In this work, a new method is suggested for the modal identification of nonlinear structures and for the use of the modal data in calculating response of the nonlinear system to harmonic excitation. Nonlinearity in mechanical structures is usually encountered in connection regions. In this study, the nonlinear part of such a structure is modeled as a single nonlinear element and modal parameters of the structure are obtained as a function of displacement amplitude. Identification and modeling of nonlinear elements can be done through modal tests conducted at different response levels. Response level dependent modal parameters are used in calculating the response of the system to harmonic excitation at any forcing level. Furthermore, the modal model of a nonlinear substructure can be used in structural coupling of the nonlinear system with a linear one, and in structural modification problems where a nonlinear structure is modified with linear elements. Validation of the modal model proposed, and the use of this model in harmonic response computation, structural coupling and structural modification problems are demonstrated with several case studies.

Bolted joints are integral parts of mechanical systems, and bolt preload loss is one of the major failure modes for bolted joint structures. Understanding the damping and frequency response to a varying preload in a single-bolted lap-joint structure can be very helpful in predicting and analyzing more complicated structures connected by these joints. In this thesis, the relationship between the bolt preload and the natural frequency, and the relationship between the bolt preload and the structural damping, have both been investigated through impact hammer testing on a single-bolted lap-joint structure. The test data revealed that the bolt preload has nonlinear effects on the structural damping and on the natural frequency of the structure. The damping ratios of the test structure were determined to increase with decreasing preload. An increase in structural damping is beneficial in most engineering circumstances, for it will reduce the vibrational response and noise subjected to external excitations. It was also observed that the modal frequency increased with increasing preload, but remained approximately constant for preload larger than 30% in the bolt yield strength. One application for studying the preload effect is the detection for loose bolts in structures. The possibility of using impact testing for estimating preload loss has been confirmed, and the modal damping was determined to be a more sensitive indicator than the natural frequency in a single-bolted lap-joint structure.

Civil infrastructure throughout the world serves as main arteries for commerce and transportation, commonly forming the backbone of many societies. Bridges have been and remain a crucial part of the success of these civil networks. However, the crucial elements have been built over centuries and have been subject to generations of use. Many current bridges have outlived their intended service life or have been retrofitted to carry additional loads over their original design. A large number of these historic bridges are still in everyday use and their condition needs to be monitored for public safety. Transportation infrastructure authorities have implemented various inspection and management programs throughout the world, mainly visual inspections. However, careful visual inspections can provide valuable information but it has limitations in that it provides no actual stress-strain information to determine structural soundness. Structural Health Monitoring (SHM) has been a growing area of research as officials need to asses and triage the aging infrastructure with methods that provide measurable response information to determine the health of the structure. A rapid improvement in technology has allowed researchers to start using new sensors and algorithms to understand the structural parameters of tested structures due to known and unknown loading scenarios. One of the most promising methods involves the use of wireless sensor nodes to measure structural responses to loads in real time. The structural responses can be processed to help understand the modal parameters, determine the health of the structure, and potentially identify damage. For example, modal parameters of structures are typically used when designing the lateral system of a structure. A better understanding of these parameters can lead to better and more efficient designs. Usually engineers rely on a finite element analysis to identify these parameters. By observing the actual parameters displayed during field testing, the theoretical FE models can be validated for accuracy. This paper will present the field testing of a historic wrought iron truss bridge, in a case study, to establish a repeatable procedure to be used as reference for the testing of other similar structures.

This study introduces new families of wavelets. The first is directly derived from the response of Second Order Underdamped Linear-Time-Invariant (SOULTI) systems, while the second is a generalization of the first to the complex domain and is similar to the Laplace transform kernel function. The first takes the acronym of SOULTI wavelet, while the second is named the Laplace wavelet. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. It is shown that it is possible to recover back the original signal once the SOULTI or the Laplace wavelet transform is applied to decompose the signal. It is found that both wavelet transforms satisfy linear differential equations called the reconstructing differential equations, which are closely related to the differential equations that produce the wavelets. The new wavelets can have well defined Time-Frequency resolutions, and they have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification and modal decomposition of LTI Multi-Degree of Freedom (MDOF) systems and it showed better results than the Short-time Fourier Transform (STFT) and the other harmonic wavelets used in time-frequency analysis. The modal decomposition is applied for modal parameters identification, and the properties of the Laplace and the SOULTI wavelet transforms allows analytical and accurate identification methods. / Ph. D. / This study introduces new families of wavelets (small wave-like functions) derived from the response of Second Order Underdamped (oscillating) Linear-Time-Invariant systems. The first is named the SOULTI wavelets, while the second is named Laplace Wavelets. These functions can be used in a wavelet transform which transfers signals from the time domain to the time-frequency domain. It is shown that it is possible to recover back the original signal once the transform is applied. The new wavelets can have well defined Time-Frequency resolutions. The time-frequency resolution is the multiplication of the time resolution and the frequency resolution. A resolution is the smallest time range or frequency range that carries a feature of the signal. The new wavelets have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying oscillating signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification, and decomposing signals into the basic oscillation frequencies, called the modes of vibration. In addition, the new wavelets are applied to infer the parameters of dynamic systems, and they show better results than the Short-time Fourier Transform (STFT) and the other wavelets used in time-frequency analysis.

