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Advances in Nano Research Volume 6, Number 3, September 2018 , pages 257-278 DOI: https://doi.org/10.12989/anr.2018.6.3.257 |
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Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter |
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Metin Aydogdu, Mustafa Arda and Seckin Filiz
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Abstract | ||
Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading. | ||
Key Words | ||
vibration; axially functionally graded; nanorod; nanobeam; nonlocal elasticity | ||
Address | ||
(1) Metin Aydogdu, Mustafa Arda: Department of Mechanical Engineering, Trakya University, 22130 Edirne, Turkey; (2) Seckin Filiz: Corlu Vocational School, Namik Kemal University, 59860 Tekirdag, Turkey. | ||