軸對稱彈性板承受任意載重之研究

Abstract

推導軸對稱彈性薄板承受任意分佈荷重下之外力－變位關係式。此荷重係 以富立葉級數之簡諧函數展開，並假定各展開項之荷重強度為沿半徑方向 呈分段線性。是以提出一形狀函數表之，基於彈性薄板理論及荷重形狀函 數，以解析解的推導模式，就靜力與動力之分析模式下，意即考慮慣性力 與否，分別加以推導。靜力之分析模式，係藉受集中荷重的基礎薄板問題 ，利用疊加原理與文中對任意分佈荷重經分段線性假設，所提出之形狀函 數加以模擬。因而推衍得任意分佈荷重下之外力－變位關係式。動力之分 析模式，係由運動方程式經解析得一含貝索函數的變位函數。再藉板之邊 界條件，推衍得頻率方程式，進而求得頻率參數。為求外力－變位關係式 ，變位函數包含二部份，其一表沿板徑向所計算得的位移函數，其一表板 緣之振動大小，即整體板的剛性變位。而解析過程將後者視作有效外力。 此後依振態疊加法求得廣義荷重及廣義質量，並於廣義荷重中引入荷重形 狀函數轉換。如此解析微分方程得一全解，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，均得於簡單荷重中，基礎薄 板問題所得之解相比較，並印證滿足。 A procedure to generate the relationship between external force and displacement for axial symmetric flexible thin plate bearingarbitrary distributive loading . Expanded by the Fourier series into harmonic function , the loading is assumed that loading intensitywithin each expanded term is piecewise linear along the direction of radius , which is represented by a shape function .Based on the thin plate theory and shape function of loading , using the analysis soluction method , the topic of static and dynamic can be generated separately . The topic of static , which is an analysis model without considering the term of inertia force in the governing equation . According to the superposition principle and the assumption for arbritrary loading , the procedure of solving the basic plate problem bearing concentrated load can generate the relationship . The topic of dynamic , which is an analysis model considering the term of inertia force in the governing equation . The total displacementsinclude two parts . The one is the deflection function of the plate measured from the edge , the other is the rigid portion of the function . In the analysis procedure , it is considering the latter as the effect force . Emplying the mode superposition method , which can get the generalization loading , generalization mass and equation . The relationship can be made by solving the equation . The results , at above , can be compared with the basic thin plate problems , and proved reasonable .