Dynamic behavior of braced thin-walled beams

Abstract

The present paper considers the dynamic behavior of beams with open thin-walled cross-sections along their length with bracings (connecting beams and truss). The effect of the constrained torsion warping, rotary inertia, and flexural-torsion coupling due to nonsymmetric cross-sections is included. In the case of simply supported beams, closed-form solutions for determining coupled natural frequencies and corresponding mode shapes are newly derived. The frequency equation, given in a determinantal form, is expanded in an explicit analytical form and then solved using the Mathcad 2001 Professional symbolic computing package. Some illustrative examples on the application of the present theory are given for coupled bending-torsion vibrations of braced thin-walled beams. As compared with FEM, numerical results demonstrate the accuracy and effectiveness of the proposed method