本文主要利用有限元素法分析雙層與部分雙層Mindlin板結構的自由振動特性；此結構分為上層和下層兩種不同的材料所組成。

　　本文運用Mindlin板理論定義位移、應變與應力，計算出單層板的應變能及動能，再以漢米爾頓原力求得單層Mindlin板的靜態平衡方程式，使用靜態的運動方程式推導出其位移場之解並表示成形狀函數(shape function)的形式。由應變能及位能找出質量矩陣及剛性矩陣，進而利用Lagrange’s equation將應變能及動能代入得到單層方板元素的運動方程式，然後依不同的邊界條件將元素結合，解出系統的模態頻率，並討論厚度變化和分割元素數對板的自然頻率影響。進一步定義雙層Mindlin板的位移、應變，求出其質量矩陣及剛性矩陣和靜態運動方程式還有雙層Mindlin板的位移場通解，一樣利用Lagrange’s equation求得其模態頻率，並討論全部雙層Mindlin板和中間部分雙層Mindlin板的振動模態作個比較。

　This study presents natural frequencies of rectangular plate with single-layered、two-layered and partial two-layered in the central part by Finite Element Method.

　Based on Mindlin’s plate theory, the displacements, strains and stresses of single-layered rectangular plate can be defined to calculate strain energy and kinetic energy. The displacements solved from static equilibrium equations are used as shape functions of one element. Then, the Finite Element Method is employed to obtain the natural frequencies of the entire plate. The effects of thickness and element number on the natural frequencies of the plate are studied.

　Furthermore, the displacements of two-layered rectangular plate are defined. The natural frequencies of rectangular composite plate with two-layered or partial two-layered in the central also are studied by FEM.

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