Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
HERNANDEZ, E.; OTAROLA, E.; RODRIGUEZ, R. y SANHUEZA, F.. Finite element approximation of the vibration problem for a Timoshenko curved rod. Rev. Unión Mat. Argent. [online]. 2008, vol.49, n.1, pp. 15-28. ISSN 1669-9637.
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.
Palabras clave : Timoshenko curved rods; finite element method; vibration problem.