Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach

Abstract

Isogeometric analysis (IGA) is based on a concept that uses the same base functions for representing both the model geometry and the solution space. The most common base functions used in the IGA are NURBS (Non-Uniform Rational B-Splines) functions for their capability to analytically represent various geometries. In this paper, the IGA is applied in the free vibration analysis of rotation-free plane curved Bernoulli-Euler beam. The stiffness and mass matrices have been developed using basic concepts of continuum mechanics and the principle of virtual work. Geometry of the undeformed and deformed beam is defined using convective coordinates and cross section basis vectors. Results of the free vibration analysis for beam with arbitrary curvature are compared with the results obtained from the conventional finite element method (FEM) software. The significant advantages of the IGA approach over the FEM are shown and discussed.