer om strukturele vibrasie en die ontwikkeling van operasionele modale analise algoritmes te ondersoek in toekomstige navorsing.

Ce travail s’inscrit dans le cadre de la mise en place d’une stratégie de SHM (Structural Health Monitoring) dédiée à la surveillance des structures en génie civil. Il a porté, d’une part, sur l’étude des méthodes de détection et de localisation de l’endommagement du bâti existant et, d’autre part, sur l’élaboration du cahier des charges d’un capteur « intégré » capable de délivrer des informations par transmission compacte des données pour les communiquer à une chaîne SHM. Des études numériques et expérimentales ont été réalisées dans cet objectif. L’état de l’art a clairement mis en évidence plusieurs points faibles des méthodes de détection et de localisation d’endommagements usuelles comme, par exemple, le manque de précision et/ou la complexité de mise en place. On observe aussi que la sensibilité de ces méthodes par rapport à plusieurs paramètres, essentiellement la direction de mesure, le positionnement des capteurs et la sévérité des endommagements, ne permet pas à ce jour de dresser un diagnostic précis de l’état de santé des structures. Pour répondre au cahier des charges d’une chaîne SHM, un Algorithme de Détection et de Localisation (ADL) a été élaboré. Cet algorithme fait appel à des méthodes utilisant les paramètres modaux, essentiellement les fréquences propres et les déformées modales. Leurs mises en œuvre séquentielles et itératives, judicieusement structurées et pilotées,a permis de répondre aux objectifs fixés. Les paramètres modaux requis sont identifiés à l’aide des techniques d’Analyse Modale Opérationnelle (AMO) et à partir de la réponse en accélérations des structures. Deux algorithmes d’AMO ont été utilisés pour leur efficacité et pour leur aptitude à l’automatisation: la méthode stochastique par sous ensemble (SSI), et la méthode de décomposition dans le domaine fréquentiel (FDD). En fusionnant les algorithmes d’AMO avec l’ADL, une chaîne complète de surveillance a été créée. La validation des algorithmes et de la chaîne de surveillance s’est faite à plusieurs niveaux. Tout d’abord, basés sur la théorie des éléments finis, des modèles numériques de la tour de l'Ophite et du pont canadien de la Rivière aux-Mulets ont permis d'évaluer l'ADL. Ces modèles sont endommagés par des signaux sismiques et fournissent les données accélérométriques, données d’entrée du logiciel que nous avons développé. Les résultats obtenus sont tout à fait satisfaisants voire meilleurs que ceux issus des méthodes usuelles. Dans un second temps, nous avons traité des données expérimentales «réelles », issues des mesures accélérométriques sur la tour de l’Ophite. La confrontation entre les résultats d’identification des fréquences propres et des déformées modales issus des algorithmes d’AMO et ceux reportés par la bibliographie, a révélé l’efficacité des algorithmes développés.Enfin, une maquette d’un bâtiment à échelle réduite a également été élaborée et instrumentée.L’application de la chaine de surveillance a permis, d’une part, de détecter et localiser l’endommagement introduit dans la structure et, d’autre part, de mettre en évidence l’intérêt de la surveillance automatique. Finalement, une étude a été menée dans le but de réduire la quantité d’informations enregistrées sur les structures et de faciliter le transfert des données servant comme entrées de la chaîne de surveillance. Les résultats de ces études ont contribué à la spécification d’un nouveau système de surveillance / The work presented in this thesis is part of the development of a Structural Health Monitoring(SHM) system dedicated to civil engineering applications. First, it studies the methods of damagedetection and localization. Furthermore, it helps elaborate the specifications of an integratedsensor capable of delivering information by compact transmission of data to an SHM chain.Numerical and experimental studies have been carried out for this purpose. The study of theliterature clearly highlighted several weak points of the traditional damage detection andlocalization methods, such as the lack of precision and the complexity of implementation. Thesensitivity of these methods with respect to several parameters, essentially the measurementdirection, the positioning of the sensors and the severity of the damage, makes it impossible todraw up an accurate diagnosis of the structures. In order to overcome these limitations, a damageDetection and Localization Algorithm (DLA) was developed. By applying Vibration-Based Damage Detection Methods, following a precise order and taking into account the sensitivity, the simplicityand the SHM level of each method, this algorithm made it possible to meet the objectives set at the beginning of this work. The required modal parameters, namely eigen-frequencies and modeshapes, were identified from the structure’s output-only response using Operational ModalAnalysis techniques (OMA). Two OMA algorithms were used for their efficiency and automationability: the Stochastic Subspace Identification method (SSI) and the Frequency DomainDecomposition method (FDD). By merging the OMA algorithms with the DLA, a complete SHMchain was created. The algorithms validation was made at several levels. First, the DLA wasevaluated using a Finite Element Model (FEM) of the Ophite tower and the Rivière aux Muletsbridge. The results obtained were quite satisfactory. Secondly, experimental data were processed,from accelerometric measurements on the Ophite tower. The confrontation between the results ofeigen-frequencies and mode shapes identification using OMA algorithms and those reported in theliterature revealed the efficiency of the developed algorithms. Finally, a scale model of a buildingwas developed, instrumented and damaged. The use of the surveillance chain allowed thedetection and localization of the damage. Moreover, it showed all the interest of using automatic surveillance. The last step of this work dealt with a study carried out to reduce the amount of datarecorded on structures in order to facilitate their transfer to the SHM chain. As a conclusion, the results of these studies contributed to the specification of a new monitoring system

