Three dimensional frequency analysis of bidirectional functionally graded thick cylindrical shells using a radial point interpolation method (RPIM)

This paper considers a functionally graded (FG) shell using a meshless radial point interpolation method (RPIM). The material is assumed to be bidirectional FG, where the variation is present in both the radial and the axial directions. Based on the three-dimensional equations of motion, the frequency equations are stated using RPIM. Numerical results are presented for a thick shell for various boundary conditions. These results illustrate the influence from the material variation concerning eigenfrequencies and eigenmodes. In addition, the study shows that the RPIM is an efficient method to solve dynamical shell problems.

► Frequency equations are obtained for a bidirectional functionally graded shell.
► Three-dimensional theory is adopted for 4 different boundary conditions.
► A meshless radial point interpolation method (RPIM) is used for this dynamical problem.
► The effects from the variation in different directions are illustrated considering eigenfrequencies and mode shapes.