%0 Journal Article
%T Transverse Vibration for Non-uniform Timoshenko Nano-beams
%J Mechanics of Advanced Composite Structures
%I Semnan University Press
%Z 2423-4826
%A Torabi, Keivan
%A Rahi, Majid
%A Afshari, Hassan
%D 2015
%\ 04/01/2015
%V 2
%N 1
%P 1-16
%! Transverse Vibration for Non-uniform Timoshenko Nano-beams
%K Nonlocal elasticity
%K Gravity
%K Timoshenko
%K Non-uniform nano-beam
%K Generalized differential quadrature method
%R 10.22075/macs.2015.327
%X In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of non-uniform Timoshenko nano-beam for pinned-pinned, clamped–clamped, clamped–pinned, clamped–free, clamped–slide, and pinned-slide boundary conditions. The non-dimensional natural frequencies and the normalized mode shapes are obtained for short and stubby nano-beams where influences varying cross-section area, small scale, shear deformation, rotational moment of inertia, acceleration gravity and the self-weight of the non-uniform Timoshenko nano-beam are discussed. The present study illus-trates that the small scale effects are more significant for smaller size of nano-beam, larger nonlocal parameter and higher vibration modes. Further, the compression forces due to gravity and the self-weight of the nano-beam also like the small scale effect are reduced the magnitude of the fre-quencies of the nano-beam.
%U https://macs.semnan.ac.ir/article_327_e19b0feb33c053f63c0ced02b44f9f4c.pdf