古典板理論在自由振動的研究上雖有自然頻率的解析解可供參考，但古典板理論中幾乎都針對薄板做探討，然而複材疊層夾心板並非屬於薄板，再加上複材疊層夾心板會受到邊界條件、材料性質、疊層方式等因素影響，因此想要得到一般廣義的自然頻率解析解並非一件容易的事。
基於這點，本文初期延續 Moh和Hwu的理論模型，以納維解法處理自由振動問題，但發現只可提供對稱正交疊層板、邊界條件為四邊簡支撐之解析解，因此為了擴充處理其他邊界條件與面材疊層方式不同之問題，我們利用萊維與哈密頓解法並配合數值方法求得自然頻率之近似解。

Analytical solutions to natural frequency analysis has been reported in the classical plate theory. It’s always for the thin plates, but the sandwich plates belong to the thick plates which considers the effect of transverse shear deformation. Besides, the natural frequency of composite sandwich plates will be affected by boundary conditions, material properties and stacking sequence. Therefore, it’s difficult to obtain the exact solutions.
For this reason, we follow the model proposed by Moh and Hwu, using Navier Solution to deal with free vibration analysis. However, only the special cases like simply supported symmetric cross-ply composite faces can be solved by Navier Solution. In order to improve it, we introduce Levy Solution and Hamilton Principle with numerical procedure. Then, we get the analytical solution for the general cases of composite sandwich plates.

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