Dissertations / Theses on the topic 'Structural analysis (Engineering) Frequency response (Dynamics)'

The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modified structure can be determined by experimental testing or numerical simulation, both of which are complex, expensive and time-consuming. Assuming that the original dynamic characteristics are already established and that the modification is a relatively simple attachment such as beam or plate modification, the modified dynamic properties may be determined numerically without solving the equations of motion of the full-modified structure. The frequency response functions (FRFs) of the modified structure can be computed by coupling the original FRFs and a delta dynamic stiffness matrix for the modification introduced. The validity of this approach is investigated by applying it to several cases, 1) 1D structure with structural modification but no change in the number of degree of freedom (DOFs). A simply supported beam with double thickness in the middle section is treated as an example for this case; 2) 1D structure with additional DOFs. A cantilever beam to which a smaller beam is attached is treated as an example for this case, 3) 2D structure with a reduction in DOFs. A four-edge-clamped plate with a cut-out in the centre is treated as an example for this case; and 4) 3D structure with additional DOFs. A box frame with a plate attached to it as structural modification with additional DOFs and combination of different structures. The original FRFs were obtained numerically and experimentally except for the first case. The delta dynamic stiffness matrix was determined numerically by modelling the part of the modified structure including the modifying structure and part of the original structure at the same location. The FRFs of the modified structure were then computed. Good agreement is obtained by comparing the results to the FRFs of the modified structure determined experimentally as well as by numerical modelling of the complete modified structure.

Floors have traditionally been designed only for strength and deflection serviceability. As technological advances have been made in medical, scientific and micro-electronics manufacturing, many types of equipment have become sensitive to vibration of the supporting floor. Thus, vibration serviceability has become a routinely evaluated limit state for floors supporting sensitive equipment. Equipment vibration tolerance limits are sometimes expressed as waveform peak acceleration, and are more often expressed as narrowband spectral acceleration, or one-third octave spectral velocity. Current floor vibration prediction methods, such as those found in the American Institute of Steel Construction Design Guide 11, Floor Vibrations Due to Human Activity, the British Steel Construction Institute P354, Design of Floors for Vibration: a New Approach and the British Concrete Centre CCIP-016 A Design Guide for Footfall Induced Vibration of Structures, have limitations. It has been observed that non-structural components such as light-weight partitions could significantly change floor dynamic properties. Current prediction methods do not provide a fundamental frequency manual prediction method nor finite element modeling guidance for floors with non-structural components. Current prediction methods only predict waveform peak acceleration and do not provide predictions for frequency domain response including narrowband spectral acceleration or one-third octave spectral velocity. Also, current methods are not calibrated to provide a specific level of conservatism. This research project provides (1) a fundamental frequency manual prediction method for floors with lightweight partitions; (2) an improved finite element modeling procedure for floors with light-weight partitions; (3) a procedure to predict the vibration response in narrow-band spectrum and one-third octave band spectrum which can be directly compared with vibration tolerance limits; and (4) a simplified experimental procedure to estimate the floor natural frequencies. An experimental program including four steel-framed building floors and a concrete was completed. Modal tests were performed on two of the steel-framed buildings and the concrete building using an electrodynamic shaker. Experimental modal analysis techniques were used to estimate the modal properties: natural frequencies, mode shapes, and damping ratios. Responses to walking excitation were measured several times in each tested bay for individuals walking at different walking speeds. During each test, the walker crossed the middle of the bay using a metronome to help maintain the intended cadence. The proposed method was used to predict the modal properties and responses to walking. The measurements are used to assess the precision of the proposed methods and to calibrate the prediction methods to provide a specific probability that the actual response will exceed the predicted response. Comparison of measurements and predictions shows the proposed methods are sufficiently accurate for design usage.

