Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity

This paper studies the free vibrational behavior of porous functionally graded nanoshells using nonlocal strain gradient theory. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoshells. Porosities are evenly and unevenly distributed thorough the thickness of the nanoshell. The gradation of material properties having porosities is described using a modified power-law function. The nanoshell is modeled via first-order shear deformation theory, and Galerkin's method is implemented to obtain vibration frequencies. Shape functions which satisfy available classical and nonclassical boundary conditions in nonlocal strain gradient theory are proposed. It is shown that the vibrational behavior of the nanoshell is influenced by the porosity volume fraction, porosity distribution, nonlocal coefficient, strain gradient coefficient, boundary conditions and radius-to-thickness ratio.