In this work, the authors develop a Reissner’s mixed variational theorem (RMVT)-based weak formulation for the three-dimensional (3 D) free vibration analysis of sandwich functionally graded (FG) truncated conical shells under various boundary conditions rotating with a constant angular velocity with respect to the central axis of the shells. The material properties of the FG layers constituting the truncated conical shell are assumed to obey a power-law distribution of the volume fractions of the constituents through their thickness direction, for which the effective material properties are estimated using the rule of mixtures. Based on the weak formulation, a semi-analytical finite annular prism (FAP) method is developed for the current issue, where the effects of the initial hoop stress due to rotation and the centrifugal and Coriolis accelerations are considered. Implementation of the current FAP method indicates that its solutions converge rapidly, and the convergent solutions closely agree with accurate solutions available in the literature. The obtained 3 D frequency parameter solutions for rotating and non-rotating sandwich FG truncated conical shells can provide a standard by which to assess those obtained using assorted two-dimensional classical, advanced, and refined shell theories.
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