本論文主旨在於利用值積元素法(Quadrature Element Method)來分析非均勻邊界條件及厚度的古典複合層板的動態特性。本文先應用微分值積法的轉化規則，推導複合層板元素的離散化代數方程式，經由元素的接合，得到整個複合層板的離散代數方程式；再求解均勻或不均勻邊界條件與厚度下複合層板的自然頻率，與文獻上的結果做比較。進而探討不同纖維角度、疊層數及長寬比對層板自然頻率的影響。由分析結果顯示，應用值積元素法在複合層板的振動分析上可以得到準確的結果。

In this thesis, the dynamic characteristic of symmetrically laminated plates with non-uniform boundaries and thickness is investigated by using the Quadrature Element Method (QEM) and the classical plate theory. First, we apply the formulation of differential quadrature to obtain the discrete algebraic governing equations of laminated plate elements, which are then assembled to get the discrete equations for the entire plate. Non-dimensional frequencies of symmetrically laminated plates with uniform or non-uniform boundaries and thickness are obtained, and compared with those in the literature. Furthermore, the non-dimensional frequencies of laminated plates for different fiber orientation angles, numbers of layers and aspect ratios are studied. Numeral results show the high accuracy and efficiency of the QEM for vibration analysis of laminated plates.

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