Dagens planering och projektering av konstruktioner präglas av ett resursutnyttjande, miljömässigt och ekonomiskt tänk, där resultatet kan medföra brister med avseende på dynamiken. Därmed är det ytterst viktigt att skapa goda förutsättningar för noggranna beräkningsmodeller som i ett projekteringsskede kan representera konstruktionernas dynamiska beteende. I denna rapport utfördes en jämförelseanalys mellan en FE-modell och en fältmätning, där Folke Bernadottes bro har använts som underlag. Syftet är att presentera skillnader och likheter i naturliga frekvenser och modformer baserat på jämförelseanalysen, samt belysa några av de viktigaste faktorerna bakom dessa. Resultatet visade för en kalibrerad FE-modell 11 % genomsnittlig skillnad för de naturliga frekvenserna och 99 % överensstämmelse med avseende på modformerna, där den mest väsentliga parametern i modellen var upplagsvillkoren. / Today's planning and design of constructions is characterized by a resource utilization, environmental and economic thinking, where the result can lead to shortcomings with regard to dynamic behaviour. Thus, it is extremely important to create good conditions for accurate calculation models that in a design phase can represent the dynamic behaviour of the structures. In this report, a comparison analysis was performed between an FE-model and a field measurement, where Folke Bernadotte's bridge has been used as basis. The purpose is to present differences and similarities in natural frequencies and mode shapes based on the comparative analysis, and to highlight some of the most important factors behind these. The result showed for a calibrated FE-model an average difference of 11 % for the natural frequencies and 99 % agreement with respect to the mode shapes, where the most important parameter in the model was the support conditions.

Due to the emergence of new materials and advanced engineering technology, slender footbridges are increasingly becoming popular to satisfy the modern transportation needs and the aesthetical requirements of society. These structures however are always &quotlively" with low stiffness, low mass, low damping and low natural frequencies. As a consequence, they are prone to vibration induced by human activities and can suffer severe vibration serviceability problems, particularly in the lateral direction. This phenomenon has been evidenced by the excessive lateral vibration of many footbridges worldwide such as the Millennium Bridge in London and the T-Bridge in Japan. Unfortunately, present bridge design codes worldwide do not provide sufficient guidelines and information to address such vibrations problems and to ensure safety and serviceability due to the lack of knowledge on the dynamic performance of such slender vibration sensitive bridge structures. A conceptual study has been carried out to comprehensively investigate the dynamic characteristics of slender suspension footbridges under human-induced dynamic loads and a footbridge model in full size with pre-tensioned reverse profiled cables in the vertical and horizontal planes has been proposed for this purpose. A similar physical suspension bridge model was designed and constructed in the laboratory, and experimental testings have been carried out to calibrate the computer simulations. The synchronous excitation induced by walking has been modelled as crowd walking dynamic loads which consist of dynamic vertical force, dynamic lateral force and static vertical force. The dynamic behaviour under synchronous excitation is simulated by resonant vibration at the pacing rate which coincides with a natural frequency of the footbridge structure. Two structural analysis software packages, Microstran and SAP2000 have been employed in the extensive numerical analysis. Research results show that the structural stiffness and vibration properties of suspension footbridges with pre-tensioned reverse profiled cables can be adjusted by choosing different structural parameters such as cable sag, cable section and pretensions in the reverse profiled cables. Slender suspension footbridges always have four main kinds of vibration modes: lateral, torsional, vertical and longitudinal modes. The lateral and torsional modes are often combined together and become two kinds of coupled modes: coupled lateral-torsional modes and coupled torsionallateral modes. Such kind of slender footbridges also have different dynamic performance in the lateral and vertical directions, and damping has only a small effect on the lateral vibration but significant effect on the vertical one. The fundamental coupled lateral-torsional mode and vertical mode are easily excited when crowd walking dynamic loads are distributed on full bridge deck. When the crowd walking dynamic loads are distributed eccentrically on half width of the deck, the fundamental coupled torsional-lateral mode can be excited and large lateral deflection can be induced. Higher order vertical modes and coupled lateral-torsional modes can also be excited by groups of walking pedestrians under certain conditions. It is found that the coupling coefficient introduced in this thesis to describe the coupling of a coupled mode, is an important factor which has significant effect on the lateral dynamic performance of slender suspension footbridges. The coupling coefficient, however, is influenced by many structural parameters such as cable configuration, cable section, cable sag, bridge span and pre-tensions, etc. In general, a large dynamic amplification factor is expected when the fundamental mode of a footbridge structure is the coupled lateral-torsional mode with a small coupling coefficient. The research findings of this thesis are useful in understanding the complex dynamic behaviour of slender and vibration sensitive suspension footbridges under humaninduced dynamic loads. They are also helpful in developing design guidance and techniques to improve the dynamic performance of such slender vibration sensitive footbridges and similar structures and hence to ensure their safety and serviceability.

