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標題: 含熱變形旋轉環形板振動之探討
Studies of Vibration of Thermally Deformed Rotating Annular Plates
作者: 許克銘
Hsu, Ke-Ming
關鍵字: Thermal;熱變形;Vibration;Annular Plates;振動;環形板
出版社: 機械工程學系所
引用: [1] Huang, N. N., and Tauchert, T. R., “ Post-buckling Response of Antisymmetric Angle-Ply Laminates to Uniform Temperature Loading,” Acta Mechanica , Vol. 72, pp. 173-183(1988). [2] Singh, G., and Rao, G. V., “ Thermal Post-bulkling Behavior of Laminated Composite Plates,” AIAA Journal, Vol. 32, No. 6, pp. 1336-1338(1993). [3] Wilcox, M. W., and Clemmer, L. E., “Large Deflection Analysis of Heated Plates,” ASCE Journal of the Engineering Mechanics Division, Vol. 90, pp. 165-189(1964). [4] Birswal, K. C., and Ghosh, A. K., “Finite Element Analysis for Stiffened Laminated Plates Using Higher Order Shear Deformation Theory,” Computer & Structure, Vol. 53,No. 1, pp. 161-171(1994). [5] Argyris, J., and Tenek, L., “High-temperature Bending, Buckling, and Post-buckling of Laminated Composite Plates using the Natural Mode Method,” Comput. Method Appl. Mech. Engrg., Vol. 117, pp. 105-142(1994). [6] Chandrashekhara, K., and Tenneti, R., “Non-linear Static and Heated Laminated Plates: A Finite Element Approach,” Composites Science and Technology, Vol. 51, pp. 85-94(1994). [7] Yu, Q., Mostaghel N., and Fu, K. C., “Effect of Initial Curvature on Natural Frequency of Thin Plate on Hinge Supports,” Journal of Engineering Mechanics, Vol. 120, No. 4, pp. 796-813(1994). [8] Rao, G. V., Sinha, G., Mukherjee, N., and Mukhopadhyay, M., “A Finite Element Free Vibration Analysis of A Thermally Stressed Spinning Plate,” Computers & Structure, Vol. 59, No. 2, pp. 377-385(1996). [9] Lee, D. M., and Lee, I., “Vibration Behaviors of Thermally Postbuckled Anisotropic Plates using First-order Shear Deformable Plate Theory,” Computers & Structures, Vol. 63, No. 3, pp. 371-378(1997). [10] Almeida, S. F. M. d., and Hansen, J. S., “Natural Frequencies of Composite Plates with Tailored Thermal Residual-stresses,” International Journal of Solids and Structures, Vol. 36, pp. 3517-3539(1999). [11] Son, H., Kikuchi, N., Ulsoy, A. G. and Yigit,A. S.,“Dynamics of Prestressed Rotating Anisotropic Plates Subject to Transverse Loads and Heat Sources,” Journal of Sound and Vibration, Vol. 226, No. 3, pp. 457-504 (2000). [12] Li, S., and Zhou, Y., “Nonlinear Vibration of Heated Orthotropic Annular Plates with Immovably Hinged Edges,” Journal of Thermal Stresses, Vol. 26, No. 7, pp. 691-700(2003). [13] Li, S. R., Batra, R. C., “Vibration of Thermally Post-Buckled Orthotropic Circular Plates,” Journal of Thermal Stresses, Vol. 30, No. 1, pp. 43-57(2007). [14] Chen, J. S., “Stability Analysis of a Spinning Elastic Disk Under a Stationary Concentrated Edge Load,” Journal of Applied Mechanics, Vol. 61, pp. 788-792(1994). [15] Young, T. H. and Wu, M. Y., “Dynamic Stability of Disks with periodically Varying Spin Rates Subjected to Stationary In-Plane Edge Loads,” Journal of Applied Mechanics, Vol. 71, pp. 450-458(2004). [16] 陳一賢,“含加強樑複合材料疊層板之大變形與靈敏度分析,”碩士論文, 中興大學機械研究所(1994). [17] 賴大渭, “含加強樑複材疊層板之熱大變形有限元素分析,” 碩士論文, 中興大學機械研究所(1995). [18] 廖榮川, “ 承受空間中固定外力之複合材料軸-圓盤系統動態響應之探討, ” 碩士論文, 中興大學機械研究所(2008). [19] Vinson, J. R., and Sierakowski, R. L., The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff Publishers(1986). [20] Chia, C. Y., Nonlinear Analysis of Plates, McGraw-Hill, New York(1980). [21] Reddy, J. N., An Introduction to the Finite Element Method, McGraw-Hill, New York, Second edition(1993).
本文主要目的為建立描述含熱變形旋轉環形板之線性振動之有限元素模式,並利用它分析不同溫度分佈對環形板的振動頻率以及其動態響應的影響。文中採用一簡單高階位移場理論,首先,考慮蒙卡門(von Karman)應變,導出板應變能的變分,並採用每個節點有七個自由度的等參四邊形九點元素。其次,利用先前已建立之旋轉圓盤之有限元素運動方程,將其中的慣性項視為外力的一部分,求出這些慣性力與外力對板所做的虛功,再採用虛功原理,推導出分析板熱大變形與定轉速下含熱變形環形板之線性振動等兩組有限元素方程。振動分析模式中也納入了旋轉對環形板造成的離心力所產生的加勁效應。
分析時首先應用牛頓-雷甫森疊代法(Newton-Raphson method) 求解靜熱變形之非線性有限元素方程,計算出因溫度變化時板之熱變形。其次,利用模態法(modal method)分析板的振動問題。於實例中,分別考慮等向性單層板和複材對稱疊層板,分析它們的熱變形、振動頻率、動態位移響應,並探討因離心力所提高板平面的拉伸勁度和不同的溫度場變化時,對系統頻率的影響。

The objective of this thesis is to investigate the vibration frequencies and dynamic responses of spinning annular plates subject to thermal loads. A simple higher-order displacement theory is used. First, by adopting the von Karman partially nonlinear strains, the variation of the strain energy of plates is derived. The plate elements being used is the nine-node isoparametric quadrilateral 2D element. Next, use is made of the finite element governing equations of the rotating annular plate established earlier. The inertial terms in above equations are treated as forcing terms, and the virtual work done by these inertial forces as well as external forces is obtained. Finally, using the principle of virtual work, two sets of governing equations, one being used to determine the plate's thermal deformation, and the other for analyzing the vibration of thermally deformed rotating annular plates, are derived. In the vibration analysis, the geometric stiffness due to the centrifugal forces is also included.
For analysis, first, Newton-Raphson method is used to solve the first set of nonlinear governing equations to obtain the static thermal deformation of plates. Next, the modal method is applied to solve vibration problem. Both plates made of isotropic materials and unidirectional reinforced composite materials are considered. Their thermal deformation, vibration frequencies, and dynamic responses are studied. The influence of the temperature distribution and geometric stiffness due to the centrifugal force effect are illustrated.
其他識別: U0005-1908201001070200
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