Free Vibration Analysis of a Functionally Graded Nanotube Under an Initial Stress Using Nonlocal Elasticity Theory

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Jafarzadeh Kermani, Mona | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49448 (09)
University: Sharif University of Technology
Department: Civil Engineering
Advisor(s): Eskandari, Morteza
Abstract:
In this study, flexural vibration of a functionally graded nanotube under an initial stress is investigated. The small scale effect is taken into consideration based on Eringen’s nonlocal elasticity theory. The material properties are assumed to vary exponentially along the depth direction. The complete effect of the initial stress is taken into account in the problem formulation. The governing equations of motion are derived by using the Hamilton’s principle on the basis of the nonlocal Timoshenko beam theory. An analytical solution of the governing equations, for free vibration of a simply-supported nanotube is presented. Numerical results are presented to investigate the effect of the length scale parameter, initial stress and gradient index on vibrational response of the FG nanotube
Keywords:
Timoshenko Beams ; Nonlocal Elasticity Theory ; Free Vibration ; Functionally Graded Materials (FGM) ; Initial Stress

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