Relevant bibliographies by topics / Torsion-free group

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  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Torsion-free group'

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Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Torsion-free group"

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Dorantes-Aldama, Alejandro, and Dmitri Shakhmatov. "Selectively sequentially pseudocompact group topologies on torsion and torsion-free Abelian groups." Topology and its Applications 230 (October 2017): 562–77. http://dx.doi.org/10.1016/j.topol.2017.08.020.

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Carlson, Jon F., David J. Hemmer, and Nadia Mazza. "The group of endotrivial modules for the symmetric and alternating groups." Proceedings of the Edinburgh Mathematical Society 53, no. 1 (2010): 83–95. http://dx.doi.org/10.1017/s0013091508000618.

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AbstractWe complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n ≥ p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelian of rank 1 if n ≥ p2 + p and has rank 2 if p2 ≤ n < p2 + p. This completes the work begun earlier by Carlson, Mazza and Nakano.
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Hossein, Sahleh, and Akbar Alijani Ali. "Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–5. https://doi.org/10.9734/BJMCS/2017/32966.

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Let <em>X</em> be a compact torsion abelian group. In this paper, we show that an extension of <em>F<sub>p</sub></em> by <em>X</em> splits where <em>F<sub>p</sub></em> is the p-adic number group and p a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by <em>X</em> is not split.
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Hill, J., P. Hill, and W. Ullery. "Abelian groups that are torsion over their endomorphism rings." Bulletin of the Australian Mathematical Society 64, no. 2 (2001): 255–63. http://dx.doi.org/10.1017/s0004972700039915.

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Using Lambek torsion as the torsion theory, we investigate the question of when an Abelian group G is torsion as a module over its endomorphism ring E. Groups that are torsion modules in this sense are called ℒ-torsion. Among the classes of torsion and truly mixed Abelian groups, we are able to determine completely those groups that are ℒ-torsion. However, the case when G is torsion free is more complicated. Whereas no torsion-free group of finite rank is ℒ-torsion, we show that there are large classes of torsion-free groups of infinite rank that are ℒ-torsion. Nevertheless, meaningful definit
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Bastos, Gervasio G., and T. M. Viswanathan. "Torsion-free Abelian Groups, Valuations and Twisted Group Rings." Canadian Mathematical Bulletin 31, no. 2 (1988): 139–46. http://dx.doi.org/10.4153/cmb-1988-021-x.

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AbstractAnderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.
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Dehornoy, Patrick. "The group of fractions of a torsion free lcm monoid is torsion free." Journal of Algebra 281, no. 1 (2004): 303–5. http://dx.doi.org/10.1016/j.jalgebra.2004.03.031.

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Amberg, Bernhard, Silvana Franciosi, and Francesco de Giovanni. "Nilpotent-by-Noetherian Factorized Groups." Canadian Mathematical Bulletin 32, no. 4 (1989): 391–403. http://dx.doi.org/10.4153/cmb-1989-057-8.

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AbstractIt is shown that a soluble-by-finite product G = AB of a nilpotent-by-noetherian group A and a noetherian group B is nilpotentby- noetherian. Moreover, a bound for the torsion-free rank of the Fitting factor group of G is given, in terms of the torsion-free rank of the Fitting factor group of A and the torsion-free rank of B.
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Parmenter, M. M. "Free torsion-free normal complements in integral group rings." Communications in Algebra 21, no. 10 (1993): 3611–17. http://dx.doi.org/10.1080/00927879308824751.

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ALBRECHT, ULRICH, and STEFAN FRIEDENBERG. "A NOTE ON B-COSEPARABLE GROUPS." Journal of Algebra and Its Applications 10, no. 01 (2011): 39–50. http://dx.doi.org/10.1142/s0219498811004410.

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Let B be a torsion-free finitely faithful S-group. This paper investigates the class of all torsion-free Abelian groups A with the property that Ext (A, B) is torsion-free. Our discussion is based on a natural extension of the concept of coseparability.
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Faticoni, Theodore G. "Torsion-free Abelian groups torsion over their endomorphism rings." Bulletin of the Australian Mathematical Society 50, no. 2 (1994): 177–95. http://dx.doi.org/10.1017/s0004972700013654.

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We use a variation on a construction due to Corner 1965 to construct (Abelian) groups A that are torsion as modules over the ring End (A) of group endomorphisms of A. Some applications include the failure of the Baer-Kaplansky Theorem for Z[X]. There is a countable reduced torsion-free group A such that IA = A for each maximal ideal I in the countable commutative Noetherian integral domain, End (A). Also, there is a countable integral domain R and a countable. R-module A such that (1) R = End(A), (2) T0 ⊗RA ≠ 0 for each nonzero finitely generated (respectively finitely presented) R-module T0,
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Dissertations / Theses on the topic "Torsion-free group"

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Soelberg, Lindsay Jennae. "Finding Torsion-free Groups Which Do Not Have the Unique Product Property." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6932.

