In this master thesis the performance of external viscous dampers attached to cables in cable-stayed bridges have been studied. A comparison has been performed between a linear and a non-linear cable model. The comparison was carried out for two bridge cables, one from the Dubrovnik Bridge and the other from the Normandie Bridge. The performance of the dampers have been measured in terms of maximum achieved damping ratio and minimum amplitude of vibration. The analysis was performed using the finite element method. The damping ratio was measured using both the half-power bandwidth method and by calculating the loss factor. The half-power bandwidth method can only be applied to a linear system. Therefore, the loss factor was evaluated for the linear model and compared to the results obtained using the half-power bandwidth method. From the comparison, it was concluded that the damping ratio evaluated using the loss factor was similar to the results obtained when using the half-power bandwidth method. However, when calculating the loss factor, it was of great importance that the resonance frequency of the system was accurately determined. The loss factor was then calculated for the non-linear model and compared to the results obtained for the linear model. Since the loss factor measures the energy dissipated in a system, it could be utilised for the non-linear model. When computing the strain energy for the non-linear model an approximate method was used to take into consideration the strain energy caused by the static deformation of the cable. From the comparison between the linear and non-linear cable models, it was concluded that the optimal damper coefficients obtained by both models are not significantly different. However, there is an uncertainty in the results due to the fact that an approximate method was used when calculating the strain energy for the nonlinear model. It was also observed that a very accurate evaluation of the system’s resonance frequency was needed to calculate the loss factor. It was also observed that the variation in amplitude of vibration for varying damper coefficient was small for all modes of vibration for the Dubrovnik Bridge Cable as well as for the first mode of vibration for the Normandie Bridge Cable. The difference in the results between the two bridge cables needs to be investigated further in order to get a better understanding of the results.

Several of the bridges along the Bothnia railway line do not fulfill the requirements regarding vertical accelerations that are stated in current design codes. The acceleration of the bridges needs to be reduced, in order to make the Bothnia line suitable for high speed railway traffic. The aim with this thesis is to investigate if it is possible to reduce the vertical acceleration of insufficient bridges to an acceptable level by using post-installed dampers. The expectation was that this method could have major economic advantages compared to other rehabilitation methods. Five different bridges with post-installed dampers were simulated in verified MATLAB codes. The simulations were performed for two cases for each bridge: one where the eccentricities between the attachment of the damper and the centre of gravity of the bridge cross section was taken into consideration, and one where the influence from the eccentricities was excluded. The results showed that it is fully possible to reduce the acceleration to an acceptable level with the use of external damper configurations. It was also shown that the eccentricities of the bridges had a high impact in this kind of simulations. Furthermore, some supplementary investigations regarding the location and position of the damper, were done as well. Finally, a brief analysis and discussion regarding the practical implementation of the post-installed was performed. One challenge is to anchor the damper and take care of the resulting forces in a favourable and safe way. / Flertalet broar längs med Botniabanan uppfyller inte de krav som ställs på de vertikala accelerationsnivåerna i gällande dimensioneringsnormer. Dessa accelerationer måste reduceras för att göra Botniabanan tillgänglig för trafik med höghastighetståg. I denna uppsats undersöks det huruvida det är möjligt att sänka accelerationen i bristfälliga broar med hjälp av eftermonterade externa dämpare. Förväntningen var att denna metod skulle ha stora ekonomiska fördelar gentemot andra upprustningsmetoder. Fem broar med eftermonterade dämpare har simulerats i verifierade MATLAB-koder. Simuleringarna utfördes på två olika sätt för varje bro: i en kod togs eccentriciteten mellan dämparinfästningen och tyngdpunktslinjen för bron i beaktande, och i den andra koden försummades all inverkan av eccentriciteten. Resultatet från simuleringarna visade att det är fullt möjligt att reducera accelerationerna till en acceptabel nivå med hjälp av externa dämpningskonfigurationer. Eccentriciteten visade sig även ha stor inverkan på resultatet i denna typ av simulering. Dessutom utfördes några kompletterande undersökningar gällande längd, position och vinkel på dämparen. Slutligen analyserades och diskuterades den praktiska implementeringen av de eftermonterade dämparna. En utmaning är att förankra dämparna och föra ner de resulterande krafterna på ett fördelaktigt och säkert sätt.

