An analytical method of free vibration analysis of elliptic cylindrical shell with ring stiffeners#br#

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (12) : 138-146.

FANG Min1，ZHU Xiang1,2，LI Tianyun1,2,HU xiaofang3

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Abstract

An analytical solution about the free vibration behaviors of a finite elliptic cylindrical shell with ring stiffeners was proposed. The vibration equations of the shell were derived based on the Flügge shell theory and the effects of ring stiffeners were evaluated via the “smeared” stiffener theory whereby the properties of the stiffeners were averaged over the shell surface. The displacements of the shell were expanded in double Fourier series in the axial and circumferential directions and the circumferential curvature was expanded in single Fourier series in the circumferential direction. A set of partial differential equations with variable coefficients was transformed into a set of linear equations with constant coefficients and then the natural frequencies of free vibration of elliptic cylindrical shell with ring stiffeners were obtained. To verify the accuracy of the present method, the finite elliptic cylindrical shell with ring stiffeners was degenerated into two models, one of which is a ringstiffened circular cylindrical shell and the other of which is an elliptic cylindrical shell without ring stiffeners. The present results of the two degenerated shells show good agreements with available results from literature. At the same time, compared with the finite element method, the accuracy of the method was verified directly, and the application scope of the method was given. The influences of main parameters of the shell and ring stiffeners on the vibration characteristics, such as ellipticity parameter, stiffeners interval ratio and height of the stiffeners, were also discussed in detail.

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elliptic cylindrical shell with ring stiffeners / free vibration / Fourier series / “smeared&rdquo / stiffener theory

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FANG Min1，ZHU Xiang1,2，LI Tianyun1,2, HU Xiaofang3. An analytical method of free vibration analysis of elliptic cylindrical shell with ring stiffeners#br#[J]. Journal of Vibration and Shock, 2018, 37(12): 138-146

References

[1] 骆东平,张玉红. 环肋增强柱壳振动特性分析[J]. 中国造船,1989(1):66-77.
LUO Dong-ping, ZHANG Yu-hong. Analysis of vibration characteristics of ring-stiffened cylindrical shell[J]. Shipbuilding of China,1989(1):66-77.
[2] 梁斌, 李戎, 刘小宛,等. 基于波动法的静水压力下环肋圆柱壳耦合振动特性研究[J]. 振动与冲击, 2014(21):142-147.
LIANG Bin, LI Rong, LIU Xiao-wan, et al. Coupled vibration of ring - stiffened cylindrical shells under hydrostatic pressure based on wave method[J].Journal of Vibration and Shock, 2014(21):142-147.
[3] 张盛,金翔,周桦,等.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,2011,04:43-50.
ZHANG Sheng, JIN Xiang, ZHOU Hua ,et al. Study on the influence of manufacturing error on the acoustic performance of the stiffened cylindrical shell[J]. Chinese Journal of Ship Research, 2011,04:43-50.
[4] 赵天奉,段梦兰,杨晓刚,等. 深水导管架桩腿制造误差与抗屈曲特性研究[J].船舶力学,2009,02:241-249.
ZHAO Tian-feng, DUAN Meng-lan, YANG Xiao-gang,et al. Study on manufacturing error and buckling resistance of pile legs in deep water jacket[J]. Journal of Ship Mechanics, 2009,02:241-249.
[5] Boyd D E, Culberson L D. Free vibrations of freely supported oval cylinders[J]. Aiaa Journal, 1971, 9(8):1474-1480.
[6] Chen Y N, Kempner J. Modal Method for Free Vibration of Oval Cylindrical Shells With Simply Supported or Clamped Ends[J]. Journal of Applied Mechanics, 1978, 45(1):142-148.
[7] Armenakas A E, Koumousis V K. Free vibrations of simply supported cylindrical shells of oval crosssection[J]. Aiaa Journal, 1983, 21(7):1017-1027.
[8] 熊路,李天匀,朱翔. 基于双Fourier级数表达的椭圆柱壳自由振动特性分析研究[A].第十四届船舶水下噪声学术讨论会论文集[C]. 2013:10.
XIONG Lu, LI Tian-yun, ZHU Xiang. Free vibration analysis of elliptic cylindrical shell based on double Fourier series representation[A]. Proceeding of the 14th Symposium on Underwater Noise of Ships[C]. 2013:10.
[9] 熊路. 典型非圆截面柱壳的声振固有特性研究[D]. 华中科技大学, 2014.
XIONG Lu. Study on acoustic-vibration inherent characteristics of typical noncircular cylindrical shells[D]. Huazhong University of Science and Technology
[10] Boyd D E, Rao C K P. A theoretical analysis of the free vibrations of ring- and/or stringer-stiffened elliptical cylinders with arbitrary end conditions. Volume 1: Analytical derivation and applications[J]. 1973.
[11] 邹时智, 黄玉盈, 何锃,等. 周向加肋非圆柱壳谐振分析的一个新矩阵方法[J]. 应用数学和力学, 2007, 28(10):1245-1252.
ZOU Shi-zhi, HUANG Yu-ying, HE Zeng, et al. A new matrix method for response analysis of circular stiffened non-cylinndrical shell[J]. Applied Mathematics and Mechanics, 2007, 28(10):1245-1252.
[12] Brodsky W L, Vafakos W P. Buckling analysis of ring-stiffened oval cylindrical shells[J]. Computers & Structures, 1974, 4(6): 1135-1158.
[13] Flügge W. Stress in shells, Berlin:Springer-Verlag, New York, 1973.
[14] Marguerre K. Stability of The Cylindrical Shells of Variable Curvature [J]. NASA, 1951, TM 1302.
[15] Romano F, Kempner J. Stresses in Short Noncircular Cylindrical Shells under Lateral Pressure [J]. ASME Journal of Applied Mechanics, 1962, 29: 669-674.
[16] Zhang XM, Liu GR, Lam KY. Vibration analysis of thin cylindrical shells using wave propagation approach [J]. Journal of Sound and Vibration. 2001, 239(3): 397-403.
[17] NL Basdekas, M Chi. Response of oddly-stiffened circular cylindrical shells [J]. Journal of Sound and Vibration, 1971, 17(2):187-206.
[18] Elsbernd GF, Leissa AW. The Vibrations of Non-circular Cylindrical Shells with Initial Stresses [J]. Journal of Sound and Vibration, 1973, 29(3):309-329.
[19] Jafari AA, Bagheri M. Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods [J]. Thin-Walled Structures, 2006, 44(1): 82-90.
[20] Hao P, Wang B, Li G, Meng Z, Tian K, Tang X. Hybrid optimization of hierarchical stiffened shells based on smeared stiffener method and finite element method [J]. Thin-Walled Structures, 2014, 82: 46-54.