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This thesis discusses the Kaplansky zero divisor conjecture. The conjecture states that a group ring of a torsion-free group over a field has no nonzero zero divisors. There are situations for which this conjecture is known to hold, such as linearly orderable groups, unique product groups, solvable groups, and elementary amenable groups. This paper considers the possibility that the conjecture is false and there is some counterexample in existence. The approach to searching for such a counterexample discussed here is to first find a torsion-free group that has subsets A and B such that AB has
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Vallino, Daniele. "Algebraic and definable closure in free groups." Thesis, Lyon 1, 2012. http://www.theses.fr/2012LYO10090/document.

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Nous étudions la clôture algébrique et définissable dans les groupes libres. Les résultats principaux peuvent être résumés comme suit. Nous montrons un résultat de constructibilité des groupes hyperboliques sans torsion au-dessus de la clôture algébrique d'un sous-ensemble engendrant un groupe non abélien. Nous avons cherché à comprendre la place qu'occupe la clôture algébrique acl_G(A) dans certaines décompositions de G. Nous avons étudié la possibilité de la généralisation de la méthode de Bestvina-Paulin dans d'autres directions, en considérant les groupes de type fini qui agissent d'une ma
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Bieniecka, Ewa. "Commutativity and free products in Thompson's Group V." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/14652.

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We broaden the theory of dynamical interpretation, investigate the property of commutativity and explore the subject of subgroups forming free products in Thompson's group V. We expand Brin's terminology for a revealing pair to an any tree pair. We use it to analyse the dynamical behaviour of an arbitrary tree pair which cannot occur in a revealing pair. Hence, we design a series of algorithms generating Brin's revealing pair from any tree pair, by successively eliminating the undesirable structures. To detect patterns and transitioning between tree pairs, we introduce a new combinatorial obje
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Ezzat, Shannon. "Representation Growth of Finitely Generated Torsion-Free Nilpotent Groups: Methods and Examples." Thesis, University of Canterbury. Mathematics and Statistics, 2012. http://hdl.handle.net/10092/7235.

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This thesis concerns representation growth of finitely generated torsion-free nilpotent groups. This involves counting equivalence classes of irreducible representations and embedding this counting into a zeta function. We call this the representation zeta function. We use a new, constructive method to calculate the representation zeta functions of two families of groups, namely the Heisenberg group over rings of quadratic integers and the maximal class groups. The advantage of this method is that it is able to be used to calculate the p-local representation zeta function for all primes p. The
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Mathews, Chad Ullery William D. "Mixed groups with decomposition bases and global k-groups." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Summer/Theses/MATHEWS_CHAD_59.pdf.

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Martos, Prieto Ruben. "The Baum-Connes conjecture for Quantum Groups : stability properties and K-theory computations." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC198/document.

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Cette thèse porte sur la conjecture de Baum-Connes pour les groupes quantiques. Le but principal de ce travail est l'étude de la stabilité de la conjecture de Baum-Connes par certaines constructions de groupes quantiques discrets.Dans un premier temps, nous réalisons une étude détaillé et approfondie de la reformulation catégorielle de la conjecture de Baum-Connes d'après les travaux de R. Meyer et R. Nest. Ensuite, nous appliquons ces techniques au cas concret des groupes quantiques discrets sans torsion.Nous réalisons une étude exhaustive des produits croisés afin de pouvoir les manipuler ai
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楊蕙芝. "Finite rank torsion free abelian group." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/68494763600973477471.

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Chen, Yung-Chain, and 陳永清. "On Hom Of Finite Rank Torsion Free Abelian Group." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/87646784711705670555.

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碩士<br>淡江大學<br>數學系<br>81<br>We wanted to understand the structure of finite rankorsion free abelian group. But in fact, there are only few restricted torsion free abelian groups that resulted in good conclusion. In this paper, we describe about hom of finite rank torsion free abelian groups and classify them by types. In generally, the type of group desides the part of structure of it. This paper has two parts. The first part contains 3 lemmas, 4 theorems and 2 corollaries, the important res
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Then, Tsai Mei, and 蔡美珍. "On tonsor product of finite rank torsion free abelian group." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/20414803127362939112.

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碩士<br>淡江大學<br>數學系<br>81<br>Suppose that R is a ring,A is a right R-module and B is a left R-module then $A\otimes_Z B$ is define to be F/N where F is the free abelian group with elements of $A \otimes_Z B$ as a basie. If anabelian group has all its elements of finite order,we shall call it a torsion group. The other extreme case is that where all the elements have infinite order,we then call the group torsion free.Define rank(A)=$dim_Q (Q\otimes_Z A)$;p-rank( A)=$dim_Q(A/pA)$ and $Z_p={m/n
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Friedenberg, Stefan [Verfasser]. "Torsion free extensions of torsion free abelian groups of finite rank / von Stefan Friedenberg." 2009. http://d-nb.info/1001679725/34.

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Books on the topic "Torsion-free group"

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Chen, Zhen-Qing, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, and Tianyi Zheng. Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43332-0.

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Direct Sum Decompositions of Torsion-Free Finite Rank Groups (Pure and Applied Mathematics). Chapman & Hall/CRC, 2007.

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Farb, Benson, and Dan Margalit. The Symplectic Representation and the Torelli Group. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0007.

