The present thesis studies transition to turbulence in a spatially developing bound-ary layer for subcritical Reynolds numbers. A fully nonlinear iterative direct-adjoint optimisation technique is employed to identify finite amplitude perturbations triggering transition in an energy efficient way. The study explores two approaches to find the Reynolds number scaling of the subcritical transition energy threshold Ec(Re) and the corresponding nonlinear optimum which is the minimal seed for subcritical transition to turbulence. The first approach focuses on shortened optimisation time horizons T compared to a reference case with T = 400. It is shown that the transition energy threshold Ec increases for T = 200/300 when compared to the reference value Ec,T =400. This is linked to the existence of local optima which maximise the objective functional for short transient times. These local optima are fully localised and feature the Orr and liftup energy growth mechanisms as observed for the reference case. However, their long-time evolution is suboptimal since it leads to a stable streak configuration which is found to relaminarise also for initial amplitudes of E0 > Ec,T =400. The second approach of using an inflow Reynolds number increased by factor 3/2 but non-shortened T is shown to be suitable to identify the scaling Ec(Re). Exploratory optimisation runs suggest a decrease in the transition energy threshold of at leastEc(3/2 · Re)/Ec(Re) < 0.47. / Denna avhandling studerar turbulensöverång i ett rumsligt-utvecklande gränsskikt vid subkritiska Reynolds tal. En icke-linjär iterativ direkt-adjoint optimeringsteknik implimenteras för att indentifiera perturbationer med ändlig amplitud som leder till övergång på ett energieffektivt sätt. Studien utforskar två metoder för att hitta skalningen av Reynolds numret till den subkritiska energytröskeln Ec(Re) för övergång och det tillhörande icke-linjära optimum minimal seed som leder till subkritisk turbulensövergång. Den första metoden fokuserar på förkortade optimeringstidshorisonter T jämfört med referensfallet med T = 400. Det visar sig att energitröskeln Ec ökar för T = 200/300 jämfört med referensvärdet Ec,T =400. Detta är kopplat till förekomsten av lokala optima som maximerar the objective functional för korta transienta tidsho-risonter. Dessa lokala optima är helt lokala i rummet och uppvisar samma Orr och liftup energitillväxtmekanismer som referensfallet. Utvärderingen på lång sikt visar sig dock vara suboptimal då den leder till en stabil streak konfiguration som återför även initiella perturbationsamplituder E0 > Ec,T =400 till ett laminärt tillstånd. Den andra metoden, som använder sig av Reynolds tal ökade med en faktor 3/2 men icke-förkortade tidshorisonter T , visar sig lämplig för att identifiera skalningen Ec(Re). Utforskande optimering antyder att en minskning i energitröskeln för övergång medminst Ec(3/2 · Re)/Ec(Re) < 0.47.

In Sweden, prefabrication in the construction industry is a very common system. In prefabricated structures, there are various kinds of connections and generally many hinged connections. Therefore, it is of high interest to study the behavior of the prefabricated buildings in relation to the connections. Two main theories that can be used to evaluate our structures are the non-linear finite element analysis (NLFEA) and the second order effects. These two theories help to study the real behavior of the structures. Software that can apply these two theories is the ATENA-GiD. Therefore, it was very interesting to explore this software and find out how it can be used for prefabricated buildings. For this reason, a simplified ten-storey building was studied which had been also used in Lindwall’s and Wester’s (2016) master thesis. Various cases were chosen for this building. The building was studied either with monolithic walls or with vertical slip connection between the prefabricated walls. Also, the hollow core (HC) slabs were modelled in two ways and the supports of the columns were modelled in three ways. Even when each slab was modelled with two materials (solid concrete for the upper and lower layer with smeared reinforcement for the lower layer and modified concrete in order to compensate for the voids), the increase in the time for analysis was not important. Also, the cracking was not extensive thanks to the relatively low wind load. The slip joint between the walls didn’t lead to the different displacement between the walls. It was found that the hinged support in the columns was modelled by using the upwind line of the base. In non-linear analysis cases, the model of the structure gave 20% larger displacements than in linear analysis cases which means that the cracking had an important influence on the second order effects despite that the cracking was not extensive. The reduction of the stiffness of the walls to 40% accounting for cracked sections in additional linear analyses to according to the Eurocode 2 was a conservative choice for this building. The most remarkable result was that when the supports of the columns were modelled with hinges there was smaller displacement than when the supports were fixed. The reason for this was the negative displacements due to the buckling of the columns of the first storey. Moreover, for the linear cases, there was a much smaller displacement (5mm) than Lindwall and Wester (2016) (17mm) and this was possibly due to the way that the hinges were modelled in my building. It is interesting to investigate other ways to model the hinges in ATENA-GiD as well as other ways to model the connections between the HC slabs and the perimetric beams. Also, the effect of creep through the modulus of elasticity could be analyzed. Finally, it would be interesting to include foundations in the model to study the possible need for anchorages.

