In this paper, a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate (FGRTP) of which the distribution of material is defined by four parameters is presented. It is assumed that the considered functionally graded materials (FGM) are distributed in the thickness direction according to four parameters. The displacement fields of any point on the FGRTP are determined by the first order shear deformation theory (FSDT), and all displacement functions are extended by ultraspherical polynomial. By applying the Ritz method to the energy function of the whole system, the constitutive equation of FGRTP is obtained and the natural frequencies are obtained by solving the eigenvalue problem. The boundary conditions are generalized to arbitrary boundary conditions by artificial elastic technique. The accuracy of the proposed method is verified by comparing with the previous literatures. The effects of different parameters on the free vibration characteristics of FGRTP are studied through some numerical examples.
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