平板廣泛應用在各工程領域中，如航太、船舶與土木等，因此本文探討平板受平面邊緣力的應力及自由振動分析。文中假設平板為均質等向性的材質，平板四邊邊界均為簡支撐端，而平板在軸向的兩對邊承受平面邊緣力。首先利用牛頓第二運動定律得到平板的運動方程式，接著利用傅立葉級數來展開施加於平板邊界上的邊緣力，並利用艾律氏應力函數(Airy’s stress function)疊加法求得平板應力分布的確切解，接著利用ANSYS建立有限元素分析模型進行平板受平面邊緣力之應力分析，經由此模擬求得結果與本文求解出的應力分布作比對，接著利用葛樂金法得到離散化的運動方程式，由此求出平板之自然頻率與模態，最後利用自由振動結果，去探討平板在不同受力型式下的挫曲負荷。從數值結果可知，隨著邊緣力作用寬度越窄，作用區域愈往邊緣中央移動，挫曲負荷愈大。

Plates are widely used in various engineering fields, such as aerospace, marine and civil engineering, etc. Therefore, stress and free vibration analyses of rectangular plates subjected to arbitrary in-plane edge loads are investigated in this thesis. Assume that the material property of the plate is homogeneous and isotropic. The plate is simply-supported on all edges, and in-plane edge loads are arbitrarily distributed on two opposite edges. First, the equations of motion of the plate are derived by Newton’s second law. Next the edge loads of the plate is expanded into a Fourier series, and the exact solution of the in-plane stress filed is obtained rigorously by using a superposition of Airy’s stress functions. An finite element model is established, and the in-plane stress simulation of the plate is carried out by ANSYS. The results obtained by ANSYS are compared with the stress distribution obtained by the present work. Then the governing equation of the lateral free vibration of the plate is discretized by Galerkin’s method, from which the natural frequencies and the corresponding model shapes of the plate are determined. Finally by the results of the free vibration analysis, the buckling loads of the plate subjected to different types of edge loads are investigated in this thesis. Numerical results show that the narrower the width of the edge loads is, and the more the application area of the edge loads moves toward the middle of the edges, the greater the buckling load is.

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