<p>Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasigeostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of two-dimensional and quasigeostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascade in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasigeostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the unexpecteddependency on an infrared Reynolds number in the spectral scaling of theenergy spectrum in the inverse energy cascade, and the validation of Charney’spredictions on the dynamics of quasigeostrophic turbulence. It has also beenshown that the scaling of the energy spectrum in the enstrophy cascade isinsensitive to intermittency in higher order statistics, but that corrections mightapply to the ”universal” Batchelor-Kraichnan constant.</p>

Sammanfattning Väldigt lite är känt om hur olika träningsmetoder påverkar teknisk utveckling hos innebandyspelare. Syftet med studien var att undersöka hur olika typer av smålagsspel i innebandy påverkar spelvolymen samt antal avslut och avslut på mål. Frågeställningarna för arbetet var: skiljer sig spelvolymen i innebandyns smålagsspel mellan spel två mot två (2v2), 3v3, 4v4 och 5v5? Skiljer sig antalet avslut i innebandyns smålagsspel mellan spel 2v2, 3v3, 4v4 och 5v5? Skiljer sig antalet avslut på mål i innebandyns smålagsspel mellan spel 2v2, 3v3, 4v4 och 5v5? Metod Två testgrupper rekryterades till studien där grupperna bestod av två olika amatörlag. Det ena laget var ett damveteranlag där 15 spelare deltog, med en medelålder på 38 år, med 2-15 års erfarenhet av organiserad innebandy. Det andra laget var ett pojklag med 21 deltagande spelare, i åldrarna 12-13 år, med 5-6 års erfarenhet av innebandy. Datainsamlingen skedde sedan under respektive lags ordinarie träning där fyra olika spelformer filmades. Ena laget filmades tio gånger för vardera spelform och det andra laget filmades tio gånger för vardera spelform förutom en, där en spelsekvens försvann på grund av oförutsedda händelser. Varje spelsekvens var en minut lång. Därefter analyserades filmmaterialet varpå spelvolym, antal avslut samt avslut på mål registrerades för varje minut spelad i de olika spelformerna. Rådata sammanställdes och genomgick sedan en statistisk analys för att undersöka om spelen skiljde sig signifikant i någon del. Resultat Grupp A visade på signifikant skillnad i spelvolym mellan alla spelformer där den högsta volymen hittades i spel 2v2, därefter följde 3v3, 4v4 och sist 5v5. Alla smålagsspel för grupp A visade signifikant fler avslut och avslut på mål jämfört med spel 5v5 men ingen signifikant skillnad hittades smålagsspelen emellan. I grupp B hittades samma mönster för spelvolym som i grupp A, dock visades ingen signifikant skillnad mellan spelformerna 4v4 och 5v5. Antalet avslut var signifikant högre i alla smålagsspel jämfört med 5v5, dock hittades endast signifikans mellan 2v2 och 5v5 när det kom till avslut på mål. Slutsats Studien indikerar att en minskning i antalet spelare verkar vara ett effektivt sätt att öka frekvensen på de tekniska aktionerna under spel. För teknikträning i spel verkar därför smålagsspel vara att föredra framför fullstort spel 5v5. Mer forskning på området behövs för att öka förståelsen kring möjliga användningsområden för innebandyns smålagsspel. / Aim Very little is known about how different types of training influence technical development in floorball. The purpose of this study was to investigate how volume of play, shots, and shots on goal, were affected in different types of small-sided games (SSG). The research questions this paper sought to answer were: in floorball, does the volume of play differ between the game formats: two versus two (2v2), 3v3, 4v4, and 5v5? In floorball, does the number of shots differ between the game formats: 2v2, 3v3, 4v4, and 5v5? In floorball, does the number of shots on goal differ between the game formats: 2v2, 3v3, 4v4, and 5v5? Method Two amateur teams were recruited for the study. One team was a women’s team of 15 players participating, with an average age of 38, with 2-15 years’ experience of organized floorballpractice. The other team was a boys’ team of 21 players participating, aged 12-13 and 5-6 years’experience of organized floorball practice. The data were collected during one of each team’sregular floorball practice sessions, where video captured the four different SSGs. One team was filmed ten times for one minute for each SSG and the other team was filmed ten times in three SSGs and nine times in one. The videos were analysed for volume of play, as well as registering shots and shots on goal. The compiled data was then statistically analysed in order to see if there were any significant difference between the game formats. Results Group A showed a significant difference