Higher speeds and higher capacity will cause the Swedish rail network to be exposed to disturbing dynamic effects. Higher speeds cause higher vertical acceleration levels of the bridge deck. In this thesis, a numerical analysis of a three span end-frame bridge subjected to train induced vibrations is performed. The aim is to identify which structural components and boundary conditions that affect the dynamic behavior of the bridge. Furthermore, the influence of soil structure interaction (SSI) will be investigated as it may have contribution to the stiffness and damping of the structural system.  In order to capture the dynamic response of the bridge, an analysis in the frequency domain was preformed where frequency response functions (FRF) and acceleration envelopes were obtained. For this purpose, a detailed FE-model in 3D was created. Three different cases were studied, model subjected to ballast, model subjected to soil and model subjected to both ballast and soil in coherence. A high speed load model (HSLM) was used to create simulation of train passages at different speeds and applied to all cases so that the bridge deck accelerations could be studied. A simplified 2D-model with impedance functions representing the soil-structure interaction was created to validate the results from the detailed 3D-model and for practical design purposes.  The result of this numerical analysis showed that the vertical accelerations were within acceptable levels of the maximum allowed limits given in governing publications. Considering the surrounding soil, the results revealed an increase of the dynamic response in the midspan at resonant frequency. However, it was identified that this behavior is not explained by the influence of soil structure interaction but rather the change in boundary conditions of the end-shields. The same dynamic behavior was identified for the simplified 2D-model, with a slight underestimation of the vertical accelerations at resonance.

Bilindustrin är i ständig utveckling och är väl medvetna om de ökande kraven från kundermed avseende på körkomfort och körupplevelse. Lastbilar med tunga laster är ofta utrustademed en påbyggnad, till exempel en låda för pallar och gods, en sopsamlare eller en stödram förbärning av timmer. SCANIA Bodybuilding Center utvecklar riktlinjer för val av olika typer avkarosseri, dvs typ av stödram och antal , fästpunkter. Målet med detta arbete är att utvecklaen bättre förståelse för hur det stödjande ramverket och dess infästningar i en lastbil påverkarrammens dynamik och sedan föreslå förbättringar till dessa riktlinjer.Viktiga parametrar som påverkar chassisdynamiken identifierades och beskrivs från början.Fysisk vibrationstestning av chassiet och påbyggnadsram med fasthållningsfäste utfördes vidi testrigg på Scania R&D. Frekvensresponsfunktionerna från mätningarna användes för attbestämma modala parametrar. Olika test utfördes genom att ändra parametrarna och upptagningenav mätningarna. Testresultaten användes för att studera egenfrekvenser egna frekvenser,modifieringsformer och dämpning i systemet. Även en ny metod för att bygga en dynamiskfinit element (FE) modell eller chassi och påbyggnadsram är presenterad i denna undersökning.Modalanalys av chassi-påbygnadsramssystemet gjordes för att studera FEMs egna frekvenseroch modeformer. Den föreslagna metoden för koppling av chassit och delramen i FEM är kritisktbedömd genom att korrelera FE-simuleringen med de experimentella resultaten. Baserat på deutförda experimenten och den numeriska simuleringen föreslås från experiment och numerisksimulering, föreslås nya rekommendationer med avseende på påbyggnadsanslutningarnas konfigurationi lastbil.
The automotive sector is continuously evolving and the companies are well aware of therising demands from customers with regard to driving comfort and experience. Trucks carryingheavy loads are often equipped with on-built bodywork, for example a box for pallets and goods, agarbage collector device or a supporting frame for carrying timber. SCANIA bodybuilding centredevelops guidelines for selecting different types of bodywork, i.e. the type of supporting frame,design and number of attachment brackets, attachment points. The purpose of this master thesisis to develop a better understanding of how the supporting frame and its attachments in a truckinfluence the chassis frame dynamics and to propose improvements to these guidelines.Major parameters influencing the chassis dynamics were identified and described from theoutset. Physical vibration testing of the chassis-subframe assembly was carried out at roadsimulator. The frequency response functions from the measurements were used to determinethe modal parameters. Several tests were performed by altering the parameters and recordingthe measurements. The results from the test cases were used to study and analyse the eigenfrequencies, mode shapes and damping in the system. Also, a new method to build a dynamicfinite element (FE) model of chassis and subframe is presented in this study. Modal analysisof the chassis-subframe assembly was done to study the eigen frequencies and mode shapes byFEM. The proposed method of coupling the chassis and the subframe is critically assessed bycorrelating the results from FE simulation with the experimental results. Based on the resultsfrom experiment and numerical simulation, new recommendations are proposed with regard tothe bodywork attachments’ configuration in the truck.

