A Mohammadi - Faculty of Engineering, Department of Mechanics, Islamic Azad University of South Tehran Branch, Tehran, Iran
H Lashini - Faculty of Mechanic and Manufacturing, University Putra Malaysia, Serdang, Malaysia
M Habibi - Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
H Safarpour - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran

In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelastic medium. For the first time, in the present study, has been considered, FG length scale parameter in double walled cylindrical FG microshells, which this parameter changes along the thickness direction. Taking into consideration the first-order shear deformation theory (FSDT), double walled cylindrical FG microshell is modeled and its equations of motions are derived using Hamilton s principle. The novelty of this study is considering the effects of double layers and MCST, in addition to considering the various boundary conditions of double walled cylindrical FG microshell. Generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motions and boundary conditions. Also, for confirmation, the result of current model is validated with the results obtained from molecular dynamics (MD) simulation. Considering length scale parameter (l=R/3) on MCST show, the results have better agreement with MD simulation. The results show that, length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor have important role on the natural frequency of double walled cylindrical FG microshell.

Double walled, Functionally graded material, Modified couple stress theory, Vibration analysis, Viscoelastic foundation