Dissertations / Theses on the topic 'Springer fibers'

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 149-152).
This thesis deals with several combinatorial problems in representation theory. The first part of the thesis studies the combinatorics of affine Springer fibers of type A. In particular, we give an explicit description of irreducible components of Fl[subscript tS] and calculate the relative positions between two components. We also study the lowest two-sided Kazhdan-Lusztig cell and establish a connection with the affine Springer fibers, which is compatible with the affine matrix ball construction algorithm. The results also prove a special case of Lusztig's conjecture. The work in this part include joint work with Pablo Boixeda. In the second part, we define the combinatorial wall-crossing transformation and the generalized column regularization on partitions and prove that a certain composition of these two transformations has the same effect on the one-row partition. This result gives a special situation where column regularization, can be used to understand the complicated Mullineux map, and also proves a special case of Bezrukavnikov's conjecture. Furthermore, we prove a condition under which the two maps are exactly the same, generalizing the work of Bessenrodt, Olsson and Xu. The combinatorial constructions is related to the Iwahori-Hecke algebra and the global crystal basis of the basic [ ... ]-module and we provide several conjectures regarding the q-decomposition numbers and generalizations of results due to Fayers. This part is a joint work with Panagiotis Dimakis and Allen Wang.
by Guangyi Yue.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 125-128).
This thesis deals with the connections of Geometry and Representation Theory. In particular we study the representation theory of small quantum groups and Frobenius kernels and the geometry of an equivalued affine Springer fiber Fl[subscript ts] for s a regular semisimple element. In Chapter 2 we relate the center of the small quantum group with the cohomology of the above affine Springer fiber. This includes joint work with Bezrukavnikov, Shan and Vaserot. In Chapter 3 we study the geometry of the affine Springer fiber and in particular understand the fixed points of a torus action contained in each component. In Chapter 4 we further have a collection of algebraic results on the representation theory of Frobenius kernels. In particular we state some results pointing towards some construction of certain partial Verma functors and we compute this in the case of SL₂. We also compute the center of Frobenius kernels in the case of SL₂ and state a conjecture on a possible inductive construction of the general center.
by Pablo Boixeda Alvarez.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics

Soit G un groupe algébrique en type classique A, B ou D. Soit e un élément nilpotent de son algèbre de Lie et Z son centralisateur. On suppose la caractéristique nulle et l'ordre de e, vu comme endomorphisme, égal à deux. Cette thèse établit les propriétés de normalité, rationalité et Cohen-Macaulay pour toute adhérence Y d'une Z-orbite dans la variété des drapeaux de G. Elle étend ainsi un résultat de N.Perrin et E.Smirnov qui traitant le cas où Y est une composante irréductible d'une fibre de Springer pour les types A et D. Nous employons le même argument principal, à savoir un raisonnement récursif basé sur (1) la birationnalité d'un morphisme vers Y et (2) la surjectivité d'une restriction de sections. Pour produire (1), nous faisons intervenir les variétés de Schubert, de Bott-Samelson et employons la théorie des sous-groupes symétriques en recourant à des références classiques sur le sujet (R-W Richardson, T-A Springer). Pour (2), nous nous basons sur un théorème de X.He et J-F Thomsen fournissant un scindage de Frobenius. Celui-ci implique alors (2) en caractéristique positive et nous opérons une réduction p pour nous ramener à la caractéristique nulle de départ. Notre travail appelle à se prolonger dans différentes pistes de réflexion et de recherche. Il pourrait avoir des implications positives pour l'étude des composantes irréductibles de la variété de Steinberg, et à travers elles, du calcul de polynômes caractéristiques introduits par A.Joseph afin de constituer des représentations irréductibles du groupe de Weyl. Notre travail pose aussi la question naturelle de la généralisation de son résultat au type C, aux types exceptionnels et à la caractéristique positive
Let G be a connected algebraic reductive group in types A, B, or D, and e be a nilpotent element of its Lie algebra with centralizer Z:=Z_G(e). We suppose the characteristic zero and that e corresponds to a nilpotent endomorphism of order two. We sketch a proof of the following result: all Z-orbit closures Y in the flag variety X of G are normal. It extends a work of Nicolas Perrin and Evgeny Smirnov which deals with an irreducible component Y of the Springer fiber X(e) in types A and D. We use the same main arguments, namely an induction based on (1): the existence of a suitable birational morphism onto Y, and (2): the surjectivity of section restrictions of an ample line bundle. For us (1) will be obtained thanks to good Weyl group elements, Schubert varieties, Bott-Samelson varieties and several fundamental results from Roger Wolcott Richardson and Tonny Albert Springer on symmetric spaces. On the other hand, (2) follows from a theorem proved by Xuhua He and Jesper Funch Thomsen which states Frobenius splittings of Y-like varieties. It thus implies (2) in positive characteristic and we just have to pass it through the zero : we then merely produce an example of the reduction modulo p method.Our work suggests several avenues of research and could be improved in several directions. It could have implications for the study of the irreducible components of the Steinberg variety and thus for the calculation of the characteristic polynomials. They have been introduced by Anthony Joseph in order to constitute irreducible representations of the Weyl group. Our work also raises the question of its generalization to the C type, the exceptional types and the positive characteristic

