Vibrations of Timoshenko beams with isogeometric approach

Abstract

A study on the free vibration analysis of Timoshenko beams is presented here. In order to determine natural frequencies of beams, a thick beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation and rotatory inertia effect. Three refinement schemes such as h-, p- and k-refinement are used in the analysis and the identification of shear locking is also conducted by using numerical examples. 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.