Free vibration analysis of curved spatial Bernoulli-Euler beam with circular cross section using isogeometric approach

Abstract

In this paper the linear free vibration analysis of an arbitrarily curved spatial Bernoulli – Euler beam with circular cross section using isogeometric approach has been presented. In order to carry out free vibration analysis of the beam, the stiffness and mass matrices have been derived using basic properties of the continuum mechanics and differential geometry. The isogeometric approach is based on the idea that both the geometry and the displacement fields are described using the same basis functions - NURBS (Non – Uniform Rational B – Spline). The validation of the proposed approach has been carried out on the spatial beam with arbitrary shape. Natural frequencies and mode shapes have shown good agreement with the results obtained using software based on classical finite element method.