A unified semi-analytic method for vibration analysis of functionally graded shells of revolution

A unified semi-analytic method is developed for free vibration analysis of functionally graded material (FGM) shells of revolution subjected to arbitrary boundary conditions, and independent and coupled shells of revolution are specific cases. Material properties vary continuously in thickness direction according to the four-parameter power-low distributions in terms of volume fractions of two constituents. The shell is firstly divided to some narrow shell segments to be treated as conical shells. Differential equations of motion based on first-order shear deformation theory (FSDT) are solved by expanding displacements as power series and Fourier series in meridional and circumferential directions, so five displacements and five forces at cross-section are only expressed as 10 unknown coefficients. Continuity conditions and elastic boundary conditions are assembled to the final governing equation. Through comparing natural frequencies of present method with the ones of opened works for several typical FGM shells of revolution with uniform/stepped thicknesses and classic/elastic boundaries, rapid convergence, high accuracy and wide application of the developed method are demonstrated. Furthermore, influences of material and geometry parameters reveal that increasing the power-law exponent does not change mode shapes and circumferential mode numbers of fundamental frequencies, and mode shapes are slightly affected by the variation of thickness.