- 作者: 芮涵芝
- 作者服務機構: 私立淡江大學物理學系
- 中文摘要: 在本文中,我們將使用蓋羅根步驟,探討在均勻邊界約束之下正交異向性圓盤其橫向振盪之第一激發對稱模。在所取近似中,橫向撓曲函數w的形式假定與彈性常數 (方程式無法摘錄) 無關,並取為(1- r/α)的多項式,“α”是圓盤的半徑。這個函數與處理對稱基模所用者比較,在展式中多出一項;橫向剪力對r的導數以及w本身都應在節半徑處消失這個條件,將用來同時決定節半徑和多出的展開係數。所呈現之數字結果,有w中之展開係數,節半徑,線性角頻率,時間函數運動方程式中之另一參數,以及非線性與線性週期比“部份計算結果與原有資料可資比較者都經比較,證實本文的近似方法,對由0.5到5的β值與所有自0到無窮大的約束係數R值,都十分良好。在我們的近似中,對撓曲函數形式之決定,我們取β=1,然後再將之用在其他β值。
- 英文摘要: In this paper we investigate the first excited symmetrical modes of transverse vibrations of orthotro-pic circular plates subject to uniform elastic edge constraints by the Galerkin procedure. The form of thetransverse deflection function w is assumed to be independent of the elastic constant (方程式無法摘錄) in the ap-proximation and is taken as a polynomial in (1 - r/a), a being the radius of the plate. This function differsfrom that used in dealing with the fundamental symmetrical modes by having one extra term in the expan-sion and the extra expansion coefficient is determined simultaneously with the nodal radius by requiringthat the derivative of the transverse shear force with respect to r must vanish there together with w itself.In the determination of the form of the transverse deflection function, the value unity for β is used. Oncethis function is found it is used for other β values in the approximation. Numerical results for the expan-sion coefficients in w, the nodal radius, the linear angular frequency, the other parameter in the nonlinearequation of motion of the time function, and the nonlinear to linear period ratio are presented. Compari-son of partial results with available ones shows that the present method of approximation is very good forvalues of β ranging from 0.5 to 5 and for all values of the restraint coefficient k.
- 中文關鍵字: vibrations; orthotropic circular plates
- 英文關鍵字: --