FREE VIBRATION ANALYSIS WITH BEAM MODELS WHICH INCLUDE BENDING WARPING, TORSION WARPING AND ANTICLASTIC BENDING EFFECTS

Vibration models for straight, constant cross-section, non-rotating cantilever beams are considered with particular regard for those models which include shear deformation and rotary inertia. A review of existing models and articles bearing on improvements to these models is given. Three new models are introduced: (1) a combined bending and torsion model for beams of arbitrary cross-section which includes torsion warping effects; (2) a symmetric bending model which includes bending warping effects; and, (3) a symmetric bending model which includes bending warping and anticlastic bending effects.;Th symmetric bending model with bending warping effects is shown to perform very comparably with other models--but without the use of a shear coefficient. Particularly good results are shown for short beams.;The symmetric bending model including anticlastic effects is shown to be of limited use since the full stiffness and inertia of bending perpendicular to the axis of the beam (chordwise bending) is not included in the model. The method to correct this limitation is discussed. {155 references}.;The combined bending and torsion model is used to predict natural frequencies for rectangular and curtate circular sector (annular sector) cross-section beams. The shear coefficient is calculated using Cowper's method and all other characteristic properties of the cross-section are exact, that is based on elasticity theory. Improved results are shown over other beam models for the thin curtate sector cross-section which is actually a thin, shallow shell.