The mathematical characterization of the sound of a musical instrument still follows Schumann’s laws [1]. According to this theory, the resonances of the instrument body, “the formants”, filter the oscillations of the sound generator (e.g., strings) and produce the characteristic “timbre” of an instrument. This is a strong simplification of the actual situation. It applies to a point source and does not distinguish between a loudspeaker and a three-dimensional instrument. In this work we investigate Finite-Element-based numerical simulations of eigenfrequencies and eigenmodes of a tuning fork in order to capture the oscillation behavior of its eigenfrequencies. We model the tuning fork as an elastic solid body and solve an eigenvalue equation derived from a system of coupled equations from linear elasticity theory on an unstructured three-dimensional grid. The eigenvalue problem is solved using the preconditioned inverse iteration (PINVIT) method with an efficient geometric multigrid (GMG) preconditioner. The latter allows us to resolve the tuning fork with a high resolution grid, which is required to capture fine modes of the simulated eigenfrequencies. To verify our results, we compare them with measurement data obtained from an experimental modal analyses of a real reference tuning fork. It turns out that our model is sufficient to capture the first eight eigenmodes of a reference tuning fork, whose identification and reproduction by simulation is novel to the knowledge of the author.

Abstract Storage tanks are above or below ground vessels for storing chemicals, petroleum and other liquid products. Above ground vertical cylindrical shells are typically thin walled structures prone to buckling and lose their stability especially when they are empty or have lower fluid level due to external loads.According to the Swedish National board of Housing, Building and Planning (Boverket), the Eurocodes and the Swedish national annex and building code for structural design, EKS (BFS 2011:10) should be used for verification of mechanical resistance of storage tanks. However the industry has been using a European design standard EN14015, for design of large site built steel tanks. The research question is if this design fulfils the requirements in the Swedish building code EKS and the Eurocodes. In order to investigate this, a parametric study of the buckling resistance of an empty tank has been performed, by comparing the design according to EN14015 With the requirements according to the Swedish building code and the Eurocodes. The finite element analysis was done with the finite element tool ABAQUS, The parametric study was carried out for three terrain categories0, I and II, for thesix snow load zones and for six basic wind velocities according to the Swedish snow and wind maps in EKS. The buckling resistance also further investigated for three reliability classes, reliability class 1, 2 and 3 according to the Swedish national annex and for two fabrication classes, fabrication class A and B usingEN1991-1-6The finite element analysis result of linear elastic and nonlinear buckling analysis with imperfections showed that, design according to EN14015 can meet the requirements of Eurocodes and EKS at lower basic wind velocities, terrain category (I and II) for smaller imperfections . But it does not meet the requirements at terrain category-0, for all reliability classes and all imperfection classes.The tank shell showed in some cases an increase in the load proportionality factorin nonlinear analysis for the load combinations considered in this study. It is thus necessary to study further on the finite element modelling of thin walled large tanks on relations of local buckling effect due to highly stiffened regions and the effect of magnitudes and applications of imperfections for large tanks using EN1993-1-6

Accurate measurement of skin friction in complex flows is important for: documentation and monitoring of fluid system performance, input information for flow control, development of turbulence models and CFD validation. The goal of this study was to explore using new materials to directly measure skin friction in a more convenient way than available devices. Conventional direct measurement skin friction sensors currently in use are intrusive, requiring movable surface elements with gaps surrounding that surface, or require optical access for measurements. Conventional direct measurement sensors are also difficult to apply in low shear environments, in the 1-10 Pa range. A new thin, flexible, nanoparticle infused, piezoresistive material called Metal Rubber" was used to create sensors that can be applied to any surface. This was accomplished by using modern computerized finite element model multiphysics simulations of the material response to surface shear loads, in order to design a sensor configuration with a reduced footprint, minimal cross influence and increased sensitivity. These sensors were then built, calibrated in a fully-developed water channel flow and tested in both the NASA 20x28 inch Shear Flow Control Tunnel and a backwards facing step water flow. The results from these tests showed accurate responses, with no amplification to the sensor output, to shear levels in the range of 1-15 Pa. In addition, the computer model of these sensors was found to be useful for studying and developing refined sensor designs and for documenting sources of measurement uncertainty. These encouraging results demonstrate the potential of this material for skin friction sensor applications. / Ph. D.

Syftet med studien är att undersöka vad de deltagande förskollärarna lyfter som väsentligt i undervisning av taluppfattning i förskolans utomhusmiljö. Studien bygger på en kvalitativ ansats med semistrukturerade intervjuer som forskningsverktyg. De individuella intervjuerna är gjorda med sex verksamma förskollärare från fem olika förskolor i sydöstra Sverige. Som teoretisk utgångspunkt används Gelman och Gallistels (1978) fem grundläggande principer då de utgör en modell för att förstå taluppfattning.    I studiens resultat synliggörs de deltagande förskollärarnas uppfattningar om vad de ser som väsentligt i undervisning av taluppfattning. Samtliga förskollärare är överens om att taluppfattning är en betydelsefull och grundläggande del av den matematik som undervisas i förskolan. Vidare framkommer att taluppfattning finns och uppmärksammas av förskollärarna i både planerade och spontana situationer. Variation i det matematiska innehållet, barns intresse samt förståelse lyfts som betydelsefulla aspekter i undervisning av taluppfattning i utomhusmiljö. Dessutom anses fantasi och kompetens som betydelsefulla egenskaper hos förskollärarna och att brister i dessa egenskaper enligt förskollärarna sätter gränser för deras undervisning i taluppfattning.   Vår slutsats utifrån studien är, för att undervisa taluppfattning i förskolan behöver förskollärare besitta en kompetens kring vad taluppfattning innebär. Vid undervisning av taluppfattning behöver förskollärare även på ett varierat sätt genomföra undervisningen utifrån barns intresse, dock kan inte barn bli intresserade av något som de inte introducerats i.