in volume of play between all SSGs, where the highest volume of play was found in 2v2, and the rest with a lower volume of play in ascending order. As for shots and shots on goal, group A showed significantly more shots and shots on goal in 2v2, 3v3, and 4v4 compared to 5v5, but no significance was found between the SSGs. Group B showed a similar pattern in volume of play as found in group A, but no significant difference between 4v4 and 5v5. The amount of shots were significantly higher in 2v2, 3v3, and 4v4 compared to 5v5. However, for shots on goal group B only showed 2v2 producing significantly more shots than 5v5. Conclusion The study indicates that reducing the number ofplayers is aneffective wayto increase technical actions. Therefore, SSGs seems to be better for skill acquisition in games than the large game of 5v5. However, more research is needed in this field for further understanding of the uses of SSG:s in floorball.

Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasi-geostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of twodimensionaland quasi-geostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascades in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasi-geostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the sensitivity toan infrared Reynolds number in the spectral scaling of the energy spectrumin the inverse energy cascade range, and the validation of Charney’s predictionson the dynamics of quasi-geostrophic turbulence. It has also been shownthat the scaling of the energy spectrum in the enstrophy cascade is insensitiveto intermittency in higher order statistics, but that corrections apply to the”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipationanomalies following a classical remark by Landau (Landau &amp; Lifshitz1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical localityassumption. / QC 20101029

Shear cracks are formed when high oblique tensile stresses, e.g. in thin webs, exceed the tensile strength. A known example of this phenomenon is the extensive shear cracks that were found on the box-girder bridges Gröndal and Alvik, which were mainly caused by insufficient amount of shear reinforcement. In order to avoid this incident (inadequate amount of shear reinforcement), the reinforcement stress is often being assumed as a ultimate limit load in order to fulfill requirements regarding crack control in the service-ability limit state (SLS). This method has led to a overestimation of the reinforcement amount in bridge-design. The aim of this master thesis is therefor to study the shear crack phenomenon and investigate if the amount of shear reinforcement in bridges can be reduced. The first part of this thesis studies the shear cracking behavior in concrete in a plane stress state, while the second part focus how design standards as well as manuals treats shear cracks. Shear cracking in the reinforced concrete panels has been studied with non-linear finite element analysis and compared to experimental testings performed by the University of Toronto. Three different loading conditions for the panels has been analyzed: pureshear, compression or tension combined with shear. The panels are to represent parts of a web in a box-girder bridge that are subjected to in-plane stresses. The non-linear finite element analysis was performed in the FE-program Atena where mainly the crack propagation and crack pattern were studied. The material model in Atena is a smeared crack model with either fixed or rotated crack direction. The panel analysis, in SLS, gave various results. For loading conditions pure shear and tension/shear, the response of the FE-analysis gave a similar result regarding crack pattern but differed in size of crack width. For compression/shear, only micro-cracks developed and did not reflect the result from the real panel tests. This may be the consequence of a too stiff FE-model and the fact that, in the real tests, some cracks occurred due to out-of-plane bending. With methods described in Eurocode 2 and the Swedish handbook for EC2, a shear crack calculation model was created in order to determine the reinforcement stress and crack width. As a reference for the shear crack calculations, a wing structure (1 m strip) has been used which is part of a railway bridge located in Abisko. These calculations were done in order to investigate if the amount of shear reinforcement could be reduced and at the same time fulfill crack control demands in SLS. The bridge department at Tyréns AB concluded, according to a truss model, that the wing section should be reinforced with a amount of 14.1 cm2/m2 while our model showed that the crack width demand could be fulfilled with a equivalent amount of 9.82 cm2/m2, i.e. a reduction around 30%.

