• 作者： 芮涵芝
• 作者服務機構： 私立淡江大學物理系
• 中文摘要： 本文提供一應用蓋羅根步驟對在一任意外界邊界約束，與內界自由、內界簡支和內界夾緊的邊界約束之下的正交異向性空心圓盤，它在與面垂直方向的振盪和靜力撓曲問題的求解方法。橫向撓曲函數取為對應圓盤的撓曲函數，與一修增項之和，二者都是（1 - r/a)的多項式和θ的傅立葉級數。對一自由的內界，修增項具當內徑趨近於零也趨近於零的性質，這是物理上所需要的。在內界處的二個邊界條件決定修增項中的展關係數，修增項不影響外界處的邊界條件。解出應力函數的相容方程式，完成諸蓋羅根積分，得一時間函數的非線性運動方程式。
• 英文摘要： This paper presents a method of solution, by the Galerkin procedure, to the problems of transversevibrations and static deflections of orthotropic annular plates under arbitrary outer edge constraints andwith free, simply supported，and clamped inner edges. The transverse deflection function is taken as thatof the corresponding circular plate plus a modification term; both are polynomials in (1-r/a) and Fourierseries in θ. For the case of a free inner edge, the modification term has the desired property that it wouldvanish at the limit where the inner radius approaches zero. The two boundary conditions at the inner edgeare used to determine the expansion coefficients in the modification term which does not enter or affectthe outer edge boundary conditions. The compatibility equation of the stress function is subsequentlysolved and the equation of motion for the time function is finally obtained by carrying out the integrationof the Galerkin equation.
• 中文關鍵字： vibrations; orthotropic annular plates
• 英文關鍵字： --