This thesis investigated the application of seismic analysis methods and the response of idealized shear frames subjected to seismic loading. To complete this research, a Design Basis Earthquake (DBE) for a project site in San Luis Obispo, CA, and five past earthquake records were considered. The DBE was produced per the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) and used for application of the Equivalent Lateral Force Procedure (ELFP) and Response Spectrum Analysis (RSA). When applying RSA, the modal peak responses were combined using the Absolute Sum (ABS), Square-Root-of-the-Sum-of-Squares (SRSS), and Complete Quadratic Combination (CQC) method. MATLAB scripts were developed to produce several displacement, velocity, and acceleration spectrums for each earthquake. Moreover, MATLAB scripts were written to yield both analytical and numerical solutions for each system through application of Linear Time History Analysis (THA). To obtain analytical solutions, two implicit forms of the Newmark-beta Method were employed: the Average Acceleration Method and the Linear Acceleration Method. To generate a comparison, the ELFP, RSA, and THA methods were applied to shear frames up to ten stories in height. The system parameters that impacted the accuracy of each method and the response of the systems were analyzed, including the effects of classical damping and nonclassical damping models. In addition to varying levels of Rayleigh damping, non-linear hysteric friction spring dampers (FSDs) were implemented into the systems. The design of the FSDs was based on target stiffness values, which were defined as portions of the system’s lateral stiffness. To perform the required Nonlinear Time History Analysis (NTHA), a SAP2000 model was developed. The efficiencies of the FSDs at each target stiffness, with and without the addition of low levels of viscous modal damping are analyzed. It was concluded that the ELFP should be supplemented by RSA when performing seismic response analysis. Regardless of system parameters, the ELFP yielded system responses 30% to 50% higher than RSA when combing responses with the SRSS or CQC method. When applying RSA, the ABS method produced inconsistent and inaccurate results, whereas the SRSS and CQC results were similar for regular, symmetric systems. Generally, the SRSS and CQC results were within 5% of the analytical solution yielded through THA. On the contrary, for irregular structures, the SRSS method significantly underestimated the response, and the CQC method was four to five times more accurate. Additionally, both the Average Acceleration Method and Linear Acceleration Method yielded numerical solutions with errors typically below 1% when compared with the analytical solution. When implemented into the systems, the FSDs proved to be most efficient when designed to have stiffnesses that were 50% of the lateral stiffness of each story. The addition of 1% modal damping to the FSDs resulted in quicker energy dissipation without significantly reducing the peak response of the system. At a stiffness of 50%, the FSDs reduced the displacement response by 40% to 60% when compared with 5% modal damping. Additionally, the FSDs at low stiffnesses exhibited the effects of negative lateral stiffness due to P-delta effects when the earthquake ground motions were too weak to induce sliding in the ring assemblies.

Orientador: Samuel da Silva
Resumo: Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito ... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat no... (Complete abstract click electronic access below)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito de métodos convencionais de analise modal experimental para caracterizar e tratar efeitos não-lineares. Os resultados via exemplos numéricos e experimentais apresentados ao longo da tese mostram as contribuições, benefícios e eficácia da proposta.
Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat nonlinear effects. The results based on numerical and experimental examples presented along the thesis show the contributions, benefits and effectiveness of the proposal.
FAPESP: 2012/09135-3
CNPq: 47058/2012-0
CNPq: 203610/2014-8

