Vibration of thin pre-twisted helical beams

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