Transverse Vibration of Free-free Bars of Uniform cross Section Taking into Account the Effect of shear

Abstract

It is well known that in studying the natural frequencies of flexural vibration of ships, especially in the higher modes of vibration, the effect of shear deflection of a ship on the natural frequency should be considered. This effect will be of considerable importance in the study of the higher modes of vibration when the hull girder is subdivided by nodal sections into comparatively short portions. The object of this paper is to investigate the nature of the effect of shear deflection on the natural frequency, for brevity, in the case of a free-free bar of uniform cross section. The approximate solution of the equation of motion of a vibrating bar, in which the correction for shear was introduced, was obtained by the use of the Galerkin's method. The frequency equation obtained in this manner is represented in the form of simultaneous equation, the solution of which can be obtained with sufficient accuracy by much less labour in comparison with the case when the natural frequency is obtained from the frequency equation which is derived from the exact solution of the fundamental equation.