# 臺灣博碩士論文加值系統

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 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.
 摘要 IExtended Abstract II誌謝 VIII目錄 IX表目錄 X圖目錄 XI參數對照表 XII第一章 緒論 1第二章 圓錐殼理論與基本假設 52.1 圓錐殼幾何關係 52.2 應變位移關係 62.3 組成方程式 72.4 Hamilton定理 72.4.1 Reissner混合變分原理 82.4.2 初始環向應力所造成之應變能 82.4.3 動能 92.5 運動學與動力學之基本假設 112.6 弱型態有限元素方程式 112.7 邊界條件 16第三章 數值範例 173.1 非旋轉與旋轉之均質等向圓錐截柱殼 173.2 非旋轉FG圓錐截柱殼 183.3 旋轉夾心FG圓錐截柱殼 19第四章 結論 23第五章 參考文獻 25