A Projection Approach to Analysis of Natural Vibrations for Beams with Non-symmetric Cross Sections

Abstract

A projection approach based on the method of integro-differential relations and semi-discretization technique is applied to analyze natural variations of rectilinear elastic beams with non-symmetric cross sections. A numerical algorithm is proposed to compose compatible approximating systems of ordinary differential equations. It is shown that the beam vibrations cannot be separated into four independent types of longitudinal, bending, and torsional motions if a non-symmetric cross section is considered. In this case, all these motions can interact with one another. Nevertheless, only one type of displacement and stress fields makes the largest contribution in the amplitudes of the corresponding vibrations. Several eigenfrequencies and eigenforms of a beam with the isosceles cross section are presented and analyzed.