Tall slender buildings are easily set in motion by wind and earthquakes but by estimating the buildings horizontal natural frequencies in the design phase, these motions can be kept within acceptable boundaries. There are many parameters that decides the natural frequency of a building and it can therefore be difficult to calculate it. There are a few ways though to estimate horizontal natural frequencies of tall buildings and two methods have been tested in this report. Both methods give the frequency of a clamped-free cantilever but one of them requires a single degree of freedom system whilst the other handles a multi degree of freedom system. The methods are called SDOF method and MDOF method in this report. A fictional building was created for this project to be the reference object in the comparison between the two methods SDOF and MDOF. The walls and floors of the building was designed with the support of both an acoustic engineer and a structural engineer to create a realistic building. A building’s natural frequency is dependent of the self-weight, stiffness and height of the building and it was therefore important to design these components with care. The fictional building is called House 1 and is a 10 story, almost square building about 20 m wide and broad and 30 m high. This report does not only compare the natural frequencies obtained from the two different calculation methods, but it also shows the difference in frequency in timber and concrete structures. Shear walls constitutes the horizontal stabilization system of the fictional building and both a CLT core and a concrete core is designed and compared. It is only the walls that comes in two different versions, the floorings consist of CLT boards for both structures tested. The horizontal natural frequencies of House 1 were about 2 Hz and 3 Hz for the CLT version and concrete version respectively. It was expected to get frequencies within that range considering the height of House 1. The CLT core having a lower frequency than the concrete core was also expected since concrete is a stiffer material than wood. To be able to make a fair comparison between the SDOF method and the MDOF method, House 1 was designed with the same dimensions and stiffness on all floors because the SDOF method requires that. The results from the two methods are almost identical with only 0.3 Hz and 0.4 Hz difference for the concrete and CLT respectively. For a shear wall structure with a consistent stiffness, weight and dimension, any of the two methods can be used to estimate the horizontal natural frequency. However, it is not realistic for a building of 30 m or higher, to have the same dimensions on the load bearing structure on all floors which makes the MDOF method more accurate in more cases than the SDOF method. / Höga slanka byggnader kan sättas i svajande rörelser av vind och jordbävningar, men genom att uppskatta byggnadernas horisontella egenfrekvenser i den tidiga konstruktionsfasen kan dessa rörelser hållas inom acceptabla gränser. Det är många parametrar som bestämmer byggnadens egenfrekvens och det kan därför vara svårt att beräkna den. Det finns dock några sätt att uppskatta horisontella egenfrekvenser hos höga byggnader och två metoder har testats i denna rapport. Båda metoderna ger frekvensen av en fast inspänd konsolbalk men en av dem kräver ett enfrihetsgradsystem medan den andra kan hantera ett system med flera frihetsgrader. Metoderna kallas SDOF-metoden och MDOF-metoden i denna rapport. En fiktiv byggnad skapades i detta projekt för att vara referensobjekt i jämförelsen mellan de två metoderna SDOF och MDOF. Byggnadens väggar och golv konstruerades med stöd av både en akustiker och en konstruktör för att skapa en realistisk byggnad. Byggnadens egenfrekvens är beroende av byggnadens egenvikt, styvhet och höjd och det var därför viktigt att utforma dessa komponenter med omsorg. Den fiktiva byggnaden kallas House 1 och är en 10 vånings-, nästan fyrkantig byggnad ca 20 m lång och bred och 30 m hög. Denna rapport jämför inte bara egenfrekvenserna erhållna från de två olika beräkningsmetoderna, den visar även skillnaden i frekvens i trä- och betongkonstruktioner. Skjuvväggar utgör det horisontella stabiliseringssystemet för den fiktiva byggnaden och både en KL-kärna och en betongkärna har utformats och jämförts. Det är bara väggarna som skiljer de två olika versionerna åt, bjälklagen består av KL-skivor i båda fallen. De horisontella egenfrekvenserna hos House 1 var ca 2 Hz och 3 Hz för KL-version respektive betongversion. Frekvenser inom detta område var väntade med tanke på höjden av House 1. Att KL-kärnan skulle ha en lägre frekvens än betongkärnan förväntades också eftersom betong är ett styvare material än trä. För att kunna göra en rättvis jämförelse mellan SDOF-metoden och MDOF-metoden, var House 1 utformad med samma dimension och styvhet på alla våningsplan eftersom SDOF-metoden kräver det. Resultaten från de två metoderna är nästan identiska med endast 0,3 Hz och 0,4 Hz skillnad för betong respektive KL. För en skjuvväggskonstruktion med en kontinuerlig styvhet, vikt och dimension kan båda de två metoderna användas för att uppskatta den horisontella egenfrekvensen. Det är dock inte realistiskt för en byggnad på 30 m eller högre att ha samma dimensioner på den lastbärande konstruktionen på alla våningar vilket gör MDOF-metoden mer korrekt i fler fall än SDOF-metoden.

