Structural Engineering and Mechanics

  • 제40권5호
  • /
  • Pages.665-688
  • /
  • 2011
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Hydroelastic vibration analysis of liquid-contained rectangular tanks

  • 투고 : 2011.02.06
  • 심사 : 2011.10.12
  • 발행 : 2011.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

키워드

참고문헌

  1. Cheung, Y.K. and Zhou, D. (2000), "Coupled vibratory characteristics of a rectangular container bottom plate", J. Fluid. Struct., 14, 339-357. https://doi.org/10.1006/jfls.1999.0272
  2. Cupial, P. (1997), "Calculation of the natural frequencies of composite plates by the Rayleigh-Ritz method with orthogonal polynomials", J. Sound Vib., 201, 385-387. https://doi.org/10.1006/jsvi.1996.0802
  3. Dickinson, S.M. and Di Blasio, A. (1986), "On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates", J. Sound Vib., 108, 51-62. https://doi.org/10.1016/S0022-460X(86)80310-8
  4. Ergin, A. and Ugurlu, B. (2003), "Linear vibration analysis of cantilever plates partially submerged in fluid", J. Fluid. Struct., 17, 927-939. https://doi.org/10.1016/S0889-9746(03)00050-1
  5. Hashemi, H.S., Karimi, M. and Taher, H.R.D. (2010), "Vibration analysis of rectangular mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method", Ocean Eng., 37, 174-185. https://doi.org/10.1016/j.oceaneng.2009.12.001
  6. Hashemi, H.S., Karimi, M. and Rokni, H.R. (2010), "Hydroelastic vibration and bucking of rectangular Mindlin plates on Pasternak foundations under linearly varying in-plane loads", Soil Dyn. Earthq. Eng., 30, 1487-1499. https://doi.org/10.1016/j.soildyn.2010.06.019
  7. Jeong, K.H. and Lee, S.C. (1998), "Hydroelastic vibration of a liquid-filled circular cylindrical shell", Comput. Struct., 66, 173-185. https://doi.org/10.1016/S0045-7949(97)00086-2
  8. Jeong, K.H., Yoo, G.H. and Lee, S.C. (2003), "Hydroelastic vibration of two identical rectangular plates", J. Sound Vib., 272, 539-555.
  9. Jeong, K.H. and Kim, J.W. (2009), "Hydroelastic vibration analysis of two flexible rectangular plates partially coupled with a liquid", Nucl. Eng. Tech., 41, 335-346. https://doi.org/10.5516/NET.2009.41.3.335
  10. Kerboua, Y., Lakis, A.A.,Thomas, M. and Marcouiller, L. (2008), "Vibration analysis of rectangular plates coupled with fluid", Appl. Math. Model., 32, 2570-2586. https://doi.org/10.1016/j.apm.2007.09.004
  11. Liang, C.C., Liao, C.C., Tai, Y.S. and Lai, W.H. (2001), "The free vibration analysis of submerged cantilever plates", Ocean Eng., 28, 1225-1245. https://doi.org/10.1016/S0029-8018(00)00045-7
  12. Ugurlu, B., Kutlu, A., Ergin, A. and Omurtag, M.H. (2008), "Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid", J. Sound Vib., 317, 308-328. https://doi.org/10.1016/j.jsv.2008.03.022
  13. Yadykin, Y., Tenetov, V. and Levin, D. (2003), "The added mass of a flexible plate oscillating in a fluid", J. Fluid. Struct., 17, 115-123. https://doi.org/10.1016/S0889-9746(02)00100-7
  14. Zhou, D. and Cheung, Y.K. (2000), "Vibration of vertical rectangular plate in contact with water on one side", Earthq. Eng. Struct. Dyn., 29, 693-710. https://doi.org/10.1002/(SICI)1096-9845(200005)29:5<693::AID-EQE934>3.0.CO;2-V
  15. Zhou, D. and Liu, W. (2007), "Hydroelastic vibrations of flexible rectangular tanks partially filled with liquid", Int. J. Numer. Method. Eng., 71, 149-174. https://doi.org/10.1002/nme.1921

피인용 문헌

  1. Experimental analysis on FEM definition of backfill-rectangular tank-fluid system vol.5, pp.2, 2013, https://doi.org/10.12989/gae.2013.5.2.165
  2. Free vibration analysis of liquid-filled open rectangular containers vol.99, 2015, https://doi.org/10.1016/j.oceaneng.2015.03.003
  3. Hydroelastic Vibration of a Rectangular Tank Partially Surrounding with a Liquid vol.25, pp.3, 2015, https://doi.org/10.5050/KSNVE.2015.25.3.207
  4. Seismic response of rectangular liquid retaining structures resting on ground considering coupled soil-structure interaction vol.15, pp.9, 2017, https://doi.org/10.1007/s10518-017-0097-7
  5. Response Suppression of Multiple Hinged Floating Structures by Using Rubber Cushion vol.2021, pp.None, 2011, https://doi.org/10.1155/2021/1208336