Ce travail de thèse a pour but de construire et d’étudier une fibration de Hitchin pour les groupes qui apparaît naturellement lorsque l’on essaie de géométriser la formule des traces. On commence par construire une telle fibration en utilisant le semi-groupe de Vinberg. Sur ce semi-groupe de Vinberg, on montre qu’il existe un certain morphisme « polynôme caractéristique » muni d’une section naturelle, de même que dans le cas des algèbres de Lie. On montre également que l’on peut construire un centralisateur régulier au-dessus de cette base des polynômes caractéristiques qui est un schéma en groupes commutatif et lisse.On s’intéresse alors à des variantes pour les groupes des fibres de Springer affines pour lesquelles on remarque que l’introduction du semi-groupe de Vinberg permet d’obtenir une condition d’intégralité analogue à celle de Kazhdan-Lusztig. Ces fibres de Springer affines sont des analogues locaux des fibres de Hitchin. On obtient alors une formule de dimension pour ces fibres.Dans un troisième temps, on s’intéresse à l’aspect global de cette fibration pour laquelle on donne une interprétation modulaire et sur laquelle on construit l’action d’un champ de Picard, issu du centralisateur régulier. L’espace total de cette fibration étant en général singulier, nous étudions son complexe d’intersection. Cet espace de Hitchin s’obtient naturellement comme l’intersection du champ de Hecke avec la diagonale du champ des G-torseurs et on démontre que sur un ouvert suffisamment gros de la base de Hitchin, le complexe d’intersection de l’espace de Hitchin s’obtient par restriction de celui du champ de Hecke corrrespondant.Enfin, dans la dernière partie de cette thèse, on établit un théorème du support dans le cas où l’espace total est singulier analogue à celui de Ngô et l’on démontre que, dans le cas de la fibration de Hitchin, les supports qui interviennent sont reliés aux strates endoscopiques
This main goal of this work is to construct and study the properties of Hitchin fibration for groups which appears naturally when we try to geometrize the trace formula. We begin by constructing this fibration using the Vinberg’s semigroup. On this semigroup, we show that there exists a characteristic polynomial morphism equipped with a natural section, analog at the Kostant’s one in the case of Lie algebras. We also show that there exists on the base of characteristic polynomials a regular centralizer scheme, which is a smooth commutative group scheme.Then, we are interested in some variant of affine Springer fibers, for which we see that the Vinberg’s semigroup appears naturally to obtain an integrality condition analog to Kazhdan-Lusztig’s one. These affine Springer fibers are local incarnation of Hitchin fibers.In a third time, we go back to the global case and give a modular interpretation of this new Hitchin fibration on which we construct an action of a Picard stack, coming from the regular centralizer.The total space of this fibration, even on the generically regular semisimple locus will be singular and we want to understand his intersection complex. This space can be obtained as the intersection of the Hecke stack with the diagonal of the stack of G-bundles and we show that on a sufficiently big open subset of the Hitchin base, the intersection complex of the Hitchin’s space is the restriction of the corresponding intersection complex on the Hecke stack.Finally, in the last part of this work, we establish a support theorem in the case of a singular total space, generalizing Ngo’s theorem et we show that in the case of Hitchin fibration, the supports that appear are related to the endoscopic strata

La thèse consiste de deux parties. Dans la première partie, on montre la pureté des fibres de Springer affines pour $\gl_{4}$ dans le cas non-ramifié. Plus précisément, on construit une famille de pavages non standard en espaces affines de la grassmannienne affine, qui induisent des pavages en espaces affines de la fibre de Springer affine. Dans la deuxième partie, on introduit une notion de $\xi$-stabilité sur la grassmannienne affine $\xx$ pour le groupe $\gl_{d}$, et on calcule le polynôme de Poincaré du quotient $\xx^{\xi}/T$ de la partie $\xi$-stable $\xxs$ par le tore maximal $T$ par une processus analogue de la réduction de Harder-Narasimhan
This thesis consists of two parts. In the first part, we prove the purity of affine Springer fibers for $\gl_{4}$ in the unramified case. More precisely, we have constructed a family of non standard affine pavings for the affine grassmannian, which induce an affine paving for the affine Springer fiber. In the second part, we introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the group $G=\gl_{d}$, and we calculate the Poincaré polynomial of the quotient $\xx^{\xi}/T$ of the stable part $\xxs$ by the maximal torus $T$ by a process analogue to the Harder-Narasimhan reduction

