The Equations of Motion and Steady State Solution of Three Dimensional Rotating Timoshenko Beam

• Main Authors: Chien-Chih Huang, 黃建志
• Other Authors: Kuo-Mo Hsiao
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/55219132923295777137

碩士 === 國立交通大學 === 機械工程系 === 88 === The objective of this paper is to derive the equations of motion and to solve the steady state axial and torsional deformations for the doubly symmetric three dimensional rotating Timoshenko beam. A co-rotational formulation combined with the rotating frame method is used here. The rotating beam is divided into several beam elements. The kinematics of beam element is defined in terms of rotating element coordinates, which are constructed at the current configuration of the beam element. The equations of motion of the beam element are derived by consistent linearization of the fully geometrically nonlinear beam theory using the d’Alembert principle and the virtual work principle in the current rotating element coordinates. The steady state equilibrium equations of the rotating beam element can be obtained from the equations of motion of the beam element. A Galerkin method is applied to the steady state equilibrium equations and an incremental iterative method based on the Newton-Raphson method is used here for the solution of the nonlinear steady state equilibrium equations. Numerical examples are studied to investigate the effect of rotating speed, setting angle, cross section of the beam and length of the beam on the steady state axial and torsional deformations for the three dimensional rotating Timoshenko beam.