This study investigated the effect of sensor mass, sensor location, and delamination location of different composite structures under dynamic loading. The study pertains to research of the use of accelerometers and dynamic response as a cost-effective and reliable method of structural health monitoring in composite structures. The composite structures in this research included carbon fiber plates, carbon fiber-foam sandwich panels, and carbon-fiber honeycomb sandwich panels. The composite structures were manufactured with the use of a Tetrahedron MTP-8 heat press. All work was conducted in the Cal Poly Aerospace Structures/Composites Laboratory. Initial delaminations were placed at several locations along the specimen, including the bending mode node line locations. The free vibration of the composite structure was forced through a harmonic horizontal vibration test using an Unholtz-Dickie shake system. A sinusoidal sweep input was considered for the test. The dynamic response of the composite test specimens were measured using piezoelectric accelerometers. Measurements were taken along horizontal and vertical locations on the surfaces of the composite structures. Square inch grids were marked on the surfaces to create a meshed grid system. Accelerometer measurements were taken at the center of the grids. The VIP Sensors 1011A piezoelectric accelerometer was used to measure vibration response. The measurements were then compared to response measurements taken from a PCB Piezotronics 353B04 single access accelerometer to determine the effects of sensor mass. Deviations in bending mode natural frequency and differences in mode shape amplitude became the criteria for evaluating the effect of sensor mass, sensor location, and delamination location. Changes in damping of the time response were also studied. The experimental results were compared to numerical models created using a finite element method. The experimental results and numerical values were shown to be in good agreement. The sensor mass greatly affected the accuracy and precision of vibration response measurements in the composites structures. The smaller weight and area of the VIP accelerometer helped to minimize the decrease in accuracy and precision due to sensor mass. The effect of sensor location was found to be coupled with the effect of sensor mass and the bending mode shape. The sensor location did not affect the vibration response measurements when the sensor mass was minimized. Off-center horizontal sensor placement showed the possibility of measuring vibration torsion modes. The effect of delamination changed the bending mode shape of the composite structure, which corresponded to a change in natural frequency. The greatest effect of the delamination was seen at the bending mode node lines, where the bending mode shape was most significantly affected. The effect of delamination was also dependent on the location of the delamination and the composite structure type. The results of this study provided considerations for future research of an active structural health monitoring system of composite structures using dynamic response measurements. The considerations included sensor mass reduction, sensor placement at constraints and bond areas and the presence of damping material.

In this work, a pioneering application of the Solution Structure Method (SSM) for structural dynamics problems is presented. Vibration analysis is an important aspect of any design-analysis cycle for which reliable computational methods are required. Unlike many meshfree methods, SSM is capable of {\it exact treatment of all prescribed boundary conditions}. In addition, the method is capable of using basis functions which do not conform to the shape of the geometric model. Together, this defines an unprecedented geometric flexibility of the SSM. This work focused on the development of numerical algorithms for 2D in-plane and 3D natural vibration analysis and 2D in-plane dynamic response. The convergence and numerical properties of the method were evaluated by comparing meshfree results with those obtained using traditional Finite Element Analysis implemented in Solidworks and ANSYS. The numerical experiments presented in this work illustrate that the Solution Structure Method possesses good convergence and in some cases, such as geometries with partially fixed boundaries, this method converges much more rapidly than traditional FEA. Finally, in addition to complex boundary conditions, this method can easily handle complex geometries without losing favorable convergence properties.

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

Major cities in Sweden experience a population growth, demanding innovative solutions regarding land exploitation for residential housing. One solution is to build closer to existing railway tracks, however difficulties arise regarding determining traffic induced vibrations from trains. This sometimes results in vibrations being too large in buildings regarding comfort, resulting in expensive measures taken as to reduce the vibrations. The scope of this thesis is to investigate the soil-structure interaction caused by traffic induced vibrations in buildings using ABAQUS FE software, where the aim is to partly investigate how a structure effects surrounding soil, partly to investigate which parameters of a structure has largest favorable impact on foundation vibrations. Major results include that ground vibrations at 2-4 meters parallel to a structure relative to the vibration source remain constant, independent on whether a house is present or not. Further results show that increasing the thickness of the foundation slab has a mitigating effect on the induced vibrations. The main conclusions of this thesis include that quadratic elements are superior to linear elements for dynamic analyses for soil, and that accelerometers should be placed at least 2-4 m next to an existing structure to obtain accurate measurements comparable to if no structure was present.
Större städer i Sverige upplever en befolkningstillväxt, vilket resulterar i att kreativa lösningar måste introduceras gällande markexploatering för bostadshus. En sådan lösning är att bygga närmre befintlig järnväg, dock resulterar detta i svårigheter gällande att kvantifiera magnituden av trafikinducerade vibrationer i byggnadsfundament orsakade av tågtrafik. En konsekvens av detta är att vibrationsnivåerna i husen ibland blir för stora sett till komfortvibrationer, vilket resulterar i att dyra åtgärder måste tas för att minska vibrationerna. Denna avhandling syftar till att genom att använda ABAQUS FE-mjukvara utforska jord-strukturinverkan i hus orsakade av trafikvibrationer. Målet är delvis att undersöka hur byggnation påverkar omgivande markvibrationer, delvis att undersöka vilka parametrar som har störst gynnsam effekt gällande dämpning av trafikinducerade vibrationer. De viktigaste resultaten indikerar att markvibrationer 2-4 meter bredvid ett hus relativt vibrationskällan förblir oförändrade oberoende av om byggnation existerar eller ej, samt att en ökning av tjockleken av grundplattan resulterar i minskade fundamentvibrationer. Slutsatserna som presenteras är flera, däribland att kvadratiska element är mer beräkningseffektiva än linjära element för dynamiska analyser för jord, samt att accelerometrar bör placeras minst 2-4 m bredvid ett befintligt hus för att erhålla mätdata jämförbara med om ett hus inte skulle finnas på platsen.

