2D vibration analysis of circular arches with constant double symmetric cross-sections using isogeometric approach

This paper introduces an isogeometric analysis for the free vibration of circular curved beams with doubly symmetric constant cross sections. Unlike conventional methods based on finite elements, the proposed approach employs NURBS functions which are capable of exactly defining the geometry of circular curved beams as the basis for the finite element analysis. The shear deformable curved beam theory is utilized to take into account the effects of axis extensibility, shear deformation and rotary inertia. A family of NURBS elements are constructed from h-, p- and k-refinement processes. Computed non-dimensional frequencies are found to be in excellent agreement with other available results in the literature. The convergence properties of isogeometric elements are studied in detail. Furthermore, numerical results are obtained for curved beams to investigate the effects of slenderness ratio and boundary condition on free vibration response. The crossover frequency is performed for curved beams with free-free boundary condition.