Natural frequencies of thin-walled curved beams

New equations of motion governing dynamic behavior of thin-walled curved beams were investigated based on the study of Kang and Yoo [Thin-walled curved beams, I: formulation of nonlinear equations, J. Eng. Mech., ASCE 120 (10) (1994) 2072-2101; Thin-walled curved beams, II: analytical solutions for buckling of arches, J. Eng. Mech., ASCE 120 (10) (1994) 2102-2125]. Explicit numerical expressions were derived to predict the complex dynamic behavior of the thin-walled curve beams. Stiffness and mass matrix of the curved beam element for finite element analyses were formulated to allow explicit evaluation of the dynamic behavior. The formulations were conducted using not only typical six degree of freedom but also additional warping degree of freedom at each node. This paper proved the validity and the convergence of the presented formulation using the curved beam element. The paper included comparisons of the natural frequencies of the thin-walled curved beams from the finite element formulations with those from other researchers' study. The presented formulation and the new equations are sufficiently accurate for use in study and evaluation of curved architectural structures and bridges.