La thèse consiste de deux parties. Dans la première partie, on montre la pureté des fibres de Springer affines pour $\gl_{4}$ dans le cas non-ramifié. Plus précisément, on construit une famille de pavages non standard en espaces affines de la grassmannienne affine, qui induisent des pavages en espaces affines de la fibre de Springer affine. Dans la deuxième partie, on introduit une notion de $\xi$-stabilité sur la grassmannienne affine $\xx$ pour le groupe $\gl_{d}$, et on calcule le polynôme de Poincaré du quotient $\xx^{\xi}/T$ de la partie $\xi$-stable $\xxs$ par le tore maximal $T$ par une processus analogue de la réduction de Harder-Narasimhan.

On appelle fibre de Springer la variété des drapeaux stables par un endomorphisme nilpotent. Nous étudions cette variété et ses composantes irréductibles. Les points fixes d’un tore sur cette variété sont paramétrés par un ensemble de tableaux dits lignes-standards. Nous construisons une décomposition en cellules de la variété naturellement paramétrée par les tableaux lignes-standards, au sens où chaque cellule contient un point fixe, et dont la codimension des cellules est analogue une longueur de Bruhat. Cela permet un calcul pratique des nombres de Betti. Lorsque l’endomorphisme nilpotent est de type crochet, deux-lignes ou deux-colonnes, nous définissons une notion de constructibilité pour les tableaux lignes-standards qui permet de décrire les points fixes des composantes. Nous déduisons un calcul de la dimension d’une intersection finie de composantes et, dans le cas deux colonnes, un critère de singularité
The variety of flags which are stable by a nilpotent endomorphism is called Springer fiber. We study this variety and its irreducible components. The fixed points of a torus on this variety are parameterized by a set of tableaux said row-standard. We construct a cell decomposition of the variety which is naturally parameterized by the row-standard tableaux, since each cell contains one fixed point, and such that the codimension of cells is analogous to a Bruhat length. This allows a handy calculation of the Betti numbers. When the nilpotent endomorphism is of hook, two-rows or two-columns type, we define a notion of constructibility for the row-standard tableaux which allows to describe the fixed points of the components. We deduce a calculation of the dimension of a finite intersection of components and, in the two-columns case, a criterion of singularity

This work describes the development of a custom sit ski for US Ski Team paralympian Greg Mallory from concept through prototype fabrication. The ski consists of a custom seat molded specifically for the athlete, carbon fiber leaf springs, and a custom binding attachment system compatible with NNN style cross country bindings. The sit ski is designed to maximize poling power through the use of an upright rather than reclined seating position, allowing for increased utilization of core muscle strength. The springs were designed based on information gathered by a custom National Instruments data acquisition system, and stiffness analysis was conducted using Castigliano’s theorem applied to classical laminate theory.

A combined experimental/analytical approach for an efficient evaluation of stiffness and characteristic curves of fiber reinforced plastic volute springs is presented in this work. Before performing the analysis mentioned in previous lines, in the early chapters, it can find the most common types of fibers, resins (matrices) and manufacturing processes used to produce composite laminates been briefly described. It also describes the analytical approaches that currently exist to determine the elastic constants of composites such as the longitudinal and transversal modulus, Poisson’s ratios and shear moduli; it also describes the improved and semi-empirical formulas to calculate the effective shear moduli and the transversal modulus. At the end of the chapter, some manufacturing methods of fiber reinforced plastic springs are described. Since fiber reinforced plastic volute springs are novel products, the fourth chapter presents and describes basic considerations that it must be taken into account when selecting material (fibers, resins, and additives) to manufacture these springs. At the end of the chapter, a method to produce volute springs is presented. The fifth chapter presents the elastic constant calculations for laminates used to manufacture volute springs. An experimental/analytical method has also been performed to determine in-plane and out-of-plane shear moduli since these material constants are of greater importance in the rate spring calculation hence any crosssection of these springs shows the major load being torsional. On the one hand the analytical method to calculate these shear moduli is based on Sumsion’s guidelines that use the theory developed by Lekhnitskii for anisotropic materials; on the other hand, it has been done torsion test of rectangular bars, which were manufactured using vacuum infusion method, to obtain shear moduli experimentally. Finally, calculated values of shear moduli are used to determine stiffness and characteristic curves of volute springs in an analytical and experimental method. It is proposed to use the in-plane shear modulus in the classical calculation method for steel volute springs and to compare results obtained with compression test results carried out on fiber reinforced plastic volute springs. Consistent results are achieved by performing this combined analytical and experimental method concluding that the best behavior of fiber reinforced plastic volute springs is when fibers have an orientation of +/ 45° concerning the main axis of the laminate.
Tesis

