軸對稱板於彈性基礎上受任意載重之研究

Abstract

推導軸對稱彈性薄板於彈性基礎上受任意分佈荷重下之外力-變位關係式。此荷重在角方向以傅立葉級數之諧和函數展開，並假定各展開項之荷重強度為沿半徑方向呈分段線性。以彈性薄板理論及分段線性荷重形狀函數，解此板之動力位移。

動力分析之模式，係由運動方程是經解析得一含Bessel function的變位函數。再藉板之邊界條件推衍得頻率方程式，進而求得頻率參數，再得板之自然頻率。後依振態疊加法推導成廣義荷重及廣義質量，並於廣義荷重中引入分段線性荷重形狀函數轉換。此微分方程得一解，即為任意分佈荷重下之外力-變位關係式。

上述推導之外力-變位關係式，皆與以有限元素法所得之解相互比較，並印證之。

Presented is the displacement field of axial symmetric plate on elastic foundation subjected to arbitrary loading. In the derivation, the arbitrary loading can be expressed as Fourier series in θ-direction and piecewise linear distribution in r-direction of cylindrical coordinates. To obtain the displacement field, the modal shapes and respective frequencies of the system are solved first. Then, the technique of superposition is employed to obtain the displacement field due to arbitrary loading. The analytical solution of the presented method has been compared with the result of finite element method for some simple cases. The comparison shows the presented method is accurate and efficient.