Finite strain nonlinear longitudinal vibration of nanorods

Mehmet Eren , Metin Aydogdu

Abstract

The nonlinear free vibration of a nanorod subjected to finite strain is investigated. The governing equation of motion in material configuration in terms of displacement is determined. By means of Galerkin method, the Fourier series solutions satisfying some typical boundary conditions are determined. The amplitude-frequency relationship and interaction between the modes are studied. The effects of nonlocal elasticity are shown for different length of nanotubes and nonlocal parameter. The results show that nonlocal effects lead to additional internal modal interaction for nanorod vibrations.

Key Words

nonlocal elasticity; mode interactions; nonlocal elastic rod model; nonlinear axial vibration; finite strain

Address

(1) Mehmet Eren — Institute of Science, Trakya University, 22030 Edirne, Turkey
(2) Metin Aydogdu — Department of Mechanical Engineering, Trakya University, 22030 Edirne, Turkey.

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