The lateral vibration of slightly bent slender beams subject to prescribed axial end displacement

Abstract

A simple analysis is presented for the prediction of the induced axial loads in initially slightly bent slender beams subject to prescribed axial end displacement. The effect upon the natural frequencies of flexural vibration of the beams is then determined. A simply supported beam and a fully clamped beam are considered and it is assumed that the initial deflection is of the same form as the first critical buckling mode for the straight beam. It is shown that the effect of relatively slight initial lack of straightness upon the induced axial load and bending natural frequencies is very significant. A practical application of the analysis would be in the prediction of the natural frequencies of vibration of heat exchanger tubing where the prescribed axial displacement takes the form of restrained thermal expansion and the results of a simple experiment concerning such are included.