正交铺设复合材料层合圆柱壳自由振动分析的辛空间波方法

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (6) : 113-120.

论文

韩少燕1，李榆银2，高汝鑫3,4

作者信息 +

Symplectic wave-based method for the free vibration analysis of cross-ply composite laminated circular cylindrical shells

HAN Shaoyan1，LI Yuyin2，GAO Ruxin3,4

Author information +

文章历史 +

摘要

针对正交铺设复合材料层合圆柱壳的自由振动分析，提出了基于辛空间的波方法。首先基于Kirchhoff-Love薄壳理论，选取合适的状态向量，推导了复合材料层合圆柱壳在辛体系中的振动控制方程；其次利用分离变量法将正交铺设复合材料层合圆柱壳的自由振动问题转化为Hamilton体系下的辛本征值问题；最后根据辛空间波形与圆柱壳模态的对应关系，得到不同边界条件下的自由振动波数，进而得到圆柱壳自由振动问题的代数方程组，求解即可得到正交铺设复合材料层合圆柱壳的固有频率和模态。数值算例对比了本文方法和其他方法的计算得到的圆柱壳固有频率，验证了本文方法的有效性和准确性。

Abstract

A symplectic wave-based method is proposed for the free vibration analysis of cross-ply laminated cylindrical shells with arbitrary boundary conditions. First, based on Kirchhoff-Love's shell theory, the governing equations of a cross-ply laminated cylindrical shell can be established in the symplectic duality system by selecting an appropriate state vector. Secondly, the characteristic equation for cross-ply composite laminated cylindrical shells is derived so that the symplectic eigenproblem can be formed. Finally, the symplectic eigensolution is substituted into the boundary conditions at both ends of the cylindrical shell, and the algebraic equation of the free vibration problem of the cylindrical shell is obtained and then solved to give the natural frequencies and modals of cross-ply composite laminated cylindrical shells. Numerical examples are given to shown the validity and accuracy of the present method through comparing the results obtained using the present and other methods.

导出引用

韩少燕1，李榆银2，高汝鑫3,4. 正交铺设复合材料层合圆柱壳自由振动分析的辛空间波方法[J]. 振动与冲击, 2024, 43(6): 113-120

HAN Shaoyan1，LI Yuyin2，GAO Ruxin3,4. Symplectic wave-based method for the free vibration analysis of cross-ply composite laminated circular cylindrical shells[J]. Journal of Vibration and Shock, 2024, 43(6): 113-120

参考文献

[1] Leissa A W. Vibration of Shells [M]. Scientific and Technical Information Office, NationalAeronautics and Space Administration, Washington, D.C., 1973. [2] Qatu M S. Vibration of Laminated Shells and Plates [M]. Elsevier, Kidlington, 2004. [3] Reddy J N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition [M]. CRC Press, Boca Raton, 2003. [4] Lam K Y, Loy C T. Analysis of rotating laminated cylindrical shells by different thin shell theories [J]. Journal of Sound and Vibration, 1995, 186(1): 23-35. [5] Qatu M S. Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells [J]. Applied Mechanics Reviews, 2002, 55(4): 325-350. [6] Qatu M S. Recent research advances in the dynamic behavior of shells: 1989-2000, Part 2: Homogeneous shells [J]. Applied Mechanics Reviews, 2002, 55(5): 415-434. [7] Shu C, Du H. Free vibration analysis of laminated composite cylindrical shells by DQM [J]. Composites Part B: Engineering, 1997, 28(3): 267-274. [8] Liew K M, Zhao X, Ferreira A J. A review of meshless methods for laminated and functionally graded plates and shells [J]. Composite Structures, 2011, 93(8): 2031-2041. [9] Thinh T I, Nguyen M C. Dynamic stiffness matrix of continuous element for vibration of thick cross-ply laminated composite cylindrical shells [J]. Composite Structures, 2013, 98: 93-102. [10] Qu Y, Hua H, Meng G. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries [J]. Composite Structures, 2013, 95: 307-321. [11] Jin G, Ye T, Chen Y, et al. An exact solution for the free vibration analysis of laminated composite cylindrical shells with general elastic boundary conditions [J]. Composite Structures, 2013, 106: 114-127. [12] Viswanathan K, Javed S. Free vibration of anti-symmetric angle-ply cylindrical shell walls using first-order shear deformation theory [J]. Journal of Vibration and Control, 2016, 22(7): 1757-1768. [13] Khalili S, Davar A, Fard A M. Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory [J]. International journal of Mechanical Sciences, 2012, 56(1): 1-25. [14] Ye T, Jin G, Shi S, et al. Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations [J]. International Journal of Mechanical Sciences, 2014, 84: 120-137. [15] Yao W, Zhong W, Lim C W. Symplectic Elasticity [M]. World Scientific, Singapore, 2009. [16] Li R, Zhong Y, Li M. Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013, 469(2153): 20120681. [17] Zhou Z, Wong K W, Xu X, et al. Natural vibration of circular and annular thin plates by Hamiltonian approach [J]. Journal of Sound and Vibration, 2011, 330(5): 1005-1017. [18] Tong Z Z, Ni Y W, Zhou Z H, et al. Exact solutions for free vibration of cylindrical shells by a symplectic approach [J]. Journal of Vibration Engineering & Technologies, 2018, 6: 107-115. [19] Gao R, Sun X, Liao H, et al. Symplectic wave-based method for free and steady state forced vibration analysis of thin orthotropic circular cylindrical shells with arbitrary boundary conditions [J]. Journal of Sound and Vibration, 2021, 491: 115756. [20] Pan C, Sun X, Zhang Y. Vibro-acoustic analysis of submerged ring-stiffened cylindrical shells based on a symplectic wave-based method [J]. Thin-Walled Structures, 2020, 150: 106698. [21] Pan C, Zhang Y. Coupled vibro-acoustic analysis of submerged double cylindrical shells with stringers, rings, and annular plates in a symplectic duality system [J]. Thin-Walled Structures, 2022, 171: 108671. [22] Fahy F J, Gardonio P. Sound and Structural Vibration, Radiation, Transmission and Response [M]. Academic Press, Amsterdam, 2007.