Vibrations of Damaged Cantilever Beams Manufactured from Functionally Graded Materials
This paper is concerned with the effect of damage on free and forced vibrations of a functionally graded cantilever beam. The modes of damage considered in the paper include a region with degraded stiffness adjacent to the root of the beam, a single delamination crack, and a single crack at the root cross section of the beam propagating in the thickness direction. Closed-form solutions are suggested for all cases considered, including both forced and free vibrations; in the case of free vibrations, these solutions are exact. The peculiarities of the frequency analysis of nonprismatic and/or axially graded beams with the root crack in the presence of static thermal loads are also discussed and it is shown that neglecting axial inertia may lead to a qualitative error (this conclusion remains valid in prismatic functionally graded material beams). Numerical examples concentrate on the effect of a single root crack on the fundamental frequency, because such damage was observed in numerous loading scenarios. It is shown that the presence of a crack that has propagated through about one-third of the thickness of the beam significantly affects the fundamental frequency.
L. W. Byrd and V. Birman, "Vibrations of Damaged Cantilever Beams Manufactured from Functionally Graded Materials," AIAA Journal, American Institute of Aeronautics and Astronautics (AIAA), Jan 2007.
The definitive version is available at https://doi.org/10.2514/1.30076
Mechanical and Aerospace Engineering
Keywords and Phrases
Cantilever Beam; Damage; Single Delamination Crack
International Standard Serial Number (ISSN)
Article - Journal
© 2007 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.