为了研究预应力和液体对圆柱壳颤振的影响,采用杂交元方法,建立了圆柱壳的气动弹性方程。由Sanders薄壳理论和经典有限元理论,从壳的精确解推导节点位移函数入手,并由一阶活塞理论得到结构的气动阻尼矩阵和刚度矩阵,最终推导出考虑预应力和内部液体影响的圆柱壳的混合有限元公式和气动弹性方程。通过特征值法验证了此种有限元方法的正确性,并重点研究了预应力和内部注有液体对圆柱壳稳定性的影响。计算结果表明:预应力和液体对圆柱壳的颤振特性有显著的影响。
In order to study the effects of initial stress and internal liquid on the flutter of a cylindrical shell, the aeroelastic equations of the cylindrical shell are established, while a hybrid finite element method of analyzing cylindrical shell flutter is employed. The structural formulation is a combination of Sanders shell theory and the classic finite element method. The nodal displacements are found from the precise solution of shell governing equations. The influence of the initial stress and internal liquid is also taken into account. The first-order piston theory is applied to derive the aerodynamic damping and stiffness matrices. Hybrid finite element formulation and aeroelastic equations are derived and solved numerically. The validity of such a finite element method is verified by the eigenvalue method. The paper focuses on an investigation of the impact of initial stress and internal liquid on the aeroelastic stability of a cylindrical shell. Numerical solutions demonstrate that they do have a marked impact on the flutter characteristics of a cylindrical shell.
[1] Olson M D, Fung Y C. Supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression. AIAA Journal, 1966, 4(5): 858-864.
[2] Olson M D, Fung Y C. Comparing theory and experiment for supersonic flutter of circular cylindrical shells. AIAA Journal, 1967, 5(10): 1849-1856.
[3] Olson M D, Evensen D A. Nonlinear flutter of a circular cylindrical shell in supersonic flow. NASA TN D-4265, 1967.
[4] Evensen D A, Olson M D. Circumferentially traveling wave flutter of circular cylindrical shell. AIAA Journal, 1968, 6(8): 1522-1527.
[5] Horn W, Barr G, Carter L, et al. Recent contributions to experiments on cylindrical shell panel flutter. AIAA Journal, 1974, 12(11): 1481-1490.
[6] Dowell E H. Flutter of infinitely long plates and shells: Part II. AIAA Journal, 1966, 4(9): 1510-1518.
[7] Dowell E H. Aeroelasticity of plates and shells. Leyden: Noordhoff International Publishing, 1975.
[8] Carter L L, Stearman R O. Some aspects of cylindrical shell panel flutter. AIAA Journal, 1968, 6(1): 37-43.
[9] Barr G W, Stearman R O. Aeroelastic stability characteristics of cylindrical shells considering imperfections and edge constraint. AIAA Journal, 1969, 7(5): 912-919.
[10] Barr G W, Stearman R O. Influence of a supersonic flow field on the elastic stability of cylindrical shells. AIAA Journal, 1970, 8(6): 993-1000.
[11] Bismarck-Nasr M N. Finite element method applied to the supersonic flutter of circular cylindrical shells. International Journal for Numerical Methods in Engineering, 1976, 10(2): 423-435.
[12] Ganapathi M, Varadan T K, Jijen J. Field-consistent element applied to flutter analysis of circular cylindrical shells. Journal of Sound and Vibration, 1994, 171(4): 509-527.
[13] Sabri F, Lakis A A. Finite element method applied to supersonic flutter of circular cylindrical shells. AIAA Journal, 2010, 48(1): 73-81.
[14] Sabri F, Lakis A A. Hydroelastic vibration of partially liquid-filled circular cylindrical shells under combined internal pressure and axial compression. Aerospace Science and Technology, 2011, 15(4): 237-248.
[15] Sabri F, Lakis A A. Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell. Journal of Sound and Vibration, 2010, 329(3): 302-316.
[16] Marsell B, Gangadhara S, ChatmanY. Using CFD techniques to predict slosh force frequency and damping rate. AIAA-2009-2683, 2009.
[17] Ibrahim R A. Liquid sloshing dynamics: theory and applications. Cambridge: Cambridge University Press, 2005.
[18] Lakis A A, Neagu S. Free surface effect on the dynamics of cylindrical shells partially filled with liquid. Journal of Sound and Vibration, 1997, 207(2): 175-205.
[19] Lakis A A, Bursuc G, Toorani M H. Sloshing effect on the dynamic behavior of horizontal cylindrical shells. Nuclear Engineering and Design, 2009, 239(7): 1193-1206.
[20] Schotte J S, Ohayon R. Various modelling levels to represent internal liquid behavior in the vibration analysis of complex structures. Computer Methods in Applied Mechanics and Engineering, 2009, 198(21): 1913-1925.
[21] Sanders J L. An improved first-approximation theory for thin shell. NASA TR R-24, 1959.
[22] Chen G B, Zou C Q, Yang C. The basis of aeroelastic design. Beijing: Beihang University Press, 2004: 208-209. (in Chinese) 陈桂彬, 邹丛青, 杨超. 气动弹性设计基础. 北京:北京航空航天大学出版社, 2004: 208-209.
[23] Krumhaar H. The accuracy of linear piston theory when applied to cylindrical shells. AIAA Journal, 1963, 1(6): 1448-1449.
CJA