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Vibroacoustic analysis of a partially submerged cylindrical shell-liquid coupling system is a typical acoustic-structure interaction problem in an acoustic half-space. Generally, the vibration and acoustic solutions of this problem almost depend on numerical method in previous studies. However, whether from the aspect of verifying the numerical methods or from the aspect of revealing the vibroacoustic mechanism of the acoustic-structure interaction system, the development of an analytical or semi-analytical method is indispensable. In this study, a semi-analytical method is proposed to address the vibroacoustic response of a horizontal cylindrical shell partially immersed in water The acoustic coordinate system is established on the free surface, and the sine series function is introduced to express the sound pressure to meet the pressure release boundary condition on the free surface automatically. Then based on the two-dimensional Flgge shell theory, the motion equation of the shell-liquid coupling system is established with using the center of the shell as the origin of the coordinate system. By using the Galerkin method, the velocity continuous condition on the fluid-structure interface is established. Then the relation matrix between the acoustic pressure amplitude and the shell displacement amplitude is derived after converting the sound pressure from different coordinate systems into that in the same coordinate system by using the geometry relationship of two coordinate systems. Then the vibration and sound radiation of this coupling system are predicted by solving the coupled matrix equations, and the coupled free vibration can also be addressed by solving the characteristic equation after setting the determinant of the coefficient matrix to be zero. To verify the accuracy and reliability of the present method, the coupled natural frequencies, the vibration response and the distribution of the sound pressure obtained from the present method are compared with those obtained from the finite element method, showing that they are in good agreement with each other. Then the shapes of the first four order modes for the coupled system are presented and compared with those of the system submerged in unbounded fluid field, and the couple between different modes, and the couple between the symmetric and antisymmetric modes are observed due to the effect of the free surface. The characteristics of the root mean square velocity of the shell with different immersed depths are discussed, which reveals that the peaks of response curves shift to the lower frequencies with increasing immersed depth. The characteristics of far field sound pressure directivity are presented and explained by the image method in detail. This study provides a novel method to analytically predict the vibroacoustic response of an elastic structure partially coupling with the fluid field when bounded in a sound half space.
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Keywords:
- cylindrical shell /
- free surface /
- Galerkin method /
- sine series
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[2] Harari A, Sandman B E 1976 J. Acoust. Soc. Am. 60 117