[pt] O uso de materiais sustentáveis e os resultados das pesquisas sobre energias renováveis têm sido aplicados nas obras civis que buscam estar à vanguarda no fornecimento de sistemas construtivos novos, leves, resistentes e de baixo custo. Dentre estes materiais, o bambu é uma solução que apresenta características químicas, físicas e mecânicas compatíveis e em muitos aspectos superiores em comparação com os materiais industrializados. Pesquisas desenvolvidas no Departamento de Engenharia Civil da PUC-Rio, desde 1979, fornecem dados de caracterização do bambu como material de construção, porém estudos mais aprofundados sobre seu desempenho estrutural se fazem necessários. Neste trabalho procura-se avaliar o comportamento de uma estrutura de pórtico plano em modelo reduzido sob carregamento estático e dinâmico. Os resultados se comparam com os de um modelo reduzido em aço. O bambu ensaiado é da espécie Phyllostachys aurea, que foi estudado na PUC–Rio anteriormente. Os dados coletados em relação às propriedades físicas, mecânicas e dinâmicas se verificam usando as normas ISO-22157-1 e ISO/TR 22157-2 que existem para estabelecer as propriedades físicas e mecânicas sujeitas à carga estática. Nos pórticos de modelos reduzidos é aplicada as cargas estáticas vertical e lateral para avaliar a resposta no regime elástico e plástico, e assim, comparar ao comportamento dos materiais segundo suas propriedades, como à deformação permanente e o comportamento rígido-plástico. Na análise dinâmica, realizam-se ensaios de vibração livre aplicando deslocamento inicial, para identificar os parâmetros modais estruturais que correspondem aos valores de amortecimento coeficiente de amortecimento (igual) 1,5 por cento e coeficiente de amortecimento (igual) 2,3 por cento e frequência natural de 13 Hz e 35 Hz, em segmentos de bambu e nos modelos de pórtico respectivamente. / [en] The use of green and ecological materials in addition to the renewable energy in civil engineering are leading provider of new building systems, lightweight, durable and inexpensive are reality at the present time. Among these materials, bamboo is a solution that has some chemical, physical and mechanical properties compatible and in many cases even superior in comparison with industrialized materials. Studies carried out in the Department of Civil Engineering of PUC-Rio, since 1979, generated technical data concerning the chemical, physical and mechanical characterization of bamboo as a building material. Further studies on its structural performance in different forms and geometry are needed for establishing the method of calculation of bamboo structures. This study presents the results of an investigation for the evaluation of the behavior of a plane frame structure subjected to lateral and vertical static and only lateral dynamic loading. This work is the first investigation on the dynamic behavior of the bamboo frame, in the available technical literature. To achieve this objective and to compare the obtained results with those of a steel model, bamboo plane frame of the same scale using the species Phyllostachys aurea, was prepared. The physical and mechanical properties of the bamboo were established using ISO-22157-1, ISO/TR22157-2 recommendations for static load. In the plane frame models a static load is applied to evaluate the response in the elastic and plastic regime. In turn the obtained data are compared with those of steel plane frame. In dynamic analysis, free vibration tests were performed in bamboo segments and plane models frame applying initial displacement. The values of damping damping coefficient (equal) 1,5 percent and damping coefficient (equal) 2,3 percent and the natural frequencies of 13 Hz and 35 Hz for the segment and the bamboo portal frame models respectively were obtained.

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.

"This dissertation proposes a vibration-based approach to detect and monitor structural damage by tracking the instantaneous modal parameters. A change in the instantaneous modal parameters indicates change in the structural health condition. In contrast to many existing structural health monitoring schemes, the proposed approach is less model dependent and works well for both sudden and evolving damage, general loading conditions and complex structures. The instantaneous modal parameters, including modal frequency, mode shape vector and modal damping ratio, are introduced as a bridge between the system properties and time varying vibration modes. The theoretical background of the time-varying vibration modes is developed. It has been shown that for slowly time-varying systems such modes exist and the instantaneous modal parameters have a clear physical interpretation and can be identified from free and forced vibration responses. A set of known techniques are used in an innovative way to identify the instantaneous modal parameters. Applicability of the identification techniques depends on the nature and availability of measurement data. Wavelet ridge method is used to identify the instantaneous modal frequencies and normalized instantaneous mode shape vectors from free vibration data. Wavelet packet sifting technique in conjunction with Hilbert transform and confidence index is proposed to identify the normalized instantaneous mode shape vector from both free and forced vibration data. Time-varying Kalman filter is integrated with the wavelet packet sifting technique to identify the instantaneous modal frequencies and the instantaneous modal damping ratios from free and forced vibration data. The proposed approach has been validated using both simulation and experimental data. The simulation data is obtained from a multi-degree-of-freedom system with time varying stiffness under different loading conditions. Experimental data include both impact testing data from the ASCE benchmark study and shaking-table test data of a full-size two-story wooden building structure, conducted at DPRI, Kyoto University, Japan. It has been shown that the proposed approach can successfully detect and monitor damage and, therefore, has great potential for real applications."