This thesis covers an investigation regarding the failure in the bridge slab of Gruvvägsbron, which was the result of the full scale test that the bridge was subjected to prior to demolition. Using the non-linear finite element software ATENA 3D, a model of the bridge was assembled, with the purpose to attempt to reenact the test procedure and realistically capture the failure load and behaviour. This in order to be able to conclude what kind of failure that occurred. The initial part of this thesis presents a summary of a conducted literature study, which aims to give deeper knowledge regarding the linear shear and punching shear phenomena and their respective failure mechanisms, and how they are applied on bridge slabs. Furthermore, the shear capacity of the bridge was calculated according to current design codes. A parameter study was conducted on the model, which initially showed a over-stiff response. The aim of this was to study the influence of key variables on the outcome of the analysis, and hopefully get closer to the failure load acquired inthe experiment. From the studied parameters, it was observed that a combined reduction of the tensile strength and fracture energy, together with a low fixed crack coefficient had the largest influence on the outcome of the analysis. It was also observed that the location of the failure and failing load was dependant on how the loading was applied to the model, i.e. via load control or deformation control. The final model failed at a load which surpassed the actual failure load by 10.5%. The mode of failure obtained in all the analyses were the result of a large shear crack propagating from the edges of the loading plate, through the slab to the slab/girder-intersection. This indicates that the type of failure that occurred was primarily due to a linear shear mechanism with a secondary punching effect. The design values calculated by keeping with the current codes resulted in too conservative values when compared to the obtained failure load from the experiment. This proves the difficulty in regarding the internal force distribution in slab struc-tures as well as the shear carrying width, which from the analysis were found to be larger than that obtained from the code. / Denna uppsats behandlar en utredning gällande brottet i plattan på Gruvvägsbron, som var resultatet av det fullskaletest som bron utsattes för innan rivning. Med hjälp av den icke-linjära finita element-programvaran ATENA 3D skapades en modell avbron, med syfte att på ett realistiskt sätt försöka återskapa experimentet och fånga brons verkliga beteende. Detta för att således kunna dra slutsatser angående brottets natur. Den första delen av denna uppsats innehåller en sammanfattning av en utförd litteraturstudie, som ämnar ge en ökad förståelse angående fenomenen skjuvning och genomstansning, tillsammans med olika brottmekanismer relaterade till dessa. Vidare har brons motstånd mot skjuv- och genomstansningbrott beräknats enligt rådande normer. En parameterstudie utfördes på modellen, då den ursprungligen uppvisade ett överstyvt beteende. Syftet med detta var att studera nyckelparametrars påverkan på analysens resultat, och eventuellt komma närmare den verkliga brottlasten i experimentet. Av de studerade parametrarna observerades att en samtida reduktion av draghållfasthet och brottenergi, samt ett lågt värde på den så kallade "fixedcrack"-koefficienten gav störst inverkan på resultatet. Vidare observerades att brottets lokalisering och brottlasten var beroende av hur lasten påfördes modellen, dvs genom last- eller deformationsstyrning. Den slutgiltiga modellen gick till brott vid en last som översteg den verkliga brottlasten med 10.5%. Brottet som skedde var i samtliga analyser resultatet av en skjuvspricka som sträckte sig från kanten av lastplattan, genom plattan, ner till mötet mellan platta och balk. Detta indikerar att den typ av brott som skedde var ett primärt skjuvbrott med en sekundär stanseffekt. Lastvärdena beräknade enligt rådande normer tycks vara för konservativa, om jämförelse görs med lasten som uppnåddes i experimentet. Detta visar på svårigheten i att bedöma den inre kraftspridningen i plattor, och även dess skjuvbärande bredd, då analysen visade att denna var betydligt större än vad som ges i koden.

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.