Apresenta uma nova técnica de identificação estocástica para estruturas sujeitas a excitação ambiente utilizando um método não recursivo, a análise estatística e a transformada wavelet. A análise estatística contribui para a seleção da melhor ordem para o sistema e automação dos procedimentos computacionais. Em geral há dificuldade para a identificação de baixas freqüências. A transformada wavelet é uma ferramenta fundamental para a compressão de dados e torna possível a identificação completa incluindo baixas freqüências e modos acoplados, além de melhorar significativamente a eficiência computacional do método. É apresentado o estudo de três sistemas simulados e os resultados obtidos são comparados aos parâmetros modais teóricos. / A new form to carry out stochastic identification of structures in operational conditions using a non recursive method, the statistic analysis and the wavelet transform, is presented. The statistic analysis contributed to select the best system order and to automation of computational procedures. In general the identification of low frequencies is a difficult task. The wavelet transform is an essential tool for compression of data making possible the complete identification including low frequencies. In addition it improves the computational efficiency. The study of three simulated system is presented and the results are compared with the analytical modal parameters.

A análise de vibrações nos sistemas estruturais e rotativos permite detectar problemas indesejáveis, como a fadiga estrutural e o desgaste excessivo, que contribuem para a redução da vida útil do sistema e seus componentes. Tradicionalmente, a medição das vibrações é realizada por sensores de contato (acelerômetros e extensômetros), que possuem como inconveniente a adição de sua massa no sistema. Como alternativa, existem os sensores de não contato (LVD e ESPI), que são equipamentos de custo elevado. Este trabalho visa o desenvolvimento de um equipamento de baixo custo que realize medições multi-pontos sem contato do comportamento vibratório de estruturas e eixos rotativos. O método proposto utiliza como base os princípios da fotogrametria em conjunto com técnicas de subamostragem, que são utilizadas em estruturas ou máquinas com frequências de vibração conhecidas (e.g máquinas rotativas). A metodologia foi inicialmente aplicada em uma viga engastada-livre, excitada periodicamente por um shaker eletrodinâmico e posteriormente em um sistema rotativo montado em um bancada de testes. A viabilidade em se utilizar o método foi verificada comparando os resultados obtidos com as medições realizadas por um vibrômetro laser Doppler, no caso do sistema estrutural, e por sensores de proximidade indutivo nas vibrações do eixo rotativo. Com base nos comparativos, conclui-se que este método, mesmo apresentando limitações de resolução, pode ser perfeitamente empregado em medições de sistemas estruturais e rotativos assim como na análise modal operacional de estruturas. / The analysis of vibrations in structural and rotating systems allows the detection of undesirable problems, such as the structural fatigue and excessive wear, which contribute to the reduction of the useful life of the systems and their components. Traditionally, the measurement of vibrations is carried out by contacting sensors (accelerometers and strain gauges), which have the inconvenience of adding mass into the system. Alternativelly, there are the non-contacting sensors (LVD and ESPI), which are high cost equipments. This work aims at developing a low cost equipment that carry out multi-point non-contact measurements of the vibratory behavior of structures and rotating shafts. The proposed method uses as a basis the principles of photogrammetry together with sub-sampling techniques, which are used in structure or machines with known vibration frequencies (e.g rotating machines). The methodology was initially applied on a cantilever beam, periodically excited by an electrodynamic shaker and later in a rotating system mounted on a test bench. The feasibility of using the method was verified comparing the results obtained with measurements from a laser Doppler vibrometer, in the case of the structural system, and with inductive proximity sensors in the rotating shaft vibration. Based on the comparison analysis, one observes that this method can be perfectly used in vibration measurements in structural and rotating systems even with limitations in resolution as well as in operational modal analysis of structures.