Movement of a bridge superstructure during a seismic event can result in damage to the bridge or even collapse of the span. An incapacitated bridge is a life-safety issue due directly to the damaged bridge and the possible loss of a life-line. A lost bridge can be expensive to repair at a time when a region's resources are most strained and a compromised commercial route could result in losses to the regional economy. This thesis investigates the use of Snapping-Cable Energy Dissipators (SCEDs) to restrain a simply supported single span bridge subjected to three-dimensional seismic loads. SCEDs are synthetic fiber ropes that undergo a slack to taut transition when loaded. Finite element models of six simply supported spans were developed in the commercial finite element program ABAQUS. Two seismic records of the 1940 Imperial Valley and 1994 Northridge earthquakes were scaled to 0.7g PGA and applied at the boundaries of the structure. The SCEDs were modeled as nonlinear springs with an initial slackness of 12.7mm. Comparisons of analyses without SCEDs were made to determine how one-dimensional, axial ground motion and three-dimensional ground motion affect bridge response. Analysis were then run to determine the effectiveness of the SCEDs at restraining bridge motion during strong ground motion. The SCEDs were found to be effective at restraining the spans during strong three-dimensional ground motion.
Master of Science

Blast resistance has recently become increasingly relevant for structural engineers. Blast loads are created by explosive devices that, upon detonation, create pressure loads that are much higher than most that a structure would ever experience. While there are many types of blast loads that are impossible to adequately prepare for, methods are presently being developed to mitigate these loads. This research investigates the possibility of using synthetic fiber ropes as a means of blast resistance. This is the third phase of a multi-stage research endeavor whose goal is to analyze Snapping-Cable Energy Dissipators (SCEDs) for reducing the effects of large-scale lateral loads.

Finite element models of portal frames were developed using the commercial finite element program ABAQUS and dynamic models were run for varying blasts and frame systems. Blast pressures of 100, 2,000, and 4,000 psi were applied to a steel portal frame and comparisons were made between unbraced frames and frames braced with springs of different stiffnesses. Additional tests were run to examine the effects of strain rate dependent yield on the results of the models. Parallel research is being conducted on the specific material behavior of the synthetic fiber ropes so that the models developed for this research can be revised for a more accurate determination of the effects of the ropes on structural systems subjected to blast loads.
Master of Science

