Free vibrations of curved box girders

The problem of coupled free vibrations of curved thin-walled girders of non-deformable asymmetric cross-section is examined in this paper. The general governing differential equations are derived for quadruple coupling between the two flexural, tangential and torsional vibrations. An approximate solution for the case of triple coupling between the two flexural and the torsional vibrations is given for a simply supported girder, uniform specific gravity of the material of the box being assumed. Section warping is considered but axial forces, rotary inertia and structural damping are neglected. A parametric study is conducted to investigate the effect of relevant parameters on natural frequencies. Eigenfunctions satisfying the orthogonality condition are given. The solution derived herein for the general case is also shown to cover a variety of special cases of straight and curved girders with doubly symmetric or singly symmetric cross-sections.