Abstract
Analytical natural frequencies and mode shapes are derived for the torsional vibration of pretwisted thin-walled cantilevered I-beams. A multifilament model of a pretwisted thin-walled I-beam undergoing warp deformation and a moderately large twist about the axis of shear centers is used to derive the nonlinear boundary-value equations. Exact torsional vibration solutions are derived from the linear terms of the nonlinear boundary-value equations. The individual and collective effects of warping and pretwist are quantified for the first three modes of torsional vibration of cantilevered I-beams having a wide spectrum of length-to-leg ( L/ b) and leg-to-thickness ( b/ t) ratios.
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