ANOTHER 2ND-ORDER BEAM VIBRATION THEORY - EXPLICIT BENDING WARPING FLEXIBILITY AND RESTRAINT

A new symmetric beam bending vibration theory which explicitly includes bending warping is presented. The governing differential equations are of sixth order and the boundary conditions allow enforcement of total fixity of the end of a beam. The motivation for the study was the desire to determine if consideration of bending warping restraint in bending theory is as important as is torsion warping restraint in torsion theory. Natural frequency predictions are given and compared with other theories for constant cross-section, cantilevered "beams" of two types: short, deep rectangular beams; and, short, thin, shallow, circular cylindrical shells. The accuracy of the new theory is comparable with Murty's, Levinson's, Bickford's and Rehfield's theories for beams with rectangular cross-sections. It is also comparable with Cowper's theory for general symmetric cross-sections. © 1990.