Indiana University-Purdue University Indianapolis (IUPUI) / Thin-walled structures find wide applications in the automotive industry as energy absorption devices. A great deal of research has been conducted to design thin-walled structures, where the main objective is to reduce peak crushing forces and increase energy absorption capacity. With the advancement of computers and mathematics, it has been possible to develop 2D patterns which when folded turn into complex 3D structures. This technology can be used to develop patterns for getting structures with desired properties. In this study, square origami tubes with folding pattern (Yoshimura pattern) is designed and studied extensively using numerical analysis. An accurate Finite Element Model (FEM) is developed to conduct the numerical analysis. A parametric study was conducted to study the influence of geometric parameters on the mechanical properties like peak crushing force, mean crushing force, load uniformity and maximum intrusion, when subjected to dynamic loading. The results from this analysis are studied and various conclusions are drawn. It is found that, when the tube is folded with the pattern having specific dimensions, the performance is enhanced significantly, with predictable and stable collapse. It is also found that the stiffness of the module varies with geometrical parameters. With a proper study it is possible to develop origami structures with functionally graded stiffness, the performance of which can be tuned as per requirement, hence, showing promising capabilities as an energy absorption device where progressive collapse from near to end impact end is desired.

Detta examensarbete har ämnat konstruktionen av en strimlare för att sönderdela kasserad PLA-plast från 3d-skrivarna i verkstaden på Mälardalens universitet. Målet med detta arbete var att underlätta återvinning men även möjliggöra återbruk av materialet genom att skapa nytt filament av den sönderdelade plasten som åter kan användas av 3d-skrivarna och därmed minska behovet av att köpa in nytt filament. För att planera detta arbete har projektgruppen använt sig av ett Gantt schema som skapades under arbetets tidiga fas.   Projektgruppens arbete har bestått av att utvärdera befintliga lösningar så som en granulator och strimlare för att sedan välja ut den bäst lämpade maskinen att konstruera för ändamålet. Under arbete utfördes även en fallstudie för att skapa en uppfattning om hur stor kraft som behövs för att sönderdela PLA-plast.   I detta uppdrag har projektgruppen använt sig av utvärderingsmetoden FMEA tillsammans med föreskrifter från arbetsmiljöverket för att konstruera bort eller minimera risker som kan orsaka skada på maskin och användare.   För att verifiera den framtagna konstruktionens hållbarhet har FEM analys använts i ett flertal fall med syftet att undersöka säkerhetsfaktorer och spänningsfördelningar under belastning.   Resultatet av detta arbete presenteras som en CAD modell i formen av en strimlare med tillhörande elektronik. Till största del möter den slutliga konstruktionen de förbestämda kraven specificerade av kunden med ett undantag gällande den önskade vikten som överskreds på grund utav den tunga snäckväxeln som implementerades i konstruktionen för att möta det utmätta kraftbehovet. Arbetet anses har skapat en grund för fortsatt arbete att byggare vidare på och vidareutveckla med nya idéer och lösningar. / This thesis consists of the construction of a shredder to shred discarded PLA-plastic from the 3d-printers in the workshop at Mälardalens University. The aim of this assignment was to ease the recycling process, but also enable the possibility to reuse the shredded plastic to make new filament that can be used by the 3d-printers and thereby decrease the need to purchase new filament.  To plan this project, the project group used a Gantt chart that was created during the project's infancy.   The work has consisted of evaluating existing solutions such as a granulator and a shredder in order to pick the best-suited machine to construct. During the assignment, a case study was also conducted with the aim of creating an understanding of how much force is needed to shred PLA-plastic.   In this assignment, the project group has used the evaluation method FMEA together with regulations from The Swedish Work Environment Authority to remove or minimize risks that can cause damage the machine or harm the user.   To verify the durability of the machine, FEM analysis was implemented in multiple cases with the purpose of examining safety factors and material stress under load.   The result for the work produced is presented as a CAD model in the form of a shredder together with the electronics. For the most part, the finished machine meets the pre-determined requirements except for the desired weight, which was exceeded because of the heavy worm gear that got implemented in the construction to meet the measured power demands. The work is considered to have created a foundation to develop further with innovative ideas and solutions.

This master’s thesis deals with the strength analysisby frame lift cage with lift capacity of 675 kg used the Finite Element Method (FEM). Furtheris performed the calculation of the guideanchoring instituted for this steel structure and the strength analysis of the used guides according to norm ČSN EN 81-1. The thesis also includes the drawing of the frame lift cage.

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