Abstract In this paper, in-plane free vibration of a rotating Euler-Bernoulli beam with uniform cross section is studied using a rotation-free isogeometric analysis formulation. Using Hamilton’s principle, the derived equations governing the in-plane bending and axial deformations are coupled by means the Coriolis terms. These two equations are transformed into a one linear gyroscopic eigenvalue problem via a weak formulation. The boundary conditions are enforced by means of Lagrange multipliers. Numerical tests of convergence are conducted and the obtained results are compared to the reference solutions to show the effectiveness and accuracy of the proposed method. Effects on natural frequencies, and mode shapes originated from Coriolis terms, angular speed, slenderness ration, hub radius and boundary conditions are numerically investigated.

中文翻译：

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包括科里奥利效应的离心加劲梁平面内自由振动的等几何分析

摘要 在本文中，使用无旋转等几何分析公式研究了具有均匀截面的旋转欧拉-伯努利梁的平面内自由振动。使用哈密顿原理，导出的控制平面内弯曲和轴向变形的方程通过科里奥利项耦合。这两个方程通过弱公式转化为一个线性陀螺特征值问题。边界条件通过拉格朗日乘子强制执行。对收敛性进行了数值测试，并将所得结果与参考解进行了比较，以证明所提出方法的有效性和准确性。数值研究了对固有频率和源自科里奥利项的振型、角速度、长细比、轮毂半径和边界条件的影响。