In Sweden, the railway sector currently faces the challenge of developing its first high-speed railway line, in response to the need to provide faster domestic and international transport alternatives. High-speed train passages on railway bridges can cause resonance in the bridge superstructure, which induce high accelerations that should not exceed the limits stipulated in the current design code. The most common bridge type adopted in Sweden is the portal frame bridge, an integral abutment bridge confined by surrounding soil. The soil possesses inherent material damping and radiation damping that allows energy dissipation of train-induced vibrations. Both the damping and the natural frequency of the soil-structure system influence the acceleration response of the bridge superstructure. Therefore, it is necessary to investigate the effect of soil-structure interaction on portal frame bridges. Within this thesis, a numerical parametric study was performed to gain knowledge of the dynamic effect of the relative deck-abutment stiffness on the soil-structure interaction of portal frame bridges. For four span lengths, three different boundary conditions were analyzed in the form of i) no soil, ii) backfill, and iii) half-space. The analysis was performed on two- and three-dimensional finite element models. The backfill and subsoil were modeled with both direct finite element approach, and with a simplified approach using Kelvin-Voigt models and frequency-dependent impedance functions. Furthermore, time was devoted to investigating the nonlinear compression-only behavior of the interaction between the backfill and the abutments to allow separation. The results presented in the thesis illuminate the essence of including soil-structure interaction in the dynamic analysis as both the modal damping ratio and the natural frequency increased drastically. The effect of backfill on short span bridges has shown to be more prominent on the reduction of the train-induced vibrations. For longer spans, the subsoil proved to be more significant. For the simplified models the modal damping ratios of the different span lengths have been quantified as a logarithmic trend of the first vertical bending mode. Two-dimensional models have been problematic when using plane stress elements due to the sensitivity of the element thickness on the response. Thus, such models are only recommended if validation with corresponding three-dimensional models and/or field measurements are possible. By allowing separation of the soil-structure interface, the effect of contact nonlinearity on the acceleration response has been more suitable with direct finite element approach - in which static effects of the soil are accounted for - contrary to the simplified nonlinear models with compression springs. / Järnvägssektorn i Sverige står inför utmaningen att utveckla den första höghastighetsbanan med syftet att erbjuda snabbare inhemska och internationella transportalternativ. Passager av höghastighetståg på järnvägsbroar kan orsaka resonans i brons överbyggnad vilket resulterar i höga accelerationer som inte får överskrida begränsningarna i dimensioneringsnormen. I plattrambroar, vilka är främst förekommande i Sverige, utförs broplattan inspänt i rambenen omslutna av jord. Jorden bidrar utöver styvhet, även med material- och strålningsdämpning där vibrationer i jorden inducerade av tågpassager tillåts dissipera. Accelerationerna i brons överbyggnad påverkas av dämpningen och egenfrekvensen av jord-struktur systemet. Med anledning av detta är det väsentligt att undersöka effeken av jord-struktur interaktionen på plattrambroar. I detta examensarbete har en numerisk parametrisk studie utförts för att erhålla kunskap om effekten av den relativa styvheten av broplattan och rambenen på jord-struktur interaktionen av plattrambroar. Fyra spännvidder har undersökts för tre olika randvillkor där i) ingen jord, ii) motfyllning samt iii) halvrymd har beaktats. Analysen utfördes på två- och tredimensionella finita element modeller. Motfyllningen respektive underliggande jord modellerades med finita element på ett direkt- samt förenklat tillvägagångssätt där Kelvin-Voigt modeller och frekvensberoende impedansfunktioner användes. Mellan motfyllningen och rambenen har separation tillåtits där det icke-linjära förhållandet av interaktionen undersöktes med tryckbeteenden för fjädrarna. Resultaten belyser vikten av att inkludera jord-struktur interaktionen i dynamiska analyser p.g.a. ökningen den medför för den modala dämpningen och egenfrekvensen. För korta spännvidder, påvisades det att effekten av motfyllningen var mer framstående för reduktionen av vibrationerna orsakade av tåg. För längre spännvidder framgick det däremot att underjorden hade en större påverkan. Effekten av jord-struktur interaktionen på spännvidderna kvantifierades som ett logaritmiskt samband för den modala dämpningen av första vertikala böjmoden. Tvådimensionella modeller har varit problematiska när plana spänningselement användes p.g.a. känsligheten i responsen orsakad av variationer i elementtjockleken. Därav rekommenderas tvådimensionella modeller endast om validering mot tredimensionella eller fältmätningar är möjliga. När separation tilläts i gränsytan av jord-struktur interaktionen, visade det sig att direkt tillvägagångssätt med finita element var mer lämplig med hänsyn till det icke-linjära kontaktbeteendet. Detta eftersom de statiska effekterna av jorden påverkade accelerationsresponsen markant. De statiska effekterna har inte varit möjliga att simulera i dem förenklade icke-linjära modeller med tryckfjädrar.

