Free vibration of a submerged cylindrical shell considering the effect of free surface in finite depth
GUO Wenjie1,2 LI Tianyun1,2,3 ZHU Xiang1,2 MIAO Yuyue1,2 YANG Guodong1,2
1.School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;
2.Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, Wuhan 430074, China;
3.Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Abstract：An analytical method is proposed to solve the vibration characteristics of a submerged finite cylindrical shell at finite depth from the free surface. Based on the image method and the Graf’s addition theorem, the analytical expression of the velocity potential of fluid is obtained. By combining the velocity potential of fluid and the energy functional variation principle, the fluid-structure coupling equation of the submerged finite cylindrical shell are deduced, then the natural frequencies of the submerged finite cylindrical shell can be calculated. It is found that, with the same modal order, the natural frequency of the submerged finite cylindrical shell with the free surface is larger than that without the free surface. The natural frequency increases as the finite cylindrical shell approaches the free surface. Moreover, the free vibration characteristics of the submerged finite cylindrical shell with the free surface tend to be the same as those without the free surface as the increase of the submerged depth. The reliability and efficiency of the present method are validated by comparison with the finite element method. The work provides more understanding on the vibration characteristics of a submerged finite cylindrical shell in finite water depths.
郭文杰1,2，李天匀1,2,3，朱翔1,2，缪宇跃1,2, 杨国栋1,2. 计及自由液面影响的水下有限深度圆柱壳自由振动分析[J]. 振动与冲击, 2017, 36(10): 1-6.
GUO Wenjie1,2 LI Tianyun1,2,3 ZHU Xiang1,2 MIAO Yuyue1,2 YANG Guodong1,2. Free vibration of a submerged cylindrical shell considering the effect of free surface in finite depth. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(10): 1-6.
[1] 徐慕冰, 圆柱壳-流场耦合系统的振动波传播与能量流研究[D]. 武汉: 华中科技大学, 1998.
XU Mubing, Wave propagation and power flow in a cylindrical shell-fluid coupled system [D]. Wuhan: Huazhong University of Science and Technology, 1998.
[2] X. M. Zhang, G. R. Liu, K. Y. Lam. Coupled vibration analysis of fluid-filled cylindrical shells [J]. Applied Acoustics, 2001, 62(3): 229-243.
[3] X. M. Zhang. Frequency analysis of submerged cylindrical shells with the wave propagation approach [J], International Journal of Mechanical Sciences, 2002, 44(7): 1259-1273.
[4] 曹雷, 马运义, 黄玉盈, 基于Riccati传递矩阵法分析水下有限长环肋圆柱壳的声辐射性能[J]. 振动与冲击, 2009, 28(9): 149-154.
CAO Lei, MA Yunyi, HUANG Yuying, Analysis of acoustic radiation of a ring-stiffened cylindrical shell with finite length in underwater based on Riccati transfer matrix method [J]. Journal of Vibration and Shock, 2009, 28(9): 149-154.
[5] 李学斌, 环肋圆柱壳自由振动分析的能量法[J]. 船舶力学, 2001, 5(2): 73-81.
LI Xuebin, Energy method for free vibration analysis of ring - stiffened cylindrical shells [J]. Journal of Ship Mechanics, 2001, 5(2): 73-81.
[6] A. Ergin, W. G. Price, R. Randall, et al. Dynamic characteristics of a submerged, flexible cylinder vibrating in finite water depths [J]. Journal of Ship Research, 36, 154-167, 1992.
[7] M. Amabili. Free vibration of partially filled horizontal cylindrical shells [J]. Journal of Sound and Vibration, 1996, 191(5): 757-780.
[8] M. Amabili. Flexural vibration of cylindrical shells partially coupled with external and internal fluids [J], Journal of Vibration and Acoustics, 1997, 119(3): 476-484
[9] A. Ergin, P. Temarel. Free vibration of a partially liquid filled and submerged horizontal cylindrical shell [J]. Journal of Sound and Vibration, 2002, 254(5): 951-965.
[10] 王斌, 汤渭霖, 半潜状态圆柱壳振动声辐射特性研究 [C], 第十二届船舶水下噪声学术讨论会论文集, 中国长沙, 2009.
WANG Bing, TANG Weilin, Vibro-acoustic characteristics analysis of semi submerged cylindrical shells [C], 12th Conference on ship underwater noise, Changsha, China, 2009: 33-37.
[11] 白振国, 吴文伟, 左成魁, 等, 有限水深环境圆柱壳声辐射及传播特性[J] 船舶力学, 2014, 18(1-2): 178-190.
BAI Zhenguo, WU Wenwei, ZUO Chengkui, et al. Sound radiation and spread characteristics of cylindrical shell in finite depth water [J]. Journal of Ship Mechanics, 2014, 18(1):178-190.
[12] T. Y. Li, Y. Y. Miao, W. B. Ye, et al. Far-field sound radiation of a submerged cylindrical shell at finite depth from the free surface [J]. The Journal of the Acoustical Society of America, 2014, 136(3): 1054-1064.
[13] 刘佩, 刘书文, 黎胜. 潜深对水下圆柱壳振动声辐射特性的影响[J]. 舰船科学技术, 2014, 36(5): 36-41.
LIU Pei, LIU Shuwen, LI Sheng.The effects of immersion depth of submerged cylindrical shell on vibro-acoustic characteristics[J].Ship Science and Technology,2014,36(5):36-41.
[14] Q. Zhou, P. F. Joseph. A numerical method for the calculation of dynamic response and acoustic radiation from an underwater structure [J]. Journal of Sound and Vibration, 2005, 283(3): 853-873.
[15] M. Junge, D. Brunner, J. Becker, et al. Interface-reduction for the Craig-Bampton and Rubin method applied to FE-BE coupling with a large fluid–structure interface [J]. International Journal for Numerical Methods in Engineering, 2009, 77(12): 1731-1752.
[16] 邹明松, 吴有生, 沈顺根, 等, 考虑航速及自由液面影响的声介质中三维结构水弹性力学研究[J], 船舶力学, 2010, 14(11): 1304-1311.
ZOU Mingsong, WU Yousheng, SHEN Shungen, et al, Three-dimensional hydro elasticity with forward speed and free surface in acoustic medium [J]. Journal of Ship Mechanics, 2010, 14(11): 1304-1311.
[17] W. M. Lee, J. T. Chen. Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method [J]. International Journal of Solids and Structures, 2010, 47(9): 1118-1129.
