Free vibration characteristics of elliptic cylindrical shell based on wave propagation method

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (12) : 189-195.

ZHANG Guan-jun ZHU Xiang LI Tian-yun MIAO Yu-yue

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Abstract

The free vibration equations of elliptic cylindrical shell are derived based on Flügge shell theory. Vibration equations are not decoupled about the circumferential wave number due to the varied circumferential curvature. The shell’s displacements are expanded in double Fourier series in wave propagation method and the circumferential curvature is expanded in single Fourier series. The partial differential equations with variable coefficients are converted into a set of linear equations which couple with each other about circumferential wave numbers. The natural frequencies of elliptic cylindrical shell are obtained by solving the coupled equations. The influences of main parameters of elliptic cylindrical shell, such as ellipticity parameter and shell length ratio, on the vibration characteristics are discussed in detail. The symmetric and anti-symmetric modes of elliptic cylindrical shell are both considered.

Key words

elliptic cylindrical shell / free vibration / natural frequency / ellipticity parameters / anti-symmetric mode

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ZHANG Guan-jun ZHU Xiang LI Tian-yun MIAO Yu-yue. Free vibration characteristics of elliptic cylindrical shell based on wave propagation method[J]. Journal of Vibration and Shock, 2017, 36(12): 189-195

References

[1] 龚有根, 贺玲凤. 含有初始凹陷缺陷圆柱壳稳定承载能力的实验研究与数值计算[J]. 实验力学, 2010, 25(1): 73～80.
Gong You-gen, He Ling-feng. Experimental study and numerical calculation of stability and load-carrying capacity of cylindrical shell with initial dent[J]. Journal of Experimental Mechanics, 2010, 25(1): 73~80.
[2] 张盛, 金翔, 周桦. 加肋圆柱壳制造误差对声学性能的影响研究[J]. 中国舰船研究, 2011, 6(4): 43～50.
Zhang Sheng, Jin Xiang, Zhou Hua. Influence of construction error on sound radiation for ring-stiffened cylindrical shell[J]. Chinese Journal of Ship Research, 2011, 6(4): 43~50.
[3] Klosner J M, Pohle, F V. Natural frequencies of an infinitely long noncircular cylindrical shell[R]. PIBAL Rept. 476, 1958.
[4] Klosner J M. Frequencies of an infinitely long noncircular cylindrical shell[R]. PIBAL Rept. 552, 1959.
[5] Culberson L D, Boyd D E. Free vibrations of freely supported oval cylinders[J]. AIAA Journal, 1971, 9(8): 1474～1480.
[6] Carl E K, Boyd D E. Free vibrations of noncircular cylindrical shell segments[J]. AIAA Journal, 1971, 9(2): 239～244.
[7] Elsbernd G F, Leissa A W. The vibrations of non-circular cylindrical shells with initial stresses[J]. Journal of Sound and Vibration, 1973, 29(3): 309～329.
[8] 朱建雄，曹志远，李国豪. 非圆柱壳在各种边界条件下的自由振动分析[J]. 力学学报. 1992, 24(2): 171-179.
Zhu Jian-xiong, Cao Zhi-yuan, Li Guo-hao. Free vibration of noncircular cylindrical shells with arbitrary boundary conditions[J]. Journal of Theoretical and Applied Mechanics, 1992, 24(2): 171-179.
[9] Khalifa M. Effects of non-uniform Winkler foundation and non-homogeneity on the free vibration of an orthotropic elliptical cylindrical shell[J]. European Journal of Mechanics-A/Solids, 2015, 49: 570-581.
[10] Ahmed, Khalifa M. Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness[J]. Mathematical Methods in the Applied Sciences, 2011, 34(14):1789-1800.
[11] 曹雷, 马运义, 黄玉盈. 环肋加强变厚度圆柱壳的自由振动[J]. 华中科技大学学报: 城市科学版, 2007, 24(2): 63-66.
Cao Lei, Ma Yunyi, Huang Yuying. Free Vibration of Ring-Stiffened Circular Cylindrical Shell with Variable Thickness[J]. Journal of Huazhong University of Science and Technology(Urban Science Edition), 2007, 24(2): 63-66.
[12] Tornabene F, Fantuzzi N, Bacciocchi M, et al. Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method[J]. Thin-Walled Structures, 2015, 97: 114-129.
[13] Namazi M M, Aghanajafi C. The Analyze of Vibration of Composite Elliptical Shell[J]. Australian Journal of Basic and Applied Sciences, 2010, (7):1542-1554.
[14] Flügge W. Stress in shells[M]. Second Edition. Berlin and New York: Spring-Verlag, 1973. 204-219.
[15] Marguerre K. Stability of the cylindrical shells of variable curvature[R]. NASA TM 1302, 1951.
[16] Romano F, Kempner J. Stresses in short noncircular cylindrical shells under lateral pressure[J]. Journal of Applied Mechanics, 1962, 29(4): 669-674.
[17] Zhang X M, Liu G R, Lam K Y. Vibration analysis of thin cylindrical shells using wave propagation approach[J]. Journal of Sound and Vibration, 2001, 239(3): 397-403.