Influence of Cross-Section Distortion on the Bending Vibration of Thin-Walled Beams of H Section

Abstract

Approximate differential equations describing the bending vibration of beams of thin-walled H section, in which the distortion of the cross-section in its own plane is taken into account, are derived from Hamilton's principle using an assumed form for the cross-section deformation. Only the simplest of the cross-sectional deformation configurations which will couple with ordinary bending is considered. The variation with wavelength of the two spectra of frequencies which result from this coupling of the bending and cross-sectional motions is shown for several section geometries. Theoretical curves show reasonable agreement with experimental results from free beams.