VIBRATION AVOIDANCE, a technique to proactively remove unwanted or excessive vibrations in multi-joint industrial robots, has shown to be desired in various applications. A trade-off between vibration avoidance performance and path deviation has been thekey criteria for assessing the effectiveness and quality of an approach. The purpose of this thesis is to compare two proposed state-of-the-art vibration avoiding approaches: input shaping and extended flexible joint model combined with specialized compensation control and explore the fusion of them. Both approaches are first investigated and evaluated in simulation. A comparison is then conducted in the four presented baseline movements on a real robot. Among the two approaches, input shaping is less comprehensive but enables rapid identification, making it suitable for simple repetitive tasks. It is also found that joint-wise path generation used in input shaping causes a loss of path fidelity, but this problem is alleviated when using an extended flexible joint model combined with specialized compensation control. The latter approach preserves synchronicity across all joints and assures multi-input multi-output (MIMO)-path fidelity. The extended flexible joint model, which is identified through a nonlinear gray-box model, is also less susceptible to modeling errors. The performance comparison with two rudimentary digital filters exhibits promising results for both proposed solutions. Finally, a fusion of the two approaches is proposed as a final solution of this work. As a result, the collaborative approach is the closest to ideal vibration avoidance but suffers from greater path deviation. The extended flexible joint model combined with compensation results in the least deviation from the baseline trajectory among all tested approaches. / VIBRATIONSDÄMPNING, en teknik för att proaktivt undvika oönskade vibrationer i fleraxlade industrirobotar, har visat sig vara önskvärd i många olika applikationer. En avvägning mellan vibrationsdämpningens prestanda och avvikelser från rörelsebanan har varit viktiga kriterier för att bedöma effektiviteten och kvalitén av ett tillvägagångssätt. Syftet med denna avhandling är att jämföra två toppmoderna tillvägagångssätt för att undvika vibrationer: ingångsformning och utökad flexibel axelmodell kombinerad med specialiserad kompensationskontroll samt utforska sammanslagning av de två. Bägge tillvägagångssätt är först undersökta och utvärderade i en simulation. En jämförelsemellan de fyra standard robotrörelserna som är presenterade är sedan genomförd på en riktig robot. Mellan de två tillvägagångssätten är ingångsformning mindre förståeligt men möjliggör en snabb identifikation vilket gör den lämplig för simpla repetitiva uppgifter. Det fastställs även att axelvis generering av rörelsebanor som används med ingångsformning orsakar lägre noggrannhet och pålitlighet vad gäller avvikelser från rörelsebanan. Detta problem är inte lika påtagligt vid användning av utökad flexibel axelmodell kombinerad med specialiserad kompensationskontroll eftersom detta tillvägagångssätt bevarar synkroniciteten över samtliga axlar och garanterar multi-input multi-output (MIMO) följdriktighet. Den utökade flexibla axelmodellen, som identifieras med hjälp av en icke-linjär gray-box modell, är även mindre mottaglig för modelleringsfel. Prestandajämförelsen med två rudimentära digitala filter uppvisar lovande resultat för bägge föreslagna lösningar. Till sist, en sammanslagning av de två tillvägagångssätt är föreslagen som en slutgiltig lösning. Det sammanslagna tillvägagångssättet är närmast perfekt vibrationsdämpning men medför större avvikelser från rörelsebanan. Den utökade flexibla axelmodellen kombinerad med kompensation resulterar i minst avvikelse från rörelsebanan bland alla testade tillvägagångssätt.