Isogeometric free vibration analysis of multi-directional functionally graded circular and annular plates with variable thickness

In this paper, the free vibration of multi-directional functionally graded (multi-directional FG) circular and annular plates with variable thickness is studied. The plates are considered inhomogeneous in multiple directions, and the thickness of plates changes in both x- and y-axes by a specific law. A numerical method based on the isogeometric analysis and first-order shear deformation (FDST) theory is employed to analyze the natural frequencies and mode shapes of the multi-directional FG plates. By using isogeometric analysis (IGA) and the non-uniform rational B-spline (NURBS) as the basis function, the precise geometric representation and high computational efficiency can be obtained. Then the effects of material variation exponents, boundary conditions, thickness variation index on the natural frequencies and mode shapes of the above considered plates are investigated and discussed.