"In this work an innovative wavelet packet based sifting process for signal decomposition has been developed and its application for health monitoring of time-varying structures is presented. With the proposed sifting process, a signal can be decomposed into its mono-frequency components by examining the energy content in the wavelet packet components of a signal, and imposing certain decomposition criteria. The method is illustrated for simulation data of a linear three degree-of-freedom spring-mass-damper system and the results are compared with those obtained using the empirical mode decomposition (EMD) method. Both methods provide good approximations, as compared with the exact solution for modal responses from a conventional modal analysis. Incorporated with the classical Hilbert transform, the proposed sifting process may be effectively used for structural health monitoring by monitoring instantaneous modal parameters of the structure for both, cases of abrupt structural stiffness loss and progressive stiffness degradation. The effectiveness of this method for practical application is evaluated by applying the methodology for experimental data and the results obtained matched with the field observations. The proposed methodology has shown better results in a comparison study which is done to evaluate performance of the proposed approach with other available SHM techniques, namely EMD technique and Continuous Wavelet Transform (CWT) method, for cases characterized by different damage scenarios and noise conditions."

O objetivo deste trabalho é estudar métodos dinâmicos de detecção de dano em vigas, em especial os métodos baseados na variação da flexibilidade medida dinamicamente. Os métodos revisados formam parte das técnicas de Detecção de Dano Não Destrutivas (DDND). Nas técnicas DDND o dano é localizado por comparação entre o estado sadio e o danificado da estrutura. Neste trabalho, o problema de vibração inverso é apresentado e a matriz de flexibilidade estática da estrutura é determinada a partir de seus parâmetros modais. Com ajuda de um Modelo de Elementos Finitos (MEF) são mostrados os diferentes padrões de variação da matriz de flexibilidade produzidos pela presença do dano. Baseando-se nestes padrões é possível identificar a posição do dano dentro da estrutura, como indicado pelos diversos exemplos apresentados. / The purpose of this work is to study dynamic methods for damage detection in beam structures. The attention is devoted to the methods based on dynamically measured flexibility. The reviewed methods are part of Nondestructive Damage Detection techniques (NDD). In the NDD techniques the damage is determined through the comparison between the undamaged and damaged state of the structure. In this work the inverse vibration problem is presented and the structure\'s flexibility matrix calculated from his modal parameters. The Finite Elements Model (FEM) is employed to show that a clear pattern exist for the changes in the flexibility matrix produced due to the presence of damage. The flexibility matrix changes is used to identify and locate damage as indicated by the several examples presented.

L'évaluation des modifications des caractéristiques d'un système dynamique non-stationnaire est étudiée suivant les modifications des paramètres modaux. Pour cela, nous étudions en premier l'obtention de ces paramètres, à l'aide des méthodes d'identification à partir des réponses vibratoires mesurées. Trois méthodes d'identification sont étudiées: la méthode de Décomposition Orthogonale Propre (POD), la méthode de Décomposition en Valeurs Singulières (SVD) et la méthode de Décomposition Orthogonale Régularisée (SOD). Ensuite, trois étapes sont considérées pour suivre les changements de masse des systèmes non-stationnaires à partir des variations des paramètres modaux: la localisation de l'instant du changement (étape 1), la détection de la position du changement (étape 2) et la quantification de la valeur du changement (étape 3). Pour l'étape 1, la transformée en ondelettes (TO) qui est une analyse temps-fréquence est appliquée. Ensuite, trois méthodes de détection de la position du changement de la masse sont développées dans l'étape 2. Enfin, la variation relative des fréquences propres est utilisée pour la quantification de la variation relative de la masse dans l'étape 3. Toutes ces méthodes ont été testées numériquement. De plus une maquette simplifiée de bâtiment a été instrumentée sous excitations de choc. Ces essais ont permis de valider les méthodes développées dans cette thèse / Modification of modal parameters is considered the main tool for the evaluation of characteristic changes of a non stationary dynamic system. Therefore, our first interest is to obtain these modal parameters from vibration measures using identification methods. Three methods are discussed here: Proper Orthogonal Decomposition (POD), Singular Value Decomposition (SVD) and Smooth Orthogonal Decomposition (SOD). Then, in order to evaluate the mass changes in non stationary systems, three steps are proposed: instant localization of mass changes (step 1), determination of geometrical location of the mass changes (step 2) and quantification of mass changes (step 3). The Wavelet transform (WT), considered to be a time-frequency analysis, is indented in step 1. In step 2, three methods for the detection of the position of the mass changes are developed. Finally, the relative variation of the natural frequencies of the system is used to evaluate the relative variation of the mass in step 3. The efficiency of these methods is verified by numerical tests. Moreover a building experimental model, instrumented with accelerometers, is studied in the case of after-shock vibrations. These experimental tests permit to validate the methods proposed in this thesis