O presente trabalho tem como objetivo desenvolver novas alternativas de identificação modal para estruturas sob excitações em condição de operação baseadas em funções de transmissibilidade. Recentes metodologias formuladas sobre conceitos de transmissibilidade têm surgido como alternativa para a identificação de parâmetros modais de estruturas. A identificação nestas metodologias é independente do espectro da excitação, sendo uma vantagem importante com respeito a metodologias anteriores no domínio da frequência que supõem a excitação como ruído branco. Dessa forma, aproveitando os diferentes trabalhos dirigidos a avaliar parâmetros modais com uso da transmissibilidade, são propostas três novas alternativas. A primeira delas propõe a decomposição de valores singulares sobre matrizes de funções de transmissibilidade escalar com densidade espectral para estimar frequências naturais e modos de vibração. A segunda alternativa propõe o conceito de funções de transmissibilidade multivariável com diferente referência para a identificação modal. E a terceira introduz uma melhora na primeira alternativa incluindo a possibilidade da estimação de taxas de amortecimento. Uma ferramenta computacional para a análise modal é desenvolvida como apoio para as simulações numéricas de verificação das metodologias de identificação modal propostas. Diferentes exemplos numéricos com uma viga submetida a excitações de ruído colorido mostram que os métodos propostos são capazes de identificar parâmetros modais sem a introdução das frequências adicionais devido às excitações de ruído colorida utilizadas. Além disso, os dados de um teste de vibrações sobre uma ponte em operação foram utilizados para verificar os métodos. / This research aims to develop new alternatives of modal identification for structures under excitation in operation condition based on transmissibility functions. Latest methodologies based on transmissibility concepts have been arising as alternatives for modal parameter identification of structures. Modal parameter identification in this type methodology is input spectrum independent being an important advantage with respect previous frequency domain methods that assumes white noise excitation. Different alternatives of modal identification based on transmissibility functions are proposed in this work. The first of them proposes singular value decomposition on scalar transmissibility functions matrices with spectral density to estimate natural frequencies and vibration modes (PSDTM-SVD method). A second alternative proposes the concept of multivariable transmissibility functions with different transferring outputs for modal parameter identification. And the third alternative proposes an enhanced PSDTM-SVD method, which permits to identify modal damping. Computational tool for modal analysis is developed as a support for the numerical simulations of verification of modal identification methodologies proposed. Different numerical examples of a beam model subjected to colored noise excitations show that the proposed methods are capable of identifying modal parameters without the introduction of the additional frequencies due to the excitations used. Furthermore, data from an operational vibration bridge test were used to verify the methods.

Apresenta uma nova técnica de identificação estocástica para estruturas sujeitas a excitação ambiente utilizando um método não recursivo, a análise estatística e a transformada wavelet. A análise estatística contribui para a seleção da melhor ordem para o sistema e automação dos procedimentos computacionais. Em geral há dificuldade para a identificação de baixas freqüências. A transformada wavelet é uma ferramenta fundamental para a compressão de dados e torna possível a identificação completa incluindo baixas freqüências e modos acoplados, além de melhorar significativamente a eficiência computacional do método. É apresentado o estudo de três sistemas simulados e os resultados obtidos são comparados aos parâmetros modais teóricos. / A new form to carry out stochastic identification of structures in operational conditions using a non recursive method, the statistic analysis and the wavelet transform, is presented. The statistic analysis contributed to select the best system order and to automation of computational procedures. In general the identification of low frequencies is a difficult task. The wavelet transform is an essential tool for compression of data making possible the complete identification including low frequencies. In addition it improves the computational efficiency. The study of three simulated system is presented and the results are compared with the analytical modal parameters.

This study presents the investigation and the verification of the modal parameters of a plate-like structure by using different modal analysis methods. A fin-like structure which is generally used in aircraft is selected as a subcategory of a plate-like test structure. In the first part of the thesis, the natural frequencies and the corresponding mode shapes of the fin are extracted by Finite Element Analysis method. Classical Modal Analysis and Testing methods comprising both impact hammer and modal shaker applications are then applied in order to obtain the modal parameters such as / resonance frequencies, mode shapes and damping ratios. In the second part, a recent modal analysis technique, Operational Modal Analysis, is also applied in the laboratory environment. Since Operational Modal Analysis method does not require any information of input forcing, the fin structure is tested under both mechanical and acoustical types of excitations without measuring the given input forces. Finally, Operational Modal Analysis and Testing is also performed under various flow conditions generated in the wind tunnel which may simulate the real operating environment for the fin structure. The modal parameters extracted under these flow conditions are then compared with the previously obtained Finite Element, Classical and Operational Modal Analyses results.

