TY - JOUR
ID - 539691
TI - A Nonlocal First Order Shear Deformation Theory for Vibration Analysis of Size Dependent Functionally Graded Nano beam with Attached Tip Mass: an Exact Solution
JO - Journal of Solid Mechanics
JA - JSM
LA - en
SN - 2008-3505
AU - Ghadiri, M
AU - Jafari, A
AD - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Y1 - 2018
PY - 2018
VL - 10
IS - 1
SP - 23
EP - 37
KW - Timoshenko Beam Theory
KW - Free vibration
KW - Functionally graded Nano beam
KW - Nonlocal elasticity theory
KW - Tip mass
DO -
N2 - In this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory in order to consider the effect of shear deformation and rotary inertia. Hamiltonâ€™s principle is applied to obtain the governing differential equation of motion and boundary conditions and they are solved applying analytical solution. The purpose is to study the effects of parameters such as tip mass, small scale, beam thickness, power-law exponent and slenderness on the natural frequencies of FG cantilever nano beam with a point mass at the free end. It is explicitly shown that the vibration behavior of a FG Nano beam is significantly influenced by these effects. The response of Timoshenko Nano beams obtained using an exact solution in a special case is compared with those obtained in the literature and is found to be in good agreement. Numerical results are presented to serve as benchmarks for future analyses of FGM cantilever Nano beams with tip mass.
UR - http://jsm.iau-arak.ac.ir/article_539691.html
L1 - http://jsm.iau-arak.ac.ir/article_539691_977b620996b5f81f455edb5c3f0c474b.pdf
ER -