Keywords: isogeometric collocation method, vibrations, structural analysis, numerical methods, NURBS, Timoshenko beam, boundary conditions, concrete steel composite beams..

The use of steel/concrete composite beams has gained popularity in the last century as a result of its ability to combine the advantages of both steel and concrete. In this paper, a study of the dynamic response of a concrete/steel composite beam using the isogeometric collocation method (IGC) is presented. This method is a pseudo-spectral method that uses NURBS as shape functions instead of polynomial functions. For the implementation of this method, first, the analytical model of a concrete/steel composite beam is presented, and then, the steps of resolution and the methodology are explained. After that, numerical tests cases are conducted for different boundary conditions. The results obtained are compared with those of preceding works.

From numerical results, the IGC can produce very accurate values of natural frequencies and the mode shapes arising from more precise definitions of the geometry. The results also show fast convergence of the isogeometric collocation method; furthermore, the use of the NURBS, instead of polynomials as shape functions, and the use of the isogeometric collocation method instead of the more usually used polynomial functions, helps the collocation method overcome its principal inadequacy: the incapacity to represent with precision the fields of solutions representing complex forms and the limited control of the mesh refinement. In addition, avoiding numerical quadrature using the isogeometric collocation method enables gains in precision and computing cost.

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