Steady State And Free Vibration Analysis of a Rotating Inclined Beam

• Main Authors: Hong-Ru Yan, 顏宏儒
• Other Authors: Kuo-Mo Hsiao
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/56307143279809733396

碩士 === 國立交通大學 === 機械工程系所 === 97 === 　　The steady state and vibration analysis of rotating inclined Euler beam with constant angular velocity is studied in this paper. Two different setting angles β=0° and 90° are considered. The steady state and free vibration are studied for β=90°. However, only steady state is studied for β=0°. A method based on the power series solution is employed to solve the natural frequency of the rotating inclined Euler beam for β=90°. A similar method based on the power series solution is proposed to solve the steady lateral deformation for β=0°. In this paper the linear equations of motion for a rotating inclined Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically non-linear beam theory in a rotating coordinate system. The effect of rotary inertia on the natural frequency of the rotating inclined beam is considered. 　　Here the rotating beam is divided into several segments. For the case β=90°, the governing equations for the lateral vibration of each segment are solved by a power series with four independent coefficients. Substituting the power series solution of each segment into the corresponding boundary conditions at two end nodes of the rotating beam and the continuity conditions at common node between two adjacent segments, a set of simultaneous linear homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. For the case β=0°, a similar procedure is used to determine the steady lateral deformation. However, a set of simultaneous linear nonhomogeneous equations, which can be solved using Gauss Elimination, are obtained. 　　Numerical examples are studied to verify the accuracy of the proposed method and to investigate the effects of inclined angle on the steady lateral deformation (β=0°) and the natural frequency (β=90°) of rotating Euler beams with different angular velocity, radius of the hub, and slenderness ratio of the beam.