Linear vibration of thin-walled beams of equal angle-section

Abstract

The linear coupling of the various possible types of motion of thin-walled beams of anglesection with equal arms is studied theoretically and experimentally. In the theory proposed the displacements are considered as comprising lateral, transverse and torsional motion of the beam as a whole along with deformation of its cross-section. By application of Hamilton's principle the differential equations of motion of the beam are derived. It is shown that in the main the various types of motion are coupled in pairs (e.g., transverse bending couples with symmetric distortion); a frequency-wavelength or dispersion relation is thus obtained for the coupled motion in the form of a simple quadratic equation in non-dimensional terms, suitable for comparison with experimental results. A series of beams were made, one dimension at a time being varied so that the effect of such variations on the natural frequencies could be studied. The experimental results show reasonable agreement with the calculated curves. Within the range of parameters investigated the torsional and lateral motions are very weakly coupled, whereas the coupling between the transverse vibration and the cross-sectional distortion is much more marked and is clearly shown by the experiments.