本文以改良Pagano方法探討具簡支承邊界之多層疊合功能性壓電材料中空圓柱殼之三維自由振動分析。其中考量三種表面條件，並使用非均質性且厚度座標方向隨指數律變化之功能性壓電材料。傳統Pagano方法多用來分析多層疊合複合材料板和殼，然而經由四部分改良後，即可應用於多層疊合功能性圓柱殼，其改良部分分別如下：以Reissner 混合變分原理替代以位移為基礎的虛位移原理進行解析；利用Euler公式將系統方程式之解由複數解型態轉換為實數解型態；應用連續近似法，將功能性材料圓柱殼藉由切割成多個離散層結構，且各單層之厚度相較於圓心至中曲面的半徑長度微小；使用傳遞矩陣法，可逐層求解系統方程式，提升計算效能；藉由以上四部分的改良，便可拓展Pagano方法的應用層面。此外，本文亦著重探討多層疊合功能性圓柱殼的中曲面之寬厚比、表面條件、各層厚度、材料參數梯度指標對頻率結果的影響，並將改良Pagano方法求得之頻率參數和既有文獻之精確解進行探討。

The three-dimensional (3D) free vibration analysis of simply-supported, functionally graded piezoelectric material (FGPM) sandwich circular hollow cylinders with different surface conditions is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. Pagano’s method is modified to be feasible for this study of FGPM sandwich cylinders, in which a displacement-based formulation is replaced by a mixed one; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions using Euler’s formula; a successive approximation method is adopted to approximately transform each FGPM layer into homogeneous piezoelectric layers with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed so that the general solutions of system equations can be obtained layer-by-layer, which is significantly less time-consuming than usual. A parametric study of the influence of the mid-surface radius-to-thickness ratio, open- and closed-circuit surface conditions, the thickness ratio of each layer, and the material-property gradient index on the natural frequencies of FGPM sandwich cylinders is carried out.

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