Analysis of coupled vibrational behavior for naturally curved and twisted beams

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Journal of Vibration and Shock ›› 2009, Vol. 28 ›› Issue (8) : 175-179.

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Analysis of coupled vibrational behavior for naturally curved and twisted beams

Yu Aimin Yang Changjin Hao Ying

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Abstract

Coupled vibrational behavior for spatial curved beams with general cross-sectional shapes, based on naturally curved and twisted beam theory, is theoretically investigated. In the governing equations of motion of the beams, all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia, transverse shear deformations and torsion-related warping are included in the present formulations. The explicit analytical expressions which give the vibrating mode shapes of the beams are derived by rigorous application of the computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. In order to demonstrate the validity of the present theory, the natural frequencies and vibration modes of a curved beam of elliptic cross section with clamped-clamped boundary condition are evaluated and compared with the FE-results using PATRAN’s beam elements.

Key words

naturally curved and twisted beam / generalized warping coordinate / coupled vibration / natural frequency / mode shape

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Yu Aimin Yang Changjin Hao Ying . Analysis of coupled vibrational behavior for naturally curved and twisted beams [J]. Journal of Vibration and Shock, 2009, 28(8): 175-179