Resumen de Finite element approximation of the vibration problem for a Timoshenko curved rod

E. Hernández, E. Otárola, R. Rodríguez, F. Sanhueza

• The aim of this paper is to analyze a mixed finite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry. Optimal order error estimates are proved for displacements and rotations of the vibration modes, as well as a double order of convergence for the vibration frequencies. These estimates are essentially independent of the thickness of the rod, which leads to the conclusion that the method is locking free. A numerical test is reported in order to assess the performance of the method.