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http://dx.doi.org/10.12989/sem.2017.61.6.721

Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory  

Ebrahimi, Farzad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University)
Barati, Mohammad Reza (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University)
Publication Information
Structural Engineering and Mechanics / v.61, no.6, 2017 , pp. 721-736 More about this Journal
Abstract
In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.
Keywords
free vibration; third order shear deformation beam theory; functionally graded nanobeam; nonlocal elasticity theory;
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Times Cited By KSCI : 2  (Citation Analysis)
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