Thesis (MScAgric (Animal Sciences))--University of Stellenbosch, 2011.
ENGLISH ABSTRACT: Kikuyu over-sown with ryegrass forms the basis of pasture based systems in the Southern Cape. During early spring, energy is the first limiting nutrient in kikuyu/ryegrass pasture, supplementation is thus essential. Supplementation consists mainly of high starch concentrates (high maize inclusion), which is expensive and could negatively affect rumen parameters. The objective of this study was to determine if milk production could be improved or maintained, and if the rumen environment would be improved, by replacing high starch concentrates with low starch (high by-product) concentrates for dairy cows on kikuyu/ryegrass pasture. Forty-five multiparous, high producing, lactating Jersey cows [body weight, 340 ± 34.7 kg; milk yield (MY), 19.6 ± 2.23kg/d; days in milk (DIM), 153 ± 33.5; lactation number, 3.6 ± 1.85; (mean ± SD)] were used in the production study. A randomised block design was used. The forty-five cows were allocated to fifteen groups of three each (blocking) on the basis of MY, DIM, and lactation number. Cows from each group were randomly allocated to one of three treatment groups (high starch, medium starch and low starch concentrate supplementation). Cows were fed 6kg (3kg during each milking) concentrate per day and were allocated fresh pasture ad lib after each milking. There were no significant differences (P > 0.05) found in milk yield and fat corrected milk yield between treatment groups. Milk fat percentage was significantly higher (P < 0.05) in the low starch treatment than in the high starch treatment. Milk fat yield was significantly higher (P < 0.05) in both the low starch and the medium starch treatment when compared to the high starch treatment. Milk protein and lactose percentages, as well as milk urea nitrogen and somatic cell count, did not differ significantly (P > 0.05) between treatments. Live weight change, as well as body condition score change, was unaffected (P > 0.05) by treatments indicating body reserves were not used to maintain milk production in the low starch treatment. A rumen metabolism study was also done with ten lactating, cannulated Jersey cows [body weight, 332 ± 56.3 kg; MY, 17.3 ± 1.73kg/d (mean ± SD)] were used. The cows were divided into two groups of five each, on the basis of lactation number, DIM, and MY. The five cows from each group were randomly allocated to one of two treatment groups (high starch and low starch concentrate supplementation) and used in a cross-over design. Cows were fed 6kg concentrate per day and were allocated fresh pasture ad lib after each milking. The volatile fatty acid (VFA) concentration was significantly higher (P < 0.05) in the high starch treatment when compared to the low starch treatment. The individual VFA’s, acetic-, propionic- and butyric acid concentrations were also significantly higher (P < 0.05) in the high starch treatments when compared to the low starch treatment. The acetic to propionic acid ratio was unaffected (P > 0.05) by treatment. Rumen ammonia-nitrogen concentration was significantly higher (P < 0.05) in the high starch treatment. Rumen pH was unaffected (P > 0.05) by supplementation type. The in sacco dry matter and neutral detergent fibre digestibilities of the kikuyu/ryegrass pasture were unaffected (P > 0.05) by treatment type. Results indicated that milk production could be maintained with low starch concentrates which also improved milk composition. Results further suggested that the rumen environment was relatively unaffected by low starch concentrate supplementation.
AFRIKAANSE OPSOMMING: Kikoejoe, oorgesaai met raaigras, vorm die basis van weidingstelsels in the Suid-Kaap. Tydens die lentemaande is energie die eerste beperkende voedingstof op kikoejoe/raaigras weidings, wat kragvoeraanvulling noodsaaklik maak. Aanvulling bestaan grootliks uit hoëstysel-kragvoer (hoë mielieinhoud) wat nie net duur is nie, maar dit kan ook die rumenomgewing benadeel. Die doel van die studie was om vas te stel of melkproduksievlakke onderhou kan word en of rumenomgewing verbeter kan word deur die vervanging van hoëstysel-kragvoer met laestysel-kragvoer (hoë neweprodukinhoud) vir melkkoeie op kikoejoe/raaigras weidingstelsels. Vyf-en-veertig meervoudige pariteit-, hoë produserende, lakterende Jerseykoeie [liggaamsmassa, 340 ± 34.7 kg; melkproduksie, 19.6 ± 2.23kg/d; dae in melk, 153 ± 33.5; laktasienommer, 3.6 ± 1.85; (gem ± standaardafwyking)] is gebruik vir die produksiestudie van die proef. Daar is gebruik gemaak van ‘n ewekansige blokontwerp. Die vyf-en-veertig koeie is opgedeel in vyftien groepe van drie elk, gebaseer op melkproduksie, dae in melk en laktasienommer. Koeie in elke groep is ewekansig aan een van drie behandelings (hoëstysel-, mediumstysel- of laestysel-kragvoeraanvulling) geallokeer. Koeie is daagliks 6kg (3kg tydens twee milkings) kragvoer gevoer en vars weiding was ad lib beskikbaar na elke melking. Daar was geen beduidende verskil (P > 0.05) in melkopbrengs of vet-gekorrigeerde melkopbrengs tussen die drie behandelings nie. Bottervetpersentasie was beduidend hoër (P < 0.05) in die laestyselbehandeling in vergelyking met die hoëstyselbehandeling. Bottervetopbrengs was beduidend hoër (P < 0.05) in beide die laestysel- en mediumstyselbehandelings in vergelyking met die hoëstyselbehandeling. Melkproteïen- en melklaktosepersentasies, asook melkureumstikstof en somatise seltelling, was onveranderd (P > 0.05) tussen behandelinge. Liggaamsmassa en liggaamskondisietelling het geen verskille (P > 0.05) getoon tussen behandelings nie, wat daarop dui dat liggaamsreserwes nie gebruik is om melkproduksie in die laestyselbehandeling te onderhou nie. ‘n Rumenmetabolismestudie is ook uitgevoer met tien lakterende, gekannuleerde Jerseykoeie [liggaamsmassa, 332 ± 56.3 kg; melkproduksie, 17.3 ± 1.73kg/d (gem ± standard afwyking)]. Die koeie is in twee groepe van vyf elk verdeel, gebasseer op laktasienommer, dae in melk en melkproduksie. Die vyf koeie van elke groep is in ‘n omslagontwerp gebruik en is ewekansig aan een van twee behandelings (hoëstysel- of laestysel-kragvoeraanvulling) geallokeer. Koeie het daagliks 6kg kragvoer ontvang en vars weiding was ad lib beskikbaar na elke melking. Die vlugtige vetsuurkonsentrasie was beduidend hoër (P < 0.05) in die hoëstyselbehandeling as in die laestyselbehandeling. Die individuele vlugtige vetsure naamlik asynsuur, propionsuur en bottersuur, was ook beduidend hoër (P < 0.05) in die hoëstyselbehandeling as in die laestyselbehandeling. Die asynsuur- tot propionsuurverhoudings het geen verskille (P > 0.05) tussen behandelings getoon nie. Rumen-ammoniakstikstof was beduidend hoër (P < 0.05) in die hoëstyselbehandeling as in die laestyselbehandeling. Rumen-pH het geen verskille (P > 0.05) getoon tussen behandelings nie. Die in sacco droëmateriaal- en neutraalbestande veselverteerbaarhede van kikoejoe/raaigras weiding het geen verskille (P > 0.05) tussen behandelings getoon nie. Die resultate het aangedui dat melkproduksie onderhou kan word en dat melksamestelling verbeter kan word met laestysel-kragvoeraanvulling. Resultate het ook daarop gedui dat die rumenomgewing nie noodwendig verbeter word deur die aanvulling van laestysel-kragvoer vir koeie op kikoejoe/raaigras weidings nie.