[pt] Análise modal consiste na caracterização de um sistema através dos seus parâmetros modais. Quando a principal excitação é causada pelo ambiente em que o sistema está inserido, essa caracterização é definida como análise modal operacional (OMA). Nestes casos, os forçamentos não são conhecidos (mensuráveis) e apenas as respostas são monitoradas. Por terem natureza aleatória, esses sinais precisam ser incorporados ao modelo numérico através de processos estocásticos. O principal objetivo desta dissertação consiste em descrever as técnicas de identificação em OMA. Para isso, duas vertentes foram criadas, uma teórica e outra experimental. Na parte teórica, as hipóteses necessárias para a identificação de um sistema por OMA são apresentadas. Uma análise dos erros causados por sinais ruidosos também é feita, permitindo que a sensibilidade dos métodos seja avaliada. Além de contemplar os principais métodos de identificação, dois novos métodos são propostos. Ambos foram desenvolvidos a partir da Decomposição Ortogonal Própria (POD) e combinam uma eficiência computacional com a possibilidade de quantificar as incertezas dos parâmetros. Na vertente experimental, o objetivo é ilustrar e validar a identificação de estruturas. Para isso, três diferentes bancadas foram criadas: um prédio de dois andares, uma pá eólica e uma ponte suspensa. Após a construção, essas estruturas foram devidamente instrumentadas por diferentes sensores. Um sistema de aquisição dados foi montado através de hardwares comerciais e analisados através de uma interfase gráfica desenvolvida especialmente para OMA pelo Laboratório de Vibrações. / [en] Modal analysis consists in the characterization of a system through its modal parameters. When the main excitation source is the system s environment, this characterization is defined as operational modal analysis (OMA). On those cases, the forces are unknown (not measured) and only the responses are monitored. Because of there random nature, those signals are incorporated into the numerical model as stochastic processes. The main goal of this dissertation is to describe the identification techniques in OMA. Therefore, two different approaches were created: a theoretical one and an experimental one. In the theoretical part, the required hypotheses for system s identification with OMA are presented. An analysis of the errors caused by noisy signals are also performed, allowing the method s sensibility to be evaluated. Besides the standard identification methods, two new ones are proposed. They both has been developed as extension of the Proper Orthogonal Decomposition (POD) and combine an efficient computational process with the possibility of quantify the parameters uncertainties. In the experimental approach, the goal is to illustrate and validate the identification of structures. Therefore, three different test bench were created: a two floor building, a wind turbine blade and a cable-stayed bridge. After their construction, those structures were proper instrumented with different sensors. A data acquisition system were built using commercial hardwares and analyzed through a graphic interface specially made for OMA and developed in the vibration laboratory.

