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IMA Journal of Numerical Analysis Advance Access originally published online on March 14, 2008
IMA Journal of Numerical Analysis 2009 29(1):180-207; doi:10.1093/imanum/drn002
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Approximation of the vibration modes of a Timoshenko curved rod of arbitrary geometry

Erwin Hernández{dagger} and Enrique Otárola{ddagger}

Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile

Rodolfo Rodríguez§ and Frank Sanhueza

GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

{dagger} Email: erwin.hernandez{at}usm.cl

{ddagger} Email: enrique.otarola{at}usm.cl

§ Corresponding author. Email: rodolfo{at}ing-mat.udec.cl

Email: fsanhuez{at}ing-mat.udec.cl

Received on 4 September 2007. Revised on 28 December 2007.


  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.

Key Words: Timoshenko curved rods; finite-element method; vibration problem


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