Finite element eigenvalue analysis of tapered and twisted Timoshenko beams

The stiffness and mass matrices of a twisted beam element with linearly varying breadth and depth are derived. The angle of twist is assumed to vary linearly along the length of the beam. The effects of shear deformation and rotary inertia are considered in deriving the elemental matrices. The first four natural frequencies and mode shapes are calculated for cantilever beams of various depth and breadth taper ratios at different angles of twist. The results are compared with those available in the literature.

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