Effect of Porosity on Free Vibration of FG Shallow Shells with Complex Plan Form

This paper presents application of the R-functions method for investigation of free vibrations of shallow shells with an arbitrary plan form. It is assumed that shell is fabricated of functionally graded materials with porosities. Two types of porosity are considered: evenly and unevenly distributed porosities. The volume fractions of metal and ceramic are described by the power law. The first order shear deformation theory is applied to describe mathematical formulation of the problem. Solution of the problem is carried out by the variational Ritz method and the R-functions theory. A very good agreement with available results is shown for FG shell with rectangular plan form. Detailed numerical study for shallow shell with complex plan form is fulfilled to show effectiveness of the proposed approach. In particular effects of porosity coefficient, the power law index, boundary conditions on fundamental frequencies are examined.