Accurate assessment of natural frequencies for uniform and non uniform Euler Bernoulli beams and frames by adaptive generalized finite element method
Purpose The purpose of this paper is devoted to present an accurate assessment for determine natural frequencies for uniform and non uniform Euler Bernoulli beams and frames by an adaptive generalized finite element method (GFEM) The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler Bernoulli beams and frames. Design/methodology/approach The variational problem of free vibration is formulated and the main aspects of the adaptive GFEM are presented and discussed. The efficiency and convergence of the proposed method in vibration analysis of uniform and non uniform Euler Bernoulli beams are checked. The application of this technique in a frame is also presented. Findings The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler Bernoulli beams and frames. The GFEM, which was conceived on the basis of the partition of unity method, allows the inclusion of enrichment functions that contain