標題: 一非均勻正交圓形板的非線性隨機振動分析}Nonlinear Random Vibration Analysis of a Nonuniform Orthotropic Circular Plate 作者: 柯至良Ke, Jyh-Liang 關鍵字: Von Karman Plate Theory馮卡門板理論Equivalent LinearizationMonte Carlo等效線性法蒙地卡羅模擬法格樂金法 出版社: 應用數學研究所 摘要: 本篇論文探討幾何非線性,非均勻厚度的軸對稱,正交異向性( orthotropic)圓形板受到隨機外力作用下的動態響應。此類問題在土木, 機械及航空太空工程上有廣泛的應用。在此利用了馮卡門板理論(Von Karman plate theory)推導統制方程式(governing equation),並且利用 格樂金法 (Galerkin procedure)導出運動方程式(equation of motion) 。此運動方程式是一個二階非線性常微分方程式,可以等效線性法( equivalent linearization)解之,並用蒙地卡羅模擬法(Monte Carlo simulation)檢驗其準確度。最後找出此圓板的統計動態響應,如位移,應 變,應力及彎矩等等。這些統計動態響應可用來作結構的可靠度分析。In this paper, the dynamic response of geometrically nonlinear circular plates under random excitation has been investigated. This kind of problem has wide ranges of application in civil engineering, mechanical engineering and aerospace engineering. Von Karman plate theory in conjunction with Galerkin technique has been adopted to obtain the dynamic response of nonlinear circular plates in terms of the deflection component. The above procedure gave a nonlinear ordinary differential equation involving the deflection component, which can be solved by stochastic equivalent linearization technique. Finally, the statistical dynamic response of the circular plates such as deflection, strain and stress has been calculated and checked by Monte Carlo simulation. URI: http://hdl.handle.net/11455/18624 顯示於類別： 應用數學系所