This paper presents a methodology for determining eigenfunctions and frequencies of the Euler-Bernoulli model for elastic beams that can include damping and devices located at intermediate or end points of the beam. The eigenfunctions or vibration modes of the beam are obtained by using solution basis generated by the dynamic solution of a fourth-order differential equation, through a block matrix formulation of the boundary and compatibility conditions. The use of the dynamic basis has been often used to reduce the calculations in obtaining the modes and frequencies. Forced responses are obtained with the Galerkin method by modifying the classical modal analysis with the inclusion of new conditions of orthogonality between modes that are suitable for problems with viscous damping or non-classical boundary conditions. / Este trabalho apresenta uma metodologia para determinar as autofunções e as frequências de um modelo Euler-Bernoulli para vigas elásticas que podem incluir amortecimento e dispositivos localizados num ponto intermediário ou nos extremos da viga. As autofunções ou modos de vibração da viga são obtidos usando uma base de solução gerada pela solução dinâmica de uma equação diferencial de quarta ordem, através de uma formulação matricial em blocos para as condições de contorno e de compatibilidade. O uso da base dinâmica tem sido frequentemente utilizada para reduzir os cálculos na obtenção dos modos e das frequências. Respostas forçadas são obtidas usando o método de Galerkin, modificando a análise modal clássica com a inclusão de novas condições de ortogonalidade entre os modos que são adequadas para problemas com amortecimento viscoso ou com condições de contorno não-clássicas

[pt] Algumas máquinas produzem solicitações dinâmicas que são transferidas às fundações por meio de movimentos vibratórios. É necessário analisar e estudar esses movimentos vibratórios durante o projeto da fundação para evitar danos aos equipamentos, à própria fundação e às estruturas vizinhas. Este tipo de analise também é muito importante para a segurança e saúde ocupacional de pessoas que venham a frequentar tais estruturas. Por esta razão as frequências naturais de vibração são importantes para o dimensionamento dinâmico de fundações, para se evitar efeitos de ressonância e amplificação de deslocamentos. Neste trabalho, estacas embutidas em fundações elásticas de Winkler foram estudadas. As vibrações longitudinais e transversais foram investigadas. As frequências naturais foram calculadas pelo método de Rayleigh-Ritz considerando estacas como elementos de barra embutidas em fundação elástica no caso da avaliação de vibrações longitudinais, e como vigas embutidas em base elástica no caso da avaliação das vibrações transversais. Na modelagem dos elementos de barra e viga utilizaram-se para aproximações dos deslocamentos funções convencionais enriquecidas com n funções adicionais. As constantes de mola de Winkler foram determinadas por provas de carga verticais e horizontais. Os resultados das vibrações longitudinais foram comparados com medições in situ com estacas reais. Os valores reais da vibração longitudinal das estacas foram obtidos pela aplicação da técnica Fast Fourier Transform nas acelerações resultantes de ensaios de carregamentos dinâmicos, que impõem uma vibração forçada no sistema estaca-solo. / [en] Some machines create dynamic efforts that are transferred to foundations by vibratory movements. Is necessary to analyze and study these movements during foundation design in order avoid damages in equipment, in foundation and in neighbor structures. This analysis is also important to safety and health of persons. For this reason natural vibration frequencies are important to dynamic design of foundations, to avoid resonance effects and displacements amplification. In this work, piles embedded in Winkler elastic foundations were studied. The longitudinal and transversal vibrations were investigated. The natural frequencies are calculated by Rayleigh-Ritz method modelling piles as bars embedded in elastic foundations in the case of longitudinal vibration evaluation, and beams embedded in elastic foundations in the case of transversal vibration evaluation. The bars and beams elements are modeled using conventional shape function enriched with n additional functions. The Winkler spring constants were evaluated by vertical and horizontal load tests. The longitudinal vibration results were compared with in situ measurements in real piles. The longitudinal vibration real values of piles were obtained by Fast Fourier Transform in acceleration data of dynamic load tests that impose a forced vibration in soil-pile system.