In this thesis, experiments and simulations are performed to study the deployment dynamics of space webs and space booms, focusing on the deployment and stabilization phases of the space web and the behavior of the bi-stable tape spring booms after long-term stowage. The space web, Suaineadh, was launched onboard the sounding rocket REXUS-12 from the Swedish launch base Esrange in Kiruna on 19 March 2012. It served as a technology demonstrator for a space web. A reaction wheel was used to actively control the deployment and stabilization states of the 2×2 m2 space web. After ejection from the rocket, the web was deployed but entanglements occurred since the web did not start to deploy at the specified angular velocity. The deployment dynamics was reconstructed by simulations from the information recorded by inertial measurement units and cameras. Simulations show that if the web would have started to deploy at the specified angular velocity, the web would most likely have been deployed and stabilized in space by the motor, reaction wheel and controller used in the experiment. A modified control method was developed to stabilize the out-of-plane motions before or during deployment. New web arms with tape springs were proposed to avoid entanglements. A deployable booms assembly composed of four 1-m long bi-stable glass fiber tape springs was designed for the electromagnetically clean 3U CubeSat Small Explorer for Advanced Missions (SEAM). The deployment dynamics and reliability of the SEAM boom design after long-term stowage were tested by on-ground experiments. A simple analytical model was developed to predict the deployment dynamics and to assess the effects of the GOLS and the combined effects of friction, viscoelastic strain energy relaxation, and other factors that act to decrease the deployment force. In order to mitigate the viscoelastic effects and thus ensure self-deployment, different tape springs were designed, manufactured and tested. A numerical model was used to assess the long-term stowage effects on the deployment capability of bi-stable tape springs including the friction, nonlinear-elastic and viscoelastic effects. A finite element method was used to model a meter-class fully coiled bi-stable tape spring boom and verified by analytical models.

QC 20170508

SEAM

Верещага Богдан Анатолійович. Дослідження впливу технології виготовлення, складу ламінату, термічної обробки на фізико-механічні властивості полімерної, композитної пластинчастої пружини. Кваліфікаційна робота на здобуття ступеня магістр за спеціальністю 132.00.02 – Прикладне матеріалознавство. – Сумський державний університет, 2021р. Кваліфікаційна робота присвячена дослідженню впливу технології виготовлення, фізико-механічних властивостей, складу ламінату, термічної обробки на фізико-механічні властивості полімерної, композитної пластинчастої пружини. За результатами досліджень системно досліджено існуючі технології виготовлення, фізико-механічні властивості, склад ламінату, та фізико-механічні властивості полімерної, композитної пластинчастої пружини.

