Free Vibration and Buckling of a Rotating Beam With an Elastically Restrained Root and End Mass

• Main Authors: Sheng-Yung Hu, 胡聖揚
• Other Authors: Kuo-Mo Hsiao
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/21364599520337101493

碩士 === 國立交通大學 === 機械工程系 === 87 === The objective of this paper is to investigate the effects of stiffness of elastically restrained root, tip mass on the natural frequency of vibration of rotating beam, and investigate the critical rotation speed for buckling of rotating off-axis beam. Here, Euler beam and Timoshenko beam are considered. The governing equations for linear vibration of rotating Euler beam and Timoshenko beam are derived by the d*Alembert principle and the virtual work principle. The effect of Coriolis force and rotary inertia on the natural frequency of the rotating beam is investigated. In order to capture all inertia effect and coupling between extensional and flexural deformation, the consistent linearization of the fully geometrically non-linear beam theory is used. A method based on the power series solution is proposed to solve the natural frequency. The rotating beam is divided into serveral segments. The governing equations of each segment are solved by a power series. From the conditions of the rotating beam at two end nodes and common node between two adjacent segments the natural frequency can be calculated. Numerical examples are studied for the nature frequency of rotating beam with different angular velocity, setting angle, and slenderness ratio, and for the critical rotation speed for buckling. The effect of Coriolis force and rotary inertia on the natural frequency of the rotating beam is investigated by numerical examples.