This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.

This diploma thesis deals with the design of an inclined three-sided vibrating screen, which is designed for sorting bulk aggregates. The aim of the diploma thesis is primarily to make a construction design with a specific comparison of various design solutions, considering the calculated operating parameters. In the construction design, is used not only the experience of the manufacturer of this type of machine, but also recommendations based on the manu-facturers of screens component. The design also includes a comparison of two types of flex-ible mounting, which is one of the basic structural units of the entire vibrating screen. The thesis is conceived from the basics, with emphasis on the simplicity and functionality of the device.

No description available.

Tato diplomová práce uvádí dynamiku klikového mechanismu šestiválcového řadového motoru za účelem návrhu klikového hřídele v CAD programu Pro/Engineer. Následuje popis vibrací klikového mechanismu a analytický výpočet jeho torzních vibrací. Hlavní část diplomové práce se pak zabývá konverzí hřídele do konečno-prvkového modelu v programu ANSYS a jeho importem do prostředí Adams/Engine. V tom je provedena modální analýza klikového ústrojí pro získání vlastních frekvencí a tvarů. Na konec práce je porovnán výstup z analytického řešení a výsledky z multi-body systému.

[pt] O presente trabalho mostra uma versão do método Rayleigh-Ritz com funções especializadas para a análise de placas circulares e anulares finas e espessas sujeitas a cargas fora do plano e em plano. As funções de aproximação para deslocamentos são polinómios em direção radial combinada com funções trigonométricas na direção circunferencial. Um recurso conveniente é o uso de funções nodais lineares, que permitem a fácil consideração de cargas nodais e condições de contorno (incluindo forças seguidoras), enriquecidos por polinômios de ordem superior, sem inclusão de nós adicionais. O modelo permite a variação da espessura e é aplicado em MAPLE18, possibilitando o cálculo de deslocamentos e tensões sob carregamento constante e de variação linear, as frequências de vibração, cargas de flambagem com alguns efeitos do nível de carga conservativa e não conservativa. Os exemplos mostram a eficácia desta abordagem na análise de tal estrutura e leva um novo enfoque a este problema clássico, que apresenta comparações interessantes e originais que descrevem o efeito de deformação de cisalhamento, no caso de vibrações o efeito das rotações inerciais e variação de espessura em placas circulares e anulares, incluindo deslocamentos, momentos e forças de cisalhamento, frequências de vibração, cargas de flambagem e uma análise de cargas seguidoras tangenciais não conservativas na estabilidade, utilizando o critério dinâmico é executada. / [en] The present work shows a version of the Rayleigh-Ritz method with specialized functions for the analysis of thin and thick circular and annular plates subjected to out-of-plane and in-plane loads. The approximation functions for displacements are polynomials in the radial direction combined with trigonometric functions in the circumferential direction. A convenient feature is the use of linear nodal functions, which allows for easy consideration of nodal loads and boundary conditions (including follower forces), enriched by higher order polynomials without inclusion of additional nodes. The model allows for thickness variation and was implemented in MAPLE18, enabling the calculation of displacements and stresses under constant and linearly varying load, frequencies of vibration, buckling loads with a few commands and the effect of the level of conservative and non-conservative on load the stability. The examples show the effectiveness of this approach in the analysis of such structures and bring new light to this classical problem, presenting interesting and novel comparisons illustrating the effect of shear deformation, in case of vibrations of the inertial rotations analysis and thickness variation in circular and annular plates, including displacements, moments and shear forces, vibration frequencies, buckling loads and a stability analysis of non-conservative tangential follower loads, using the dynamic criterion is performed.