本文以傳統殼理論為出發點，建立多種疊層結構體之數學理論模型，並先以Navier Solution推導疊層板、疊層圓柱殼、夾心圓柱殼之面材皆為對稱正交以及夾心板之面材為反對稱正交且邊界條件皆設為簡支撐之自然頻率明示解，再搭配Levy Solution與Rayleigh-Ritz Method相互做驗證，以三種方法貫穿本文並且搭配數值範例分析自由振動問題以求解自然頻率，但因疊層結構體之控制方程、邊界條件、面材疊層方式等因素，造成使用此三種方法之限制，皆將於本文一一說明優缺點以及討論數值結果。

By following the classical theory of thin elastic shells, we develop mathematical models for laminated structures. By Navier Solution, we derive exact solution for symmetric cross-ply laminated simply supported such as laminated plate, laminated cylindrical shell, sandwich cylindrical shell and antisymmetric cross-ply laminated for simply supported sandwich plate. In order to prove its accurate, we introduce Levy Solution and Rayleigh-Ritz Method with numerical procedure. Using three methods to deal with free vibration analysis and obtain natural frequency. Beside, these methods will be affected by governing equations, boundary conditions and stacking sequence. We will discuss features about these methods and show numerical examples in this article.

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