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Vibrations of Damaged Functionally Graded Cantilever Beams

AIP Conference Proceedings, 2008
The paper discusses closed‐form solutions of the problems of free and forced vibrations of a functionally graded cantilever FGM beam with and without damage. The mode of damage considered in the paper is represented by cracks that are perpendicular to the axis of the beam.
Larry W. Byrd +7 more
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On buckling of axially functionally graded beams

Pollack Periodica, 2012
In his study Aydogdu analyzed the vibration and buckling of axially functionally graded simply supported beams. By using pre-defined frequency and buckling loads he determined the Young’s modulus in axial direction as a function of axial coordinate. In this study it is demonstrated that there is error in his calculation; moreover, corrected computation
Maróti, György, Elishakoff, Isaac
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Functionally graded piezoelectric beam under arbitrary loading

2009 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA 2009), 2009
Analytical solutions for functionally graded beams under arbitrary loading are presented in this paper. The material coefficients vary exponentially along the thickness of the beams. The arbitrary loading is expanded in terms of sinusoidal series. For plane stress problems, the stress function and electric displacement function are assumed to consist ...
null De-jin Huang, null Hao-jiang Ding
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Functionally Graded Beams as Surrogate Structural Models: Shear Beam with Exponentially Graded Rigidity