Static deflection and free vibration analysis of functionally graded and porous cylindrical micro/nano shells based on the three-dimensional elasticity and modified couple stress theories

Abstract

In this work, for the first time, bending and free vibration of porous and functionally graded cylindrical micro/nano shells are studied based on the modified couple stress and three dimensional elasticity theories. The well-known power law and even type function are respectively used to consider the variation of functionally graded material properties and porosity distribution. The governing equations are extracted using the Hamilton’s principle. The generalized differential quadrature method is applied to solve the governing equations of cylindrical micro/nano shells with simply supported boundary conditions. In the numerical result section, the influence of gradient of material properties, porosity volume fraction, and length scale parameter on the bending and free vibration of micro/nano shells are studied. The results of present article can be used as a benchmark for validating future mechanical studies of micro/nano shells.

Keywords:

• FG porous cylindrical shell
• modified couple stress theory
• three-dimensional elasticity
• free vibration
• bending
• GDQ