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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 146505, 29 pages
http://dx.doi.org/10.1155/2011/146505
Research Article

A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam

1Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
2Department of Mechanical Engineering, De Lin Institute of Technology, Tucheng 236, Taiwan

Received 30 March 2011; Accepted 19 May 2011

Academic Editor: Delfim Soares Jr.

Copyright © 2011 Ming Hsu Tsai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A corotational finite element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.