Isogeometric vibration analysis of multi-directional functionally gradient circular, elliptical and sector plates with variable thickness

Abstract

This study aims to investigate the free vibration of multi-directional functionally gradient (multi-directional FG) circular, elliptical and sector plates with variable thickness. A numerical analysis procedure based on the isogeometric analysis (IGA) and high-order shear deformation theory (HSDT) is applied. For the HSDT, the effect of shear deformation can be considered, and no shear correction coefficient is needed. By using isogeometric analysis with the non-uniform rational B-spline (NURBS) as the basis function, the precise geometric models and high-order approximation are obtained so that the C1 continuity of HSDT can be directly achieved without any additional variables. The plates in this paper are considered inhomogeneous in multiple directions, and the thickness of plates also changes along both x- and y-axes. To verify the correctness and validity of the current numerical analysis procedure, several numerical examples for the above plates are obtained and results are compared with those from the literature. Then the effects of material variation parameters, boundary conditions (BCs), thickness variation index are investigated and discussed specifically.