Abstract: “Referring to the previous theoretical and numerical studies on the static/dynamic analyses of elastic helicoidal bars, only circular or square cross-sections were considered up today. The main purpose of this study is to investigate the dynamic behavior of the elastic cylindrical helices having hollow circle and elliptical hollow sections. For this purpose, a mixed finite element formulation with the Timoshenko beam assumptions is employed. Frenet triad is adopted as the local coordinate system in the helix geometry. Isoparametric curved elements involve two nodes, where each node has 12 DOF, namely three translations, three rotations, two shear forces, one axial force, two bending moment and one torque. Numerical solutions are performed to analyze the free vibration behavior of the cylindrical helices and benchmark results are presented. Parametric studies are carried out to investigate the influence of the parameters e.g. section geometry, boundary conditions, density of the material”

Keywords: cylindrical helix, elliptical hollow section, mixed finite element method, free vibration