Vibration Analysis of Timoshenko Beams using Isogeometric Analysis

TL;DR

This paper presents an isogeometric finite element method for analyzing free vibrations of Timoshenko beams, accurately capturing geometry and dynamic behavior with high-order basis functions, and avoiding shear locking in thin beams.

Contribution

The study introduces a novel isogeometric analysis framework for Timoshenko beams that enhances accuracy and efficiency through NURBS-based modeling and refinement techniques.

Findings

Accurate natural frequency and mode shape calculations.

No shear locking in thin beams with higher order basis functions.

Benchmark results for Timoshenko beam vibrations provided.

Abstract

In this paper, the finite free-form beam element is formulated by the isogeometric approach based on the Timoshenko beam theory to investigate the free vibration behavior of the beams. The non-uniform rational B-splines (NURBS) functions which define the geometry of the beam are used as the basis functions for the finite element analysis. In order to enrich the basis functions and to increase the accuracy of the solution fields, the h-, p-, and k-refinement techniques are implemented. The geometry and curvature of the beams are modelled in a unique way based on NURBS. All the effects of the the shear deformation, and the rotary inertia are taken into consideration by the present isogeometric model. Results of the beams for non-dimensional frequencies are compared with other available results in order to show the accuracy and efficiency of the present isogeometric approach. From numerical results, the present element can produce very accurate values of natural frequencies and the mode shapes due to exact definition of the geometry. With higher order basis functions, there is no shear locking phenomenon in very thin beam situations. Finally, the benchmark tests described in this study are provided as future reference solutions for Timoshenko beam vibration problem.