La France Métropolitaine est composée de régions à sismicité modérée mais néanmoins vulnérables aux tremblements de terre. En effet, 85% des bâtiments existants ont été construits avant l’apparition des règles de construction parasismique. Pour évaluer la vulnérabilité sismique de ces structures, il existe différentes méthodes à grande échelle telles que Hazus ou Risk-UE, non adaptées à l’échelle d’un bâtiment. Deux typologies de structures ont été étudiées dans ce travail : les structures récentes en béton armé représentatives des grands bâtiments stratégiques, et les structures en maçonnerie non renforcée, représentatives des centres villes historiques. Compte-tenu de la sismicité modérée, les structures récentes en béton armé ont un comportement linéaire élastique. Dans ce cadre, l’instrumentation d’un bâtiment, tel que la Tour de l’Ophite, est essentielle car elle permet de déterminer les vibrations ambiantes d’une structure et d’en extraire les paramètres modaux (fréquences propres, amortissements et déformées modales) qui incluent naturellement des informations sur la qualité des matériaux utilisés, leur vieillissement, leur endommagement, etc. De plus, un outil, basé sur la méthode stochastique par sous-espaces à l’aide des matrices de covariance (SSI-COV), a été développé afin de détecter au mieux les modes propres très proches (modes doubles), lors du traitement des données issues de l’instrumentation de la Tour de l’Ophite. Un modèle numérique par Eléments Finis est également proposé afin de prédire, dans le domaine linéaire, les déplacements de la Tour de l’Ophite soumise à un séisme identique à celui des Abruzzes en Italie en 2009. Pour les structures en maçonnerie non renforcée, un modèle de comportement non-linéaire des matériaux, avec une approche de type endommagement fragile, a été développé et utilisé pour la simulation numérique du comportement ductile des panneaux, remplaçant ainsi la mise en œuvre d’essais expérimentaux lourds et coûteux. A partir des travaux précédents, une méthodologie analytique d’évaluation de la vulnérabilité sismique des bâtiments existants, validée par comparaison avec le code numérique TreMuRi, est proposée et appliquée à un bâtiment. Par exemple, la généricité de notre méthodologie a permis de mener une investigation sur un matériau local, les murs en galets. / France is a country composed of moderate seismic hazard regions however vulnerable to earthquakes. 85% of existing buildings have been built before the application of paraseismic codes. Several current large-scale seismic vulnerability assessment methods are used, such as Hazus or Risk-UE, but they are inappropriate for specific building analysis. Two structure types have been evaluated in this thesis; the recent reinforced concrete structures for high strategic buildings, and the unreinforced masonry structures, for historical city centres. In view of the moderate seismic risk, recent reinforced concrete structures have an elastic behaviour. In this context, the instrumentation of a building, such as the Ophite Tower, is essential as it determines the ambient vibrations of a structure and extracts modal parameters (natural frequencies, modal shapes and damping), which naturally include information such as quality of materials, ageing, damage, etc. Moreover, as a tool based on the Covariance driven Stochastic Subspace Identification method (SSI-COV), it was developed in order to improve the detection of very close natural modes (double modes), during data processing from the instrumentation of Ophite Tower. A Finite Element numerical model (linear) was also proposed to predict the displacements of Ophite Tower under a seismic motion similar to Abruzzes earthquake (Italy, 2009). For unreinforced masonry structures, a model for nonlinear behaviour of materials with a brittle cracking approach has been developed. This is used for the numerical simulation of the ductile behaviour of panels and replaces the expensive experimental tests. From previous works, an analytical seismic vulnerability assessment method of existing buildings, validated par comparison with TreMuRi code, was proposed and applied to a building. For example, the genericity of this methodology has led to an investigation of a local material (pier walls).

O presente trabalho tem como objetivo desenvolver novas alternativas de identificação modal para estruturas sob excitações em condição de operação baseadas em funções de transmissibilidade. Recentes metodologias formuladas sobre conceitos de transmissibilidade têm surgido como alternativa para a identificação de parâmetros modais de estruturas. A identificação nestas metodologias é independente do espectro da excitação, sendo uma vantagem importante com respeito a metodologias anteriores no domínio da frequência que supõem a excitação como ruído branco. Dessa forma, aproveitando os diferentes trabalhos dirigidos a avaliar parâmetros modais com uso da transmissibilidade, são propostas três novas alternativas. A primeira delas propõe a decomposição de valores singulares sobre matrizes de funções de transmissibilidade escalar com densidade espectral para estimar frequências naturais e modos de vibração. A segunda alternativa propõe o conceito de funções de transmissibilidade multivariável com diferente referência para a identificação modal. E a terceira introduz uma melhora na primeira alternativa incluindo a possibilidade da estimação de taxas de amortecimento. Uma ferramenta computacional para a análise modal é desenvolvida como apoio para as simulações numéricas de verificação das metodologias de identificação modal propostas. Diferentes exemplos numéricos com uma viga submetida a excitações de ruído colorido mostram que os métodos propostos são capazes de identificar parâmetros modais sem a introdução das frequências adicionais devido às excitações de ruído colorida utilizadas. Além disso, os dados de um teste de vibrações sobre uma ponte em operação foram utilizados para verificar os métodos. / This research aims to develop new alternatives of modal identification for structures under excitation in operation condition based on transmissibility functions. Latest methodologies based on transmissibility concepts have been arising as alternatives for modal parameter identification of structures. Modal parameter identification in this type methodology is input spectrum independent being an important advantage with respect previous frequency domain methods that assumes white noise excitation. Different alternatives of modal identification based on transmissibility functions are proposed in this work. The first of them proposes singular value decomposition on scalar transmissibility functions matrices with spectral density to estimate natural frequencies and vibration modes (PSDTM-SVD method). A second alternative proposes the concept of multivariable transmissibility functions with different transferring outputs for modal parameter identification. And the third alternative proposes an enhanced PSDTM-SVD method, which permits to identify modal damping. Computational tool for modal analysis is developed as a support for the numerical simulations of verification of modal identification methodologies proposed. Different numerical examples of a beam model subjected to colored noise excitations show that the proposed methods are capable of identifying modal parameters without the introduction of the additional frequencies due to the excitations used. Furthermore, data from an operational vibration bridge test were used to verify the methods.