DOI QR코드

DOI QR Code

Liquid boundary effect on free vibration of an annular plate coupled with a liquid

  • Kyeong-Hoon Jeong (SMART System Development Division, Korea Atomic Energy Research Institute)
  • 투고 : 2023.01.19
  • 심사 : 2023.04.03
  • 발행 : 2023.04.25

초록

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

키워드

과제정보

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF- 2020M2D7A1079180).

참고문헌

  1. Amabili, M. (1996), "Effect of finite fluid depth on the hydroelastic vibrations of circular and annular plates", J. Sound Vib., 193(4), 909-925. https://doi.org/10.1006/jsvi.1996.0322.
  2. Amabili, M., Frosali