The increasing need for High-Speed Railway (HSR) to reduce the travelling time requires increasing research within this field. Bridges are main components of any railway network, including HSR networks, and the optimization of their design for this purpose would contribute to a faster and more cost effective development of the HSR network. The initial investment, the running and maintenance costs of the bridges can be decreased through better understanding of the their dynamic behaviour. This thesis studies the dynamic behaviour of end-shield railway bridges under HSR operation. 2D beam analysis is used to study the effect of the distribution of the train’s axle load. Relatively accurate 3D FE-models are developed to study the effect of Soil-Structure Interaction (SSI) and the dynamic response of the bridges. Modelling alternatives are studied to develop an accurate model. A full scale test of a simply supported Bridge with end-shields using load-controlled forced excitation was performed and the results were used to verify the theoretical models. A manual model updating process of the material properties of the 3D FE-model is performed using FRFs from the field measurements. A Simple 2D model is also developed, where a spring/dashpot system is implemented to simplify SSI, and updated to reproduce the field measured responses. The conclusions of the project emphasize the importance of SSI effects in the dynamic analysis of end-shield bridges for predicting their dynamic behaviour. The conclusions also show that the modelling of the surrounding soil and the assumption of the soil material parameters have significant effect on the dynamic response. Even the boundary conditions, bedrock level and the ballast on the railway track affects the response. The results also show that the bridge’s concrete section behaves as uncracked section under the studied dynamic loading.

