A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam. (21st June 2011)

• Record Type: Journal Article
• Authors: Tsai, Ming Hsu; Lin, Wen Yi; Zhou, Yu Chun; Hsiao, Kuo Mo
• Other Names: Soares Delfim Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2011(2011)
• Publication Date: 2011-06-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2011/146505
• Languages: English
• ISSNs: 1024-123X

Abstract

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.