Postbuckling Theory of a Spinning Disk Under Space-Fixed Edge Load

• Main Authors: Han-Wen Chung, 鍾漢文
• Other Authors: Jen-San Chen
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/48142079345211750057

碩士 === 國立臺灣大學 === 機械工程學研究所 === 87 === In this thesis we study the post-buckling behavior of a spinning disk under space-fixed edge load. Hamilton's principle is first used to derive the three equations of motion based on von Karman's plate model. The equations of motion are carefully nondimensionalized such that they can reduce to the conventional equation without considering Von Karman's effect when the thickness of the plate approaches zero. In order to simplify the equations of motion involving in-plane deformation, Lame's potentials are employed. Since the equations of motion are linear with respect to Lame's potentials, we can divide them into three parts, each of which has different physical meaning. After employing Galerkin's procedure, we can derive the model equations for the steady state transverse deflection in a cubic polynomial form. Further analysis shows that there exists one and three steady state deflections when the disk rotates below and beyond the critical speed, respectively. The relations between the modified critical speed and the amplitude of the edge loads are also discussed.