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Vibration analysis of rotating functionally graded tapered beams with hollow circular cross-section

机译：空心圆形截面的功能梯度圆锥形旋转梁的振动分析

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摘要

The dynamic modeling and free vibrations of rotating functionally graded (FG) tapered cantilever beams with hollow circular cross-section are studied in this paper. To capture the additional dynamic stiffening terms, the axial shrinkage of the beam caused by the transverse displacement is considered. The dynamic equations of the system governing stretching motion, flapwise bending motion, and chordwise bending motion are derived via employing assumed modes method and Lagrange's equations. Based on the first order approximate coupling (FOAC) dynamic model, natural frequencies and mode shapes of the beam system are calculated by solving eigenvalue problem of the deduced dimensionless vibration equations. Influences of the angular speed, the hub radius, the slenderness ratio, the ratio of hollow radius to the root radius, the taper ratio, and the functional gradient index on natural frequencies are studied. Frequency veering and mode shape interaction are discussed when the bending-stretching mode coupling effect of the beam is considered. (C) 2019 Elsevier Masson SAS. All rights reserved.
机译：研究了空心圆形截面的功能梯度（FG）旋转锥形悬臂梁的动力学建模和自由振动。为了捕获其他动态刚度项，考虑了由横向位移引起的梁的轴向收缩。通过采用假定模态方法和拉格朗日方程，推导了控制伸展运动，襟翼向弯曲运动和弦向弯曲运动的系统动力学方程。基于一阶近似耦合（FOAC）动力学模型，通过求解推导的无量纲振动方程的特征值问题，计算梁系统的固有频率和模态形状。研究了角速度，轮毂半径，细长比，空心半径与齿根半径之比，锥度比和功能梯度指数对固有频率的影响。当考虑梁的弯曲-拉伸模式耦合效应时，讨论了频率转向和模式形状相互作用。 （C）2019 Elsevier Masson SAS。版权所有。

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