Frequency analysis of immersed cylindrical shell with finite immersion depth
Wang Peng1,2 Li Tianyun 1,2 Zhu Xiang 1,2 Miao Yuyue 1,2 Zhang Guanjun 1,2
1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science & Technology, Wuhan430074;
2.Hubei Key Laboratory of Naval architecture & Ocean Engineering Hydrodynamics (HUST), Wuhan 430074
Abstract:The natural frequencies of cylindrical shell with finite immersion depth is predicted using the wave propagation approach and the image method. Both the influences of free surface and hydrostatic pressure are considered in theoretical derivation. Based on the numerical analysis, some conclusions are made. Compared with a shell ideally immersed in fluid, free surface will increase structure modal frequency, but the hydrostatic pressure will reduce it. The influence of free surface is quite obvious for relatively small immersion depth, and so is the effect of hydrostatic pressure for relatively large immersion depth. The influence of hydrostatic pressure on structure natural frequency is different for every mode, which will result in the alternate of modal frequency. When the immersion depth is large enough, the shell will face the problem of instability.
[1] Butler D J. Vibrations of an infinitely long cylindrical shell in a semi-infinite acoustic medium[R]. COLUMBIA UNIV NEW YORK, 1958.
[2] Chang K Y, DiMaggio F L. Vibrations of cylindrical shells in a semi-infinite acoustic medium[J]. The Journal of the Acoustical Society of America, 1971, 49(3B): 759-767.
[3] Skidan O, Klosner J M, Baron M L. Sound radiation from a cylinder immersed in an acoustic fluid bounded by an elastic half‐space[J]. The Journal of the Acoustical Society of America, 1974, 56(2): 427-439.
[4] 李天匀, 江丰, 叶文兵等. 有限浸没深度无限长圆柱壳辐射声场波动特性[J]. 中国舰船研究, 2013, 8(1):73-79.
LI Tianyun, JIANG Feng, YE Wenbing, et al. The Wave Characteristics of the Acoustic Radiation from Cylindrical Shells Within Finite Depth from the Free Surface[J]. Chinese Journal of Ship Research, 2013, 8(1):73-79.
[5] 叶文兵, 李天匀, 朱翔等. 刚性壁存在下的水下圆柱壳结构的声振特性研究 (英文)[J]. 船舶力学, 2013, 17(3): 313-325.
YE Wenbing, LI Tianyun, ZHU Xiang, et al. Acoustic Radiation of Cylindrical Shells Submerged in the Fluid in Presence of the Seabed or Dock[J]. Journal of Ship Mechanics, 2013, 17(3): 313-325.
[6] Ergin A, Price W G, Randall R, Temarel P. Dynamic characteristics of a submerged, flexible cylinder vibrating in finite water depths[J]. Journal of ship research, 1992, 36(2): 154-167.
[7] 王宗利, 金占礼,林启荣等. 潜水深度对结构自振特性影响的数值分析[J]. 机械强度, 2001, 23(3): 344-346.
WANG Zongli, JIN Zhanli, LIN Qirong, et al. Numerical analysis of the influence of water depth on the vibration characteristics of submerged structures[J]. Journal of Mechanical Strength, 2001, 23(3): 344-346.
[8] 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.
[9] 刘佩. 潜深对圆柱壳振动声辐射的影响及相似性研究[D]. 大连:大连理工大学, 2013.
LIU Pei. The impact of diving depth on vibration and acoustic radiation of cylindrical shell and research of similarity[D]. Dalian: Dalian University of Technology, 2013.
[10] 刘志忠. 静压条件下圆柱壳 流场耦合系统振动功率流和声辐射特性研究[D]. 武汉:华中科技大学, 2009.
LIU Zhizhong. Characteristics of power flow and sound radiation in cylindrical shell-fluid system considering hydrostatic pressure[D]. Wuhan:Huazhong University of Science & Technology, 2009.
[11] Zhang X M. Frequency analysis of submerged cylindrical shells with the wave propagation approach[J]. International Journal of Mechanical Sciences, 2002, 44(7): 1259-1273.
[12] Lee W M, Chen J T. 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.
[13] Lam K Y, Loy C T. Effects of boundary conditions on frequencies of a multi-layered cylindrical shell[J]. Journal of Sound and vibration, 1995, 188(3): 363-384.