[3] Fuller C R 1988 J. Sound Vib. 122 479
[4] Pan A, Fan J, Wang B, Chen Z G, Zheng G Y 2014 Acta Phys. Sin. 63 214301 (in Chinese)[潘安, 范军, 王斌, 陈志刚, 郑国垠 2014 物理学报 63 214301]
[5] Liu P, Liu S W, Li S 2013 Ship Sci. Technol. 36 36 (in Chinese)[刘佩, 刘书文, 黎胜 2013 舰船科学技术 36 36]
[6] Huang H 1981 Wave Motion 3 269
[7] Hasheminejad S M, Azarpeyvand M 2005 J. Appl. Math. Mech. 85 66
[8] Bai Z G, Wu W W, Zuo C K, Zhang F, Xiong C X 2014 J. Ship Mech. 18 178 (in Chinese)[白振国, 吴文伟, 左成魁, 张峰, 熊晨熙 2014 船舶力学 18 178]
[9] Guo W J, Li T Y, Zhu X, Miao Y Y, Zhang G J 2017 J. Sound Vib. 393 338
[10] Guo W J, Li T Y, Zhu X, Zhang S 2017 Chin. J. Ship Res. 12 62 (in Chinese)[郭文杰, 李天匀, 朱翔, 张帅 2017 中国舰船研究 12 62]
[11] Amabili M 1996 J. Sound Vib. 191 757
[12] Amabili M 1997 J. Vib. Acoust. 119 476
[13] Ye W B, Li T Y, Zhu X 2012 Appl. Mech. Mater. 170 2303
[14] Selmane A, Lakis A A 1997 J. Sound Vib. 5 111
[15] Ergin A, Temarel P 2002 J. Sound Vib. 254 951
[16] Krishna B V, Ganesan N 2006 J. Sound Vib. 291 1221
[17] Hidalgo J A, Gama A L, Moreire R M 2017 J. Sound Vib. 408 31
[18] Escaler X, Torre O D, Goggins J 2017 J. Fluid Struct. 69 252
[19] Li T Y, Wang P, Zhu X, Yang J, Ye W B 2017 J. Vib. Acoust. 139 041002
[20] Li H L, Wu C J, Huang X Q 2003 Appl. Acoust. 64 495
[21] Li T Y, Wang L, Guo W J, Yang G D, Zhu Xiang 2016 Chin. J. Ship Res. 11 106 (in Chinese)[李天匀, 王露, 郭文杰, 杨国栋, 朱翔 2016 中国舰船研究 11 106]
[22] Zhu X, Ye W B, Li T Y, Chen C 2013 Ocean Eng. 58 22
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[1] Williams W, Parke N G, Moran D A, Sherman C H 1964 J. Acount. Soc. Am. 36 2316
[2] Harari A, Sandman B E 1976 J. Acoust. Soc. Am. 60 117
[3] Fuller C R 1988 J. Sound Vib. 122 479
[4] Pan A, Fan J, Wang B, Chen Z G, Zheng G Y 2014 Acta Phys. Sin. 63 214301 (in Chinese)[潘安, 范军, 王斌, 陈志刚, 郑国垠 2014 物理学报 63 214301]
[5] Liu P, Liu S W, Li S 2013 Ship Sci. Technol. 36 36 (in Chinese)[刘佩, 刘书文, 黎胜 2013 舰船科学技术 36 36]
[6] Huang H 1981 Wave Motion 3 269
[7] Hasheminejad S M, Azarpeyvand M 2005 J. Appl. Math. Mech. 85 66
[8] Bai Z G, Wu W W, Zuo C K, Zhang F, Xiong C X 2014 J. Ship Mech. 18 178 (in Chinese)[白振国, 吴文伟, 左成魁, 张峰, 熊晨熙 2014 船舶力学 18 178]
[9] Guo W J, Li T Y, Zhu X, Miao Y Y, Zhang G J 2017 J. Sound Vib. 393 338
[10] Guo W J, Li T Y, Zhu X, Zhang S 2017 Chin. J. Ship Res. 12 62 (in Chinese)[郭文杰, 李天匀, 朱翔, 张帅 2017 中国舰船研究 12 62]
[11] Amabili M 1996 J. Sound Vib. 191 757
[12] Amabili M 1997 J. Vib. Acoust. 119 476
[13] Ye W B, Li T Y, Zhu X 2012 Appl. Mech. Mater. 170 2303
[14] Selmane A, Lakis A A 1997 J. Sound Vib. 5 111
[15] Ergin A, Temarel P 2002 J. Sound Vib. 254 951
[16] Krishna B V, Ganesan N 2006 J. Sound Vib. 291 1221
[17] Hidalgo J A, Gama A L, Moreire R M 2017 J. Sound Vib. 408 31
[18] Escaler X, Torre O D, Goggins J 2017 J. Fluid Struct. 69 252
[19] Li T Y, Wang P, Zhu X, Yang J, Ye W B 2017 J. Vib. Acoust. 139 041002
[20] Li H L, Wu C J, Huang X Q 2003 Appl. Acoust. 64 495
[21] Li T Y, Wang L, Guo W J, Yang G D, Zhu Xiang 2016 Chin. J. Ship Res. 11 106 (in Chinese)[李天匀, 王露, 郭文杰, 杨国栋, 朱翔 2016 中国舰船研究 11 106]
[22] Zhu X, Ye W B, Li T Y, Chen C 2013 Ocean Eng. 58 22
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