碩士
逢甲大學
紡織工程所
94
In this thesis, composite springs were made of different fiber prepreg .ie carbon fibers, E-glass fibers and Kevlar 49 fibers, with relevant mechanical sprig constant (K) and fatigue tested after parts cured. According to the experimental results, the structure of composite springs mixed with carbon fibers and glass fibers have the higher load per unit compression displacement which is better than other composition. After comparing with other structures, the C50G50 structure of spiral spring has good properties with more cost effective. Its load per unit compression displacement reaches 469.3 lb/in and the displacement is 1.590 in. Fatigue resistance was tested by fixing compression displacement, which was set as 70 percent of maximum compression displacement of the composite spring with 300,00times a cycle. Based on the fatigue test, the decreases of load during fatigue test are both in the range of 5 percent for the springs made of carbon fibers and glass fibers (C50G50, C30G70) and the sprigs made of high modulus carbon fibers and glass fibers (HC50G50, HC30G70).

碩士
國立中興大學
機械工程學系所
103
In this thesis, a finite element model based on two-noded straight beam finite elements, with each node of nine degrees of freedom, is developed to study the dynamic characteristics of helical springs having rectangular cross sections. The helical springs could be made of isotropic materials or fiber-reinforced composite materials. The straight beam element being adopted has included the effects of the transverse shear deformation, torsion, cross-section warping, chordwise curvature, axial, transversal and lateral displacements. The equation of motion of the straight beam element developed in [11] is used, which is derived by employing Hamilton’s principle together with the finite element method. In order to apply the straight beam element to the analyses of the dynamic characteristics of the helical spring, the relation between the spring geometry and the local coordinate systems chosen for straight beam elements must be obtained first. For this purpose, Frenet-Serret formulas [13] are used to derive the coordinate transformation matrix between local coordinate systems of beam elements and global coordinate system. By using the obtained coordinate transformation matrices and considering the continuity of the displacement of the common node between two adjacent straight beam elements, the displacement transformation matrices for these two beam elements are found. With displacement transformation matrices and the mass and stiffness matrices of the straight beam elements, the global mass and stiffness matrices of helical springs are then derived. In the numerical examples, first, the steel helical springs free of constraints and with one of its ends fixed are analyzed. The results are compared with those obtained from commercial software Ansys. It is shown that in both boundary conditions the natural frequencies obtained from the present model and those of Ansys are better in agreement when the width to thickness ratio (b/h) of spring is three. Next, the single-layered and laminated composite helical springs are studied, in which the influences of the width to thickness ratio (b/h), the fiber angle, and the angles of lamination on the natural frequencies and mode shapes are investigated. It is found that for different b/h ratios, natural frequencies of the single-layered composite spring vary irregularly with fiber angles. When analyzing composite laminated springs, only cases with b/h = 3 are considered. For springs with lamination [0/θ/0/-θ]s regardless of being free or fixed at one end, the maximum values of the natural frequencies appear at the angle θ close to 45 degrees. When the spring is fixed at one end, both 2nd and 3rd modes of composite springs with laminations [0/θ/0/-θ]s and [90/θ/0/-θ]s are coupling mode of w and ϕ. When the springs are free, springs of both laminations also have this coupling mode to appear either at 7th or 8th mode.

碩士
逢甲大學
紡織工程所
94
In this experiment, composite spiral springs were made with three kinds of fibre prepreg i.e carbon fibres, kevlar fibres and E-glass fibres. Different kinds of cured springs were then assembled as respective shock absorber systems and their performance such as the compression load under 1-in deformation, the damping properties of assembled absorber system and the lateral impact resistance were explored. The experimental results show that the composite spring made of carbon / E-glass composition structure can gain the highest compression load under 1-in deformation with no damage occurred in the body of the spring. For the carbon / E-glass composition is 50% to 50%, the maximum compression load of the spring can be 470 lb/in with a maximum deformation of 1.6 in. As far as the damping properties are concerned, the absorber system composed of half to half carbon and E-glass fibres will be able to obtain the best damping performance, which fits to an economic and practical consideration. With the same composition of carbon and E-glass fibres, composite springs can also have higher energy absorption, which means c50g50 composition will be the ideal structure of the shock absorber system applied on bike.

Leaf springs are a part of the suspension system attached between the axle and the chassis of the vehicle to support weight and provide shock absorbing capacity of the vehicle. For more than half a century the leaf springs are being made of steel which increases the weight of the vehicle and is prone to rusting and failure. The current study explores the feasibility of composite leaf spring to reduce weight by designing, manufacturing and testing the leaf spring for the required load cases. An off the shelf leaf spring of Ford F-150 is chosen for making of composite hybrid spring prototype. The composite hybrid prototype was made by replacing all the leaves with glass fiber unidirectional laminate except the first leaf. Fatigue tests are then done on steel and composite hybrid leaf spring to observe the failure locations and mechanism if any. High frequency fatigue tests were then done on composite beams with varying aspect ratio in a displacement-controlled mode to observe fatigue location and mechanism of just glass fiber composite laminate. It was observed that specimens with low aspect ratio failed from crack propagation initiated from stress concentrations at the loading tip in 3-point cyclic flexure test and shear forces played a dominant role in propagation of crack. Specimens with high aspect ratio under the same loading did not fail in cyclic loading and preserved the same stiffness as before the cyclic loading. The preliminary fatigue results for high aspect ratio composite beams predict a promising future for multi-leaf composite springs.

