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Department of Mechanics and Theory of Structures, Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
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Department of Mechanics and Theory of Structures, Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
Institute of Applied Mechanics, Graz University of Technology , Graz , Austria
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Department of Mechanics and Theory of Structures, Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
Department of Mechanics and Theory of Structures, Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
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.
This research was partly funded by the Austrian Science Fund (FWF) 10.55776/P36019. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
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