Static Displacement and Coupled Frequencies of a Twisted Bar

Abstract

T ELASTIC BODY CONSIDERED is a straight bar with constant rectangular cross section and an initial structural twist of 6 (constant) radians per unit of length. The object of the paper is twofold: (1) to calculate the static displacement components u(z) and v{z) in the direction of the principal axes u and v at each section due to the uniform loads wu and wv also in the direction of the principal axes; (2) to approximate by the energy method, using the displacement functions mentioned in (1), the first two natural frequencies of the bar. The method used is applicable to any end conditions but only the fixed-free case is considered. In the case of a fixed-free bar without twist the two fundamental frequencies corresponding to vibrations normal and parallel to the minor principal axis v are given by the formulas