Dynamic Analysis of Rotating Nonuniform Pretwisted Beams

• Main Authors: Ching Tien Wu, 吳璟典
• Other Authors: Sen Yung Lee
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/76640184129812936018

碩士 === 國立成功大學 === 機械工程學系 === 89 === The governing differential equations for the coupled bending-bending vibration of a rotating beam with a tip mass, arbitrary pretwist, an elastically restrained root, subjected to the external transverse forces in the y and z directions, and rotating at a constant angular velocity, are derived by using Hamilton’s principle. The frequency equation of the system is derived and expressed in terms of the transition matrix of the transformed vector characteristic governing equation. An efficient algorithm for determining the semi-analytical transition matrix of the system is derived. The orthogonality condition for the eigenfunctions of the system with elastic boundary conditions is also derived. Using the method of mode superposition derives the analytical solution of force vibration of rotating pretwisted beam. The influence of the tip mass, the parameters of the rotatory inertia of the tip mass, the rotating speed, the elastically restrained boundary conditions, the geometric parameter of the cross-section of the beam, the setting angle, and the uniform and nonuniform pretwists on the natural frequencies are investigated. The frequency response on the steady response of the beam is also investigated.