本文基於Reissner混合變分原理（Reissner's mixed variational theorem，RMVT），發展有限環形柱體元素法，據以解析旋轉夾心功能性（functionally graded，FG）圓錐截柱殼，受制於不同變化邊界條件下之自然振動分析。假設FG圓錐截柱殼的材料成份體積分量沿厚度方向呈冪次函數分佈，其有效材料性質則利用兩相材料混合定律推估。文中考慮由於旋轉所引起的初始環向應力、離心加速度和Coriolis加速度對該圓錐截柱殼自然振頻的影響。分析結果顯示本有限環形柱體元素法解收斂迅速，且其收斂解與文獻中的精確解高度契合。本文所獲得旋轉和不旋轉的夾心FG圓錐截柱殼之自然頻率參數解可視為標準驗證解，用以評估各種二維古典，進階和改良殼理論解之精確度。

In this work, the authors develop a Reissner's mixed variational theorem (RMVT)-based weak formulation for the three-dimensional (3D) 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 3D 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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