QC 20170403

For intermediate floors in residential and office buildings, as well as in parking garages and malls, there is a wide use of hollow core concrete slabs in Sweden today. Hollow core slabs are precast and prestressed concrete elements with cylindrical-shaped voids extending along the length of the slab. These structural elements have the advantage compared to cast-in-situ concrete slabs that they have a high strength, due to the prestressing, and that the voids allow for a lower self-weight. Additionally, the voids allow for a reduction in the use of concrete material. These characteristics offer possibilities to build long-span floors with slender designs. However, a consequence of the slenderness of the slabs is that such floors have an increased sensitivity to vibrations induced by various dynamic loads. In residential and office buildings vibrations are primarily caused by human activity, and therefore concerns related to the serviceability of such floors are raised. These vibrations are often not related to problems with structural integrity, but rather to different aspects of comfort of the residents or workers. The aim of this thesis is to provide additional information regarding the dynamic behavior of hollow core floors. An experimental modal analysis has been performed on an existing floor in an office building. The dynamic properties in the form of natural frequencies, mode shapes, damping ratios and frequency response functions were derived and analyzed from these measurements. Subsequently, several finite element models were developed, aiming to reproduce the experimental dynamic behavior of the studied floor. The measurements initially showed some unexpected dynamic responses of the floor. For this reason, more advanced methods of signal analyses were applied to the data. The analyses showed that the slab has some closely spaced modes and that the modes of the floor are complex to a certain degree. The finite element models were studied with different configurations. In particular, the effect the model size, boundary conditions, material properties and potential structural discontinuities have on the dynamic response of the slab was studied. Sufficiently good agreement has been achieved between the experimental and numerical results in terms of natural frequencies and mode shapes. The acceleration amplitude responses of the numerical models were generally higher than the ones obtained from the measurements, which leads to difficulties in matching of the frequency response functions.
Håldäck i betong används idag i stor utsträckning som bjälklag i bostads- och kontorsbyggnader, liksom i parkeringsgarage och köpcentra. Håldäcksbjälklag består av prefabricerade och förspända betongelement, med cylindriska hål som sträcker sig i plattans längsriktning. Dessa konstruktionselement har fördelen, jämfört med platsgjutna betongplattor, att de har en hög hållfasthet på grund av förspänningen och att hålen möjliggör en lägre egenvikt. Dessutom gör hålen att en mindre mängd betongmaterial behövs. Dessa egenskaper ger möjligheter att bygga golv med långa spännvidder och slank design. En konsekvens av slankheten är emellertid att sådana golv har en ökad känslighet för vibrationer som orsakas av olika dynamiska belastningar. I bostads- och kontorsbyggnader orsakas vibrationer främst av mänsklig aktivitet, och därför finns det en del oro relaterad till sådana golvs brukbarhet. Dessa vibrationer är oftast inte relaterade till frågor om strukturell integritet, utan snarare till olika aspekter av boendes eller arbetares känsla av komfort. Syftet med detta examensarbete är att bidra till kunskapen om håldäcksbjälklags dynamiska beteende. En experimentell modalanalys har utförts på ett befintligt golv i en kontorsbyggnad. De dynamiska egenskaperna i form av egenfrekvenser, modformer, dämpning och frekvenssvarsfunktioner erhölls och analyserades med hjälp av dessa mätningar. Därefter utvecklades flera finita element modeller för att reproducera det experimentellt uppmätta dynamiska beteendet hos det studerade golvet. Mätningarna visade initialt något oväntade dynamiska responser från golvet. Av denna anledning applicerades mer avancerade signalanalysmetoder på datan. Analyserna visade att plattan har några moder inom ett litet frekvensintervall och att moderna till en viss grad är komplexa. De finita element modellerna studerades med olika konfigurationer. I synnerhet studerades effekten av modellstorleken, randvillkoren, materialegenskaperna och potentiella strukturella diskontinuiteter på golvets dynamiska respons. Tillräckligt bra överensstämmelse har uppnåtts mellan de experimentella och numeriska resultaten i form av egenfrekvenser och modformer. Accelerationsamplituderna för de numeriska modellerna var i allmänhet högre än de som erhölls under mätningarna, vilket leder till svårigheter att matcha frekvenssvarsfunktionerna.

Les parties tournantes des turbomachines aéronautiques sont composées d'une succession de roues aubagées qui permettent le transfert de l'énergie entre l'air et le rotor. Ces roues aubagées constituent des pièces particulièrement sensibles car elles doivent répondre en termes de dimensionnement à des impératifs de performances aérodynamiques, d'aéroacoustique et de tenue mécanique à la rotation,à la température et à la charge aérodynamique. Le contact avec frottement existant au niveau des attaches aube-disque joue un rôle important sur les niveaux vibratoires.Ce travail porte sur l'étude de l'usure par fretting sous chargements dynamiques dans les interfaces frottantes. En effet, les vibrations de l'aube peuvent produire des micro-glissements en pied d'aubequi peuvent entraîner un phénomène d'usure par fretting. Les connaissances sur le comportement de l'usure sous sollicitations dynamiques sont faibles. Seuls existent des outils numériques pour modéliser l'usure dans le cas de sollicitations quasi-statiques. Nous proposons dans cette thèse des méthodes pour calculer l'évolution de l'usure au cours des cycles de chargement dynamique basées sur une approche multi-échelle en temps. La réponse vibratoire de la structure est liée à une échelle de temps rapide qui est calculée par une méthode d'équilibrage harmonique, dans laquelle les déplacements et les efforts sont projetés sur la base de Fourier. Différentes approches temps-fréquence de calcul des coefficients de Fourier des forces de contact sont présentées. La cinétique d'usure est liée à une échelle lente et différentes méthodes sont proposées pour l'intégrer. La prise en compte des géométries usées dans le modèle éléments finis se fait par l'ajout d'un vecteur des profondeurs d'usure dans le terme de pénalité des lagrangiens dynamiques. Des exemples académiques valident et illustrent les méthodes proposées. Ces méthodes sont ensuite appliquées à l'étude de l'usure par fretting en pied d'aube de soufflante. L'étude numérique met en lumière le couplage entre vibration et usure par fretting aux interfaces de contact. La modification du comportement dynamique global de la roue aubagée est aussi observée.

Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies. Further, most structural systems are likely to exhibit nonlinear and time-varying behavior when subjected to extreme events such as severe earthquake, wind and sea wave excitations. In such cases, a reliable identification approach is behavior and for assessing its reliability. Current work addresses two research themes in the field of stochastic engineering dynamics related to the above challenges. In the first part of the dissertation, the recently developedWiener Path Integral (WPI) technique for determining the joint response probability density function (PDF) of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output of a filter equation with Gaussian white noise as its input, it is possible to define an augmented response vector process to be considered in the WPI solution technique. A significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms. In such cases, it is shown that the use of a filter approximation facilitates the implementation of the WPI technique in a straightforward manner, without compromising its accuracy necessarily. Further, in addition to dynamical systems subject to stochastic excitation, the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as non-Gaussian and non-homogeneous stochastic fields. Several numerical examples pertaining to both single- and multi-degree-of freedom systems are considered, including a marine structural system exposed to flow-induced non-white excitation, as well as a beam with a non-Gaussian and non-homogeneous Young’s modulus. Comparisons with MCS data demonstrate the accuracy of the technique. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear time-variant multi-degree-of-freedom oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear subsystems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sampling theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. A nonlinear time-variant system with fractional derivative elements is used as a numerical example to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

In the first part of the dissertation, a novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. In comparison to standard stochastic averaging, the requirement of “a priori” determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. Further, the herein proposed Hilbert transform based stochastic averaging is adapted for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Next, the potential of the stochastic averaging technique to be used in conjunction with performance-based engineering design applications is demonstrated by proposing a stochastic version of the widely used incremental dynamic analysis (IDA). Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, IDA surfaces are determined providing the conditional PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to the computationally expensive Monte Carlo simulation, the methodology developed herein determines the IDA surfaces at minimal computational cost. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Several numerical examples are considered for assessing the reliability of the technique, even in the presence of incomplete and corrupted data. These include a 2-DOF time-variant Duffing oscillator endowed with fractional derivative terms, as well as a 2-DOF system subject to flow-induced forces where the non-stationary sea state possesses a recently proposed evolutionary version of the JONSWAP spectrum. In the third part of this dissertation, a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) is developed for dynamic cerebral autoregulation (DCA) performance quantification. DCA is the continuous counter-regulation of the cerebral blood flow by the active response of cerebral blood vessels to the spontaneous or induced blood pressure fluctuations. Specifically, various metrics of the phase shift and magnitude of appropriately defined GHW-based transfer functions are determined based on data points over the joint time-frequency domain. The potential of these metrics to be used as a diagnostics tool for indicating healthy versus impaired DCA function is assessed by considering both healthy individuals and patients with unilateral carotid artery stenosis. Next, another application in biomedical engineering is pursued related to the Pulse Wave Imaging (PWI) technique. This relies on ultrasonic signals for capturing the propagation of pressure pulses along the carotid artery, and eventually for prognosis of focal vascular diseases (e.g., atherosclerosis and abdominal aortic aneurysm). However, to obtain a high spatio-temporal resolution the data are acquired at a high rate, in the order of kilohertz, yielding large datasets. To address this challenge, an efficient data compression technique is developed based on the multiresolution wavelet decomposition scheme, which exploits the high correlation of adjacent RF-frames generated by the PWI technique. Further, a sparse matrix decomposition is proposed as an efficient way to identify the boundaries of the arterial wall in the PWI technique.

