Vibration of thin pre-twisted helical beams

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

9 Scopus Citations
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Author(s)

  • A. Y T Leung

Detail(s)

Original languageEnglish
Pages (from-to)1177-1195
Journal / PublicationInternational Journal of Solids and Structures
Volume47
Issue number9
Publication statusPublished - 1 May 2010

Abstract

A helical beam has non-zero curvature and tortuosity. When there is a pre-twist, the Frenet triad is not necessary coincident with the principal triad. When an initially straight rod undergoing a large deformation, it will be curved and twisted during each deformation sequence. The purpose of the paper is to establish the governing equations and the associated natural boundary conditions for a pre-twisted helical beam by variational principles and differential geometry. Although circular helix is taken as example, the formulation is valid for inhomogeneous and non-uniform parameters along the centerline that variable curvature and tortuosity can be treated without difficulties. The method can be used to treat helical anisotropy. If the pre-twist rate of a ring is 0.5, we show a thick Möbius ring for the first time. The solution of the natural vibration problem is through Chebyshev discretization and Clenshaw-Curtis integration by means of the Galerkin formulation. © 2010 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Chebyshev discretization, Clenshaw-Curtis integration, Helical beam, Natural vibration, Pre-twist, Thick Möbius ring

Citation Format(s)

Vibration of thin pre-twisted helical beams. / Leung, A. Y T.
In: International Journal of Solids and Structures, Vol. 47, No. 9, 01.05.2010, p. 1177-1195.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review