本論文的主旨在於利用值積元素法(Quadrature Element Method)來分析含矩形缺口之矩形Mindlin平板的動態行為。首先應用微分值積轉化規則，推導矩形Mindlin平板元素的離散化代數方程式；再經由元素的接合，得到系統的離散化代數方程式。本文求解矩形、L形及U形平板在不同邊界條件下的自然頻率，並與有限元素法的結果做比較。由分析結果顯示，應用微分值積元素法在具有矩形缺口之矩形Mindlin平板的振動分析上，可以得到準確的結果。

In this thesis, the dynamic characteristics of rectangular Mindlin plates with rectangular openings is investigated by using the quadrature element method (QEM). First, we apply the formulation of differential quadrature to obtain the discrete algebraic governing equations of Mindlin plate elements, which are then assembled to get the discrete equations for the entire plate. Natural frequencies of rectangular, L-shaped and U-shaped plates with different boundary conditions are obtained, and compared with those obtained by the finite element method. Numerical results show the high accuracy and efficiency of the QEM for vibration analysis of rectangular Mindlin plates with rectangular openings.

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