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.

翻译：在本文中,基于Timoshenko 光束理论的等离子测量法,为调查波束的自由振动行为,设计了有限的自由形式光束元素。定义波束几何的不统一理性B-波纹(NURBS)功能,用作限定光束分析的基础功能。为了丰富基础功能,提高解决方案域的精确度,采用了h-、p-和k-再精化技术。波束的几何和曲度以NURBS为基础,以独特的方式建模。当前等离子变形和旋转惯性的所有效果都被纳入到目前的等离子测量模型中。将非维频率的波束结果与其他现有结果进行比较,以显示当前等离子测量方法的精确度和效率。从数字结果看,目前的元素可以产生非常精确的自然频率值和精确的几何度定型模型。在更高的顺序基础功能下,剪裁的所有效果和旋转惯性都由目前的等数模型模型来考虑。在将来的光度模型测试中,没有将Shear-lememimal 测试的解决方案作为最后的参照点进行。