Vibration analysis of a double layer microshell utilizing a modified couple stress theory

In this paper, dynamic modeling of a double layer cylindrical functionally graded (FG) microshell is considered. Modeling is based on the first-order shear deformation theory (FSDT), and the equations of motion are derived using the Hamilton's principle. It assumes that functionally graded length scale parameter changes along the thickness. Generalized differential quadrature method (GDQM) is used to discretize the model and solve the problem.  In this research the size effect is investigated using a new modified couple stress theory (MCST) which has been considered for the first time in the present study. The accuracy of the presented model is validated with some cases in the literature. Considering the microshell as double layer and utilizing the MCST in addition to considering the various boundary conditions are the novelty of this study. Furthermore, the effects of length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor on the natural frequency of double layer cylindrical FG microshell are studied.