Isogeometric vibration analysis of free-form Timoshenko curved beams
Isogeometric vibration analysis of free-form Timoshenko curved beams
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DOI：
10.1007/s11012-014-0062-3
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发表时间：
2015
期刊：
影响因子：
2.7
通讯作者：
A. Luu;Nam-Il Kim;Jaehong Lee
中科院分区：
文献类型：
--
作者：
A. Luu;Nam-Il Kim;Jaehong Lee
本文基于Roshenko曲梁理论，采用等几何法建立了有限自由曲梁单元，用于研究任意曲率曲梁的自由振动特性。非均匀有理B样条（NURBS）函数定义的几何形状的曲梁被用作有限元分析的基函数。为了丰富基函数和提高解的精度，我们采用了h-、p-和k-加密技术。自由曲面梁的几何形状和曲率以一种独特的方式基于NURBS建模。消除了常曲率曲梁与变曲率曲梁自由振动分析之间的差距。该等几何模型考虑了轴向伸长、剪切变形和转动惯量的影响。抛物线和椭圆曲线梁的无量纲频率的结果与其他可用的结果进行了比较，以显示本等几何方法的精度和效率。此外，还对椭圆厚圆环的自由振动进行了分析。特别地，以奇恩豪森三次曲梁为例，研究其动力学行为。
In this paper, the finite free-form curved beam element is formulated by the isogeometric approach based on the Timoshenko Rcurved beam theory to investigate the free vibration behavior of the curved beams with arbitrary curvature. The non-uniform rational B-splines (NURBS) functions which define the geometry of the curved 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, theh-,p-, andk-refinement techniques are implemented. The geometry and curvature of free-form curved beams are modelled in a unique way based on NURBS. The gap between the free vibration analysis of the curved beams with constant curvature and those with variable curvature is eliminated. All the effects of the axis extensibility, the shear deformation, and the rotary inertia are taken into consideration by the present isogeometric model. Results of the parabolic and elliptic curved beams for non-dimensional frequencies are compared with other available results in order to show the accuracy and efficiency of the present isogeometric approach. Furthermore, the free vibration analysis of the elliptic thick rings is presented. Particularly, the Tschirnhausen’s cubic curved beam is considered to study the dynamic behavior as an example of free-form curved beams.