Title of article :
Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory
Author/Authors :
Salamat-talab، نويسنده , , M. and Nateghi، نويسنده , , A. Asgar Torabi، نويسنده , , J.، نويسنده ,
Issue Information :
ماهنامه با شماره پیاپی سال 2012
Abstract :
In this paper, Modified couple stress theory is developed for third-order shear deformation functionally graded (FG) micro beam. Classical Continuum theories are not able to capture size effects while higher order continuum theories consider material length scale parameters to improve the results in micro scales by interpreting size dependencies. By applying Hamilton’s principle, governing equations, boundary and initial conditions are derived for a FG micro beam. It is assumed that properties of the FG micro beam follow a power law form through thickness. In addition, Poisson’s ratio is assumed constant in the current model. Bending and free vibration of the simply supported FG micro beam is analyzed to illustrate size effects. It is observed that if the thickness of the beam is in the order of the material length scale parameter, size effects are more considerable. It is shown that size dependencies of FG micro beams are quite different from isotropic homogeneous beams as they have maximum and minimum size effects for certain values of power index of material distribution and Poisson’s ratio. Moreover, it is shown that the results obtained by the present model deviates significantly from those in which Poissonʹs effect is neglected. Also, the effect of Poisson’s ratio on the deflection and natural frequency based on modified couple stress theory is proven to be different from Classical one. The numerical results for simply supported thin beams show that the first natural frequency estimated by the current model is higher than the classical one. In addition, it is observed that size effect is more significant for higher vibration modes.
Keywords :
FG micro beam , Higher-order shear deformation beam theory , Size dependency , Higher order continuum theory , Modified couple stress theory
Journal title :
International Journal of Mechanical Sciences
Journal title :
International Journal of Mechanical Sciences