Eigenfrequency Analysis of Cable Structures With Inclined Cables

William Paulsen; Greg Slayton

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William Paulsen, Greg Slayton. Eigenfrequency Analysis of Cable Structures With Inclined Cables[J]. Applied Mathematics and Mechanics, 2006, 27(1): 35-46.

Citation:

William Paulsen, Greg Slayton. Eigenfrequency Analysis of Cable Structures With Inclined Cables[J]. Applied Mathematics and Mechanics, 2006, 27(1): 35-46.

Citation:

William Paulsen, Greg Slayton. Eigenfrequency Analysis of Cable Structures With Inclined Cables[J]. Applied Mathematics and Mechanics, 2006, 27(1): 35-46.

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Eigenfrequency Analysis of Cable Structures With Inclined Cables

Department of Computer Science and Mathematics, Arkansas State University, Arkansas 72467, USA

Received Date: 2004-11-24
Rev Recd Date: 2005-09-06
Publish Date: 2006-01-15

Abstract

Abstract

The approximate eigenfrequencies for the in_plane vibrations of a cable structure consisting of inclined cables,together with point masses at various points were computed.It was discovered that the classical transfer matrix method was inadequate for this task,and hence the larger exterior matrices to determine the eigenfequency equation were used.Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matries were made.
- eigenfrequency,
- transfer matrice,
- exterior matrice,
- cable structure

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References(11)

References

[1]	Irvine H M.Cable Structures[M].Cambridge:M I T Press,1981.
[2]	Simpson A.Determination of the inplane natural frequencies of multispan transmission lines by a transfer-matrix method[J].Proc IEEE,1966,113(5):870—878.
[3]	Triantafyllou M S.The dynamics of taut inclined cable[J].Quart J Mech Appl Math,1984,37(3):421—440. doi: 10.1093/qjmam/37.3.421
[4]	Abramowitz M,Stegun I.Handbook of Mathematical Functions[M].New York:Dover,1981.
[5]	Bender C M,Orszag S A.Advanced Mathematical Methods for Scientists and Engineers[M].New York:Springer-Verlag,1999.
[6]	Grinfogel L.Dynamics of elastic taut inclined cables[Z]. thesis presented to the Massachusetts Institute of Technoloy,at Cambridge M A,in partial fulfillment of the requirements for the degree of Master of Science,1984.
[7]	Paulsen W H.Eigenfrequencies of the non-collinearly coupled Euler-Bernoulli beam system with dissipative joints[J].Quarterly of Applied Mathematics,1997,55(3):437—457.
[8]	Krantz S G,Paulsen W H.Asymptotic eigenfrequency distributions for the N-beam Euler-Bernoulli coupled beam equation with dissipative joints[J].J Symbolic Computaion,1991,11:369—418. doi: 10.1016/S0747-7171(08)80111-3
[9]	Triantafyllou M S,Grinfogel L.Natural frequencies and modes of inclined cables[J].J Struct Engrg,1986,112(1):139—148. doi: 10.1061/(ASCE)0733-9445(1986)112:1(139)
[10]	Boothby W.An Introduction to Differentiable Manifolds and Riemannian Geometry[M].Orlando,Florida:Academic Press Inc,1986.
[11]	Irvine H M,Caughey T K.The linear theory of free vibrations of a suspended cable[J].Proc R Soc Lond,1974,341:299—315. doi: 10.1098/rspa.1974.0189