Vibration of thin pre-twisted helical beams
Author(s)
Date Issued
2010
Publisher
Elsevier
Journal
International Journal of Solids and Structures
Volume
47
Issue
9
Start page
1177
End page
1195
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.
SFU Affiliated Publication
No
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