Isogeometric Analysis of In-Plane Free Vibrations of a Curved Timoshenko Beam

This paper presents an isogeometric formulation for the linear in-plane free vibration analysis of arbitrarily curved Timoshenko beams. The model is developed using curvilinear coordinates, ensuring a consistent kinematic description and accurate representation of strongly curved geometries. The beam geometry is described exactly using B-spline and NURBS basis functions within the isogeometric analysis framework, while the same functions are employed to approximate the displacement field. A detailed numerical study is conducted to evaluate the convergence characteristics and spectral accuracy of the proposed formulation. The convergence properties are examined through systematic h-, p-, and k-refinements. The obtained results demonstrate good convergence behavior; improved accuracy is achievable with a reduced number of degrees of freedom when higher continuity is employed. The strongly curved beam model yields greater accuracy than the standard simplified approach. The proposed formulation provides a robust and efficient framework for vibration analysis of curved beam structures. It offers a reliable basis for further extensions to more complex structural and dynamic problems.