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In this article, an analytical solution for buckling of moderately thick functionally graded (FG) sectorial plates is presented. It is assumed that the material properties of the FG plate vary through the thickness of the plate as a power function. The stability equations are derived according to the Mindlin plate theory. By introducing four new functions, the stability equations are decoupled. The decoupled stability equations are solved analytically for both sector and annular sector plates with two simply supported radial edges. Satisfying the edges conditions along the circular edges of the plate, an eigenvalue problem for finding the critical buckling load is obtained. Solving the eigenvalue problem, the numerical results for the critical buckling load and mode shapes are obtained for both sector and annular sector plates. Finally, the effects of boundary conditions, volume fraction, inner to outer radius ratio (annularity) and plate thickness are studied. The results for critical buckling load of functionally graded sectorial plates are reported for the first time and can be used as benchmark.

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In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one.