In this master thesis the performance of external viscous dampers attached to cables in cable-stayed bridges have been studied. A comparison has been performed between a linear and a non-linear cable model. The comparison was carried out for two bridge cables, one from the Dubrovnik Bridge and the other from the Normandie Bridge. The performance of the dampers have been measured in terms of maximum achieved damping ratio and minimum amplitude of vibration. The analysis was performed using the finite element method. The damping ratio was measured using both the half-power bandwidth method and by calculating the loss factor. The half-power bandwidth method can only be applied to a linear system. Therefore, the loss factor was evaluated for the linear model and compared to the results obtained using the half-power bandwidth method. From the comparison, it was concluded that the damping ratio evaluated using the loss factor was similar to the results obtained when using the half-power bandwidth method. However, when calculating the loss factor, it was of great importance that the resonance frequency of the system was accurately determined. The loss factor was then calculated for the non-linear model and compared to the results obtained for the linear model. Since the loss factor measures the energy dissipated in a system, it could be utilised for the non-linear model. When computing the strain energy for the non-linear model an approximate method was used to take into consideration the strain energy caused by the static deformation of the cable. From the comparison between the linear and non-linear cable models, it was concluded that the optimal damper coefficients obtained by both models are not significantly different. However, there is an uncertainty in the results due to the fact that an approximate method was used when calculating the strain energy for the nonlinear model. It was also observed that a very accurate evaluation of the system’s resonance frequency was needed to calculate the loss factor. It was also observed that the variation in amplitude of vibration for varying damper coefficient was small for all modes of vibration for the Dubrovnik Bridge Cable as well as for the first mode of vibration for the Normandie Bridge Cable. The difference in the results between the two bridge cables needs to be investigated further in order to get a better understanding of the results.

At the moment of writing, an expansion of the Swedish railway network has started, by constructions of new lines for high-speed trains. The aim is to create a high-speed connection between the most populous cities in Sweden - Stockholm, Göteborg and Malmö, and the rest of Europe. Thereby, the likelihood of faster, longer and heavier foreign trains crossing the Swedish lines is increased. However, this could be problematic since the dynamic response in railway bridges and, consequently, the risk of resonance increases with increasing train speeds. Bridges are usually designed based on contemporary conditions and future requirements are rarely considered, due to e.g. cost issues. Prospectively, the dynamic performance of existing bridges may become insufficient. Hence, the current expansion of the high-speed railway network results in an increased demand of innovative design solutions for new bridges and cost-efficient upgrading methods for existing lines. The aim of the present thesis is to propose a vibration mitigation strategy suitable for new and existing high-speed railway bridges. The main focus is a retrofit method with fluid viscous dampers installed between the bridge superstructure and the supports, which is intended to reduce the vertical bridge deck acceleration below the European design code limits. Furthermore, the intention is to investigate the efficiency of such a system, as well as to identify and analyse the parameters and uncertainties which could influence its functionality. In order to examine the applicability of the proposed retrofit, case studies, statistical screenings and sensitivity analyses are performed and analysed. Two different models, a single-degree-of-freedom system and a finite element model, are developed and compared. From the different models, it is possible to study the influence from the damper parameters, the variability of the material properties and different modelling aspects on the bridge response. After the installation of the fluid viscous dampers, it is found that the acceleration level of the bridge deck is significantly reduced, even below the design code requirements. / I skrivande stund har en utbyggnad av det svenska järnvägsnätet initierats. Målet är att skapa en höghastighetsanslutning mellan de folkrikaste städerna i Sverige - Stockholm, Göteborg och Malmö, och vidare ut i Europa. Därmed ökar sannolikheten att snabbare, längre och tyngre utländska tåg korsar de svenska järnvägslinjerna. Dock kan detta bli problematiskt i och med att järnvägsbroars dynamiska respons och, följaktligen, risken för resonans ökar med ökad tåghastighet. Broar dimensioneras ofta utifrån nuvarande förutsättningar och hänsyn tas sällan till framtida hållbarhetskrav, exempelvis p.g.a. kostnadsbesparingar. Ur ett framtidsperspektiv kan därför det dynamiska beteendet hos befintliga broar komma att bli otillräckligt. Utbyggnaden av höghastighetsnätverket ökar därmed behovet av innovativa konstruktionslösningar för nya broar och kostnadseffektiva uppgraderingsmetoder för befintliga sträckor. Syftet med föreliggande avhandling är att föreslå en metod för att minska de vibrationsnivåer som kan uppstå i både nybyggda och befintliga järnvägsbroar för höghastighetståg. Huvudfokus är en eftermonteringsmetod med viskösa dämpare, som har installerats mellan brons överbyggnad och landfästen, för att minska brobanans vertikala acceleration under gällande europeiska dimensioneringskrav. Vidare avses att undersöka effektiveteten av ett sådant system, samt att identifiera och analysera de parametrar och osäkerheter som kan påverka dess funktionalitet. Fall- och parameterstudier, samt statistiska metoder används och utvärderas för att undersöka tillämpbarheten av den föreslagna vibrationsdämpningsmetoden. Två olika modeller, ett enfrihetsgradssystem och en finit elementmodell, har skapats och jämförts. Utifrån dessa modeller kan påverkan av dämparens parametrar, variabiliteten hos materialegenskaperna och behandlingen av olika modelleringsaspekter studeras. Från resultaten är det tydligt att brobanans accelerationsnivå avsevärt reduceras efter monteringen av viskösa dämpare, till och med under dimensioneringskraven. / <p>QC 20170425</p>