The analysis of vehicle-structure interaction systems plays a significant role in the design and maintenance of bridges. In recent years, the assessment of the health of existing bridges and the design of new ones has gained significance, in part due to the progress made in the development of faster moving locomotives, the desire for lighter bridges, and the imposition of performance criteria against rare events such as occurrence of earthquakes and fire. A probabilistic analysis would address these issues, and also assist in determination of reliability and in estimating the remaining life of the structure. In this thesis, we aim to develop tools for the probabilistic analysis techniques of state estimation, parameter identification and global response sensitivity analysis of vehicle-structure interaction systems, which are also applicable to the broader class of structural dynamical systems. The thesis is composed of six chapters and three appendices. The contents of these chapters and the appendices are described in brief in the following paragraphs. In chapter 1, we introduce the problem of probabilistic analysis of vehicle-structure interactions. The introduction is organized in three parts, dealing separately with issues of forward problems, inverse problems, and global response sensitivity analysis. We begin with an overview of the modelling and analysis of vehicle-structure interaction systems, including the application of spatial substructuring and mesh partitioning schemes. Following this, we describe Bayesian techniques for state and parameter estimation for the general class of state-space models of dynamical systems, including the application of the Kalman filter and particle filters for state estimation, MCMC sampling based filters for parameter identification, and the extended Kalman filter, the unscented Kalman filter and the ensemble Kalman filter for the problem of combined state and parameter identification. In this context, we present the Rao-Blackwellization method which leads to variance reduction in particle filtering. Finally, we present the techniques of global response sensitivity analysis, including Sobol’s analysis and distance-based measures of sensitivity indices. We provide an outline and a review of literature on each of these topics. In our review of literature, we identify the difficulties encountered when adopting these tools to problems involving vehicle-structure interaction systems, and corresponding to these issues, we identify some open problems for research. These problems are addressed in chapters 2, 3, 4 and 5. In chapter 2, we study the application of finite element modelling, combined with numerical solutions of governing stochastic differential equations, to analyse instrumented nonlinear moving vehicle-structure systems. The focus of the chapter is on achieving computational efficiency by deploying, within a single modeling framework, three sub structuring schemes with different methodological moorings. The schemes considered include spatial substructuring schemes (involving free-interface coupling methods), a spatial mesh partitioning scheme for governing stochastic differential equations (involving the use of a predictor corrector method with implicit integration schemes for linear regions and explicit schemes for local nonlinear regions), and application of the Rao-Blackwellization scheme (which permits the use of Kalman’s filtering for linear substructures and Monte Carlo filters for nonlinear substructures). The main effort in this work is expended on combining these schemes with provisions for interfacing of the substructures by taking into account the relative motion of the vehicle and the supporting structure. The problem is formulated with reference to an archetypal beam and multi-degrees of freedom moving oscillator with spatially localized nonlinear characteristics. The study takes into account imperfections in mathematical modelling, guide way unevenness, and measurement noise. The numerical results demonstrate notable reduction in computational effort achieved on account of introduction of the substructuring schemes. In chapter 3, we address the issue of identification of system parameters of structural systems using dynamical measurement data. When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. In this chapter, strategies are proposed based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples include a laboratory study on a beam-moving trolley system. In chapter 4, we consider the combined estimation of the system states and parameters of vehicle-structure interaction systems. To this end, we formulate a framework which uses MCMC sampling for parameter estimation and particle filtering for state estimation. In chapters 2 and 3, we described the computational issues faced when adopting these techniques individually. When used together, we come across both sets of issues, and find the complexity of the estimation problem is greatly increased. In this chapter, we address the computational issues by adopting the sub structuring techniques proposed in chapter 2, and the parameter identification method based on modified measurement models presented in chapter 3. The proposed method is illustrated on a computational study on a beam-moving oscillator system with localized nonlinearities, as well as on a laboratory study on a beam-moving trolley system. In chapter 5, we present global response sensitivity indices for structural dynamical systems with random system parameters excited by multiple random excitations. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger’s metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the l2 norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. The applicability of the proposed procedures to the case of random system parameters is demonstrated using suitable illustrations. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations due to random support motions and guide-way unevenness. In chapter 6 we summarize the contributions made in chapters 2, 3, 4, and 5, and on the basis of these studies, present a few problems for future research. In addition to these chapters, three appendices are included in this thesis. Appendices A and B correspond to chapter 3. In appendix A, we study the effect on the nature of the posterior probability density functions of large measurement data set and small measurement noise. Appendix B illustrates the MCMC sampling based parameter estimation procedure of chapter 3 using a laboratory study on a bending–torsion coupled, geometrically non-linear building frame under earthquake support motion. In appendix C, we present Ito-Taylor time discretization schemes for stochastic delay differential equations found in chapter 5.

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.