碩士
國立中興大學
機械工程學系所
103
In this thesis, a three-node, 6 degree of freedom per node, curved beam element including the effect of initial curvature and torsion of beam is proposed. In this curved beam element, the lateral and axial displacements, as well as the deformation due to both twisting and shearing of beam are also considered. The curved beam element is employed to analyze circular helical springs with circular cross section, where the springs are made of unidirectional fiber-reinforced composite layers having a preselected set of lamination angles. To study the initial torsion and initial curvature effects in the above curved beam element, the current element is further simplified into other two types of element, a curved beam element without initial torsion and a straight beam element. Using these three types of elements, the effectiveness of curved and straight beam elements to simulate both static and dynamic characteristics of springs then can be evaluated. To ensure the elements being derived and the computer program being developed are correct, first, springs made of an isotropic material are analyzed and the results expressed as the spring constants are compared with the analytical solution derived using the virtual work method. It is found that for the problem being analyzed all three types of elements yield a little bit smaller spring constant values than the analytical one, and the difference of the results between analytical method and any of three types of element is at its largest not exceeding 8%. Next, the vibration characteristics of springs made of an isotropic material are analyzed using these three types of element. The results are compared with those of ANSYS and they are found in good agreement. To study the effect of lamination angle η on the static and dynamic characteristic of springs made of unidirectional fiber-reinforced composite material, composite solid springs with a single lamination angle (or composite solid springs) and laminated composite hollow springs with a particular set of lamination angles (or laminated composite hollow springs) are analyzed. Static analyses of composite solid springs indicate that discrepancies among the three types of elements are more conspicuous when η=〖15〗^o~〖45〗^o, and the values of spring constant seem attain their largest values as η approaches 〖45〗^o. This could be attributed by the bending and twisting deformation coupling of the off-axis composite layer as the coupling effect is strongest when 〖η=45〗^o and one knows that the spring deformed accompanied by both bending and twisting. From dynamic analysis, one finds that all three types of element yield similar trend of natural frequency to η relation. There are a few modes don’t match exactly (like the modes swing directions are different), or have a little bit greater natural frequency discrepancies at certain η values. Finally, the analyses of laminated composite hollow springs show almost the same trends of results as the composite solid springs. But the discrepancies among the mode shapes and natural frequencies become smaller. This might be due to the deformation coupling of layers of the different lamination angles, as well as more layers with 〖η=0〗^o.

碩士
國立中興大學
機械工程學系所
105
In this thesis the free vibration of rectangular cross-section helical springs is studied using two types of beam element. The first type element is the 3 node, 18 degree-of-freedom, curved beam element and the second, the 3 node, 23 degree-of-freedom, straight beam finite element. The springs are assumed to be made of isotropic materials or fiber-reinforced composite materials. In both elements, the axial and lateral displacement, as well as the deformation due to both shearing and twisting of beam are considered, while in straight beam element, additional flexural deformations of beam’s flexibility in its width direction and the warping of cross section are included. The curved beam element of rectangular cross section is adapted from Ref. [14] where springs of circular cross section are treated. The straight beam element are derived based on displacement field of Ref. [18] and by following the same procedure of obtaining the displacement transformation matrix considered by Ref. [4]. The circular cylindrical spring deformation is described in terms of Frenet-Serret local coordinates. The Hamilton’s principle together with finite element method is used to derive the element’s mass and stiffness matrices for both curved and straight beam elements. For the case of curved beam element matrices, they can be directly assembled to obtain the corresponding global mass and stiffness matrices. In contrast, the straight beam element matrices must be transformed first using the displacement transform matrix before being assembled to obtain the global ones. In the numerical examples, natural frequencies and mode shapes of isotropic helical springs of 3 turns and the width to thickness ratio b/h=1, 3, 5 are studied and compared with those of ANSYS for the free-free and fix-free boundary conditions. It is found that the present curved beam element performs well when b/h = 1 or close to one, while the straight beam element although doesn’t work well when b/h = 1, do obtain much better results than curved beam element comparing with those of ANSYS for the studied cases b/h = 3, 5. Also studied in the numerical examples are the effects of Poisson’s ratio, fiber angles of composite laminate.