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Advances in Nano Research Volume 6, Number 2, June 2018 , pages 113-133 DOI: https://doi.org/10.12989/anr.2018.6.2.113 |
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Modeling the size effect on vibration characteristics of functionally graded piezoelectric nanobeams based on Reddy's shear deformation beam theory |
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Farzad Ebrahimi and Ramin Ebrahimi Fardshad
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| Abstract | ||
| In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail. | ||
| Key Words | ||
| functionally graded piezoelectric nanobeam; free vibration; nonlocal elasticity theory; Reddy beam theory | ||
| Address | ||
| (1) Farzad Ebrahimi: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran; (2) Ramin Ebrahimi Fardshad: Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran. | ||