A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams

被引:168
|
作者
Ebrahimi, Farzad [1 ]
Barati, Mohammad Reza [1 ]
机构
[1] Imam Khomeini Int Univ, Fac Engn, Dept Mech Engn, Qazvin, Iran
关键词
Free vibration; Third-order shear deformation beam theory; Functionally graded nanobeam; Nonlocal elasticity theory; NONLINEAR FORCED VIBRATION; WALLED CARBON NANOTUBES; NEUTRAL AXIS POSITION; ELASTICITY THEORY; FORMULATION; STABILITY;
D O I
10.1007/s13369-015-1930-4
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, free vibration characteristics of functionally graded (FG) nanobeams based on third-order shear deformation beam theory are investigated by presenting a Navier-type solution. Material properties of FG nanobeam are supposed to change continuously along the thickness according to the power-law form. The effect of small scale is considered based on nonlocal elasticity theory of Eringen. Through Hamilton's principle and third-order shear deformation beam theory, the nonlocal governing equations are derived and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results for FG nanobeams as compared to some cases in the literature. The numerical investigations are presented to investigate the effect of the several parameters such as material distribution profile, small-scale effects, slenderness ratio and mode number on vibrational response of the FG nanobeams in detail. It is concluded that various factors such as nonlocal parameter and gradient index play notable roles in vibrational response of FG nanobeams.
引用
收藏
页码:1679 / 1690
页数:12
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