TY - JOUR
ID - 327
TI - Transverse Vibration for Non-uniform Timoshenko Nano-beams
JO - Mechanics of Advanced Composite Structures
JA - MACS
LA - en
SN - 2423-4826
AU - Torabi, Keivan
AU - Rahi, Majid
AU - Afshari, Hassan
AD - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Y1 - 2015
PY - 2015
VL - 2
IS - 1
SP - 1
EP - 16
KW - Nonlocal elasticity
KW - Gravity
KW - Timoshenko
KW - Non-uniform nano-beam
KW - Generalized differential quadrature method
DO - 10.22075/macs.2015.327
N2 - 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.
UR - https://macs.semnan.ac.ir/article_327.html
L1 - https://macs.semnan.ac.ir/article_327_e19b0feb33c053f63c0ced02b44f9f4c.pdf
ER -