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This chapter discusses the basic properties and applications of a symplectic representation, denoted by Ψ‎, and its kernel, called the Torelli group. After describing the algebraic intersection number as a symplectic form, the chapter presents three different proofs of the surjectivity of Ψ‎, each illustrating a different theme. It also illustrates the usefulness of the symplectic representation by two applications to understanding the algebraic structure of Mod(S). First, the chapter explains how this representation is used by Serre to prove the theorem that Mod(Sɡ) has a torsion-free subgrou
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Arnold, D. M. Finite Rank Torsion Free Abelian Groups and Rings. Springer London, Limited, 2006.

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Faticoni, Theodore G. Direct Sum Decompositions of Torsion-Free Finite Rank Groups. Taylor & Francis Group, 2010.

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Faticoni, Theodore G. Direct Sum Decompositions of Torsion-Free Finite Rank Groups. Taylor & Francis Group, 2007.

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Faticoni, Theodore G. Direct Sum Decompositions of Torsion-Free Finite Rank Groups. Taylor & Francis Group, 2007.

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Faticoni, Theodore G. Direct Sum Decompositions of Torsion-Free Finite Rank Groups. Taylor & Francis Group, 2019.

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Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups. Springer, 2023.

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Book chapters on the topic "Torsion-free group"

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Călugăreanu, Grigore, Simion Breaz, Ciprian Modoi, Cosmin Pelea, and Dumitru Vălcan. "Torsion-free groups." In Exercises in Abelian Group Theory. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0339-0_18.

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Călugăreanu, Grigore, Simion Breaz, Ciprian Modoi, Cosmin Pelea, and Dumitru Vălcan. "Torsion-free groups." In Exercises in Abelian Group Theory. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0339-0_8.

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Chen, Zhen-Qing, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, and Tianyi Zheng. "Adapted Approximate Group Dilations." In Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43332-0_9.

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Chen, Zhen-Qing, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, and Tianyi Zheng. "Vague Convergence and Change of Group Law." In Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43332-0_4.

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Fuchs, László. "Torsion-Free Groups." In Springer Monographs in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19422-6_12.

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Arnold, David M. "Torsion-Free Abelian Groups." In Abelian Groups and Representations of Finite Partially Ordered Sets. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8750-1_2.

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May, Warren. "Endomorphisms of Valuated Torsion-free Modules." In Abelian Groups. CRC Press, 2022. http://dx.doi.org/10.1201/9781003071761-19.

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Hill, Paul, and Charles Megibben. "Equivalence Theorems for Torsion-free Groups." In Abelian Groups. CRC Press, 2022. http://dx.doi.org/10.1201/9781003071761-17.

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Fuchs, László. "Torsion-Free Groups of Infinite Rank." In Springer Monographs in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19422-6_13.

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Melnikov, Alexander G. "Enumerations and Torsion Free Abelian Groups." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73001-9_59.

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Conference papers on the topic "Torsion-free group"

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Ting, Tan Yee, Nor'ashiqin Mohd Idrus, Rohaidah Masri, Nor Haniza Sarmin, and Hazzirah Izzati Mat Hassim. "Homological functor of a torsion free crystallographic group of dimension five with a nonabelian point group." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882560.

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Mohammad, Siti Afiqah, Nor Haniza Sarmin, and Hazzirah Izzati Mat Hassim. "The central subgroup of the nonabelian tensor square of a torsion free space group." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954593.

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Blagoveshchenskaya, E. A., V. V. Garbaruk, I. V. Kuznetsova, et al. "Common Features of Algorithmic Approaches to Sub-word Parallelism and Torsion-free Abelian Group Decompositions." In 2019 IEEE International Conference on Electrical Engineering and Photonics (EExPolytech). IEEE, 2019. http://dx.doi.org/10.1109/eexpolytech.2019.8906863.

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Fenn, Roger, and Colin Rourke. "Characterisation of a class of equations with solutions over torsion-free groups." In Conference in honour of David Epstein's 60th birthday. Mathematical Sciences Publishers, 1998. http://dx.doi.org/10.2140/gtm.1998.1.159.

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Zyman, Marcos. "Localization and I A-automorphisms of finitely generated, metabelian, and torsion-free nilpotent groups." In A Festschrift in Honor of Anthony Gaglione. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793416_0016.

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He, Hui, Mohamad Metghalchi, and James C. Keck. "Estimation of the Thermodynamic Properties for Branched Hydrocarbons." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0833.

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Abstract A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modific
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Din, Naveed A., and S. Olutunde Oyadiji. "Modal Characteristics of Swept Cantilevered Plates." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58560.

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The aim of this paper is to produce modal data which can be used to synthesise assumed shapes for use in Rayleigh-Ritz approximations of the free vibrations of cantilevered swept plates. The modal data is generated via the use of the FEA technique to predict the natural frequencies and mode shapes of aluminium alloy plates of aspect ratio 2.0 and of swept angles varying from 0° to 20° in steps of 2°. The first fifty natural frequencies and mode shapes of swept cantilevered plates were calculated using ABAQUS FE programme which includes the ABAQUS/CAE pre-and post-processor. To classify each mo
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