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Open AccessArticle

Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

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School of Mechanical Engineering, University of Adelaide, South Australia 5005, Australia
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Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK
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Author to whom correspondence should be addressed.
Vibration 2019, 2(2), 201-221; https://doi.org/10.3390/vibration2020013
Received: 3 May 2019 / Revised: 3 June 2019 / Accepted: 4 June 2019 / Published: 14 June 2019
A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated. View Full-Text
Keywords: functionally graded; asymmetric oscillations; stability; nonlinear functionally graded; asymmetric oscillations; stability; nonlinear
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Ghayesh, M.H.; Farajpour, A.; Farokhi, H. Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams. Vibration 2019, 2, 201-221.

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