Abstract

The aim of this paper is to analyse 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, rotations and shear stresses 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. Numerical tests are reported in order to assess the performance of the method.