کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
278710 | 1430318 | 2010 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Vibration of thin pre-twisted helical beams Vibration of thin pre-twisted helical beams](/preview/png/278710.png)
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.
Journal: International Journal of Solids and Structures - Volume 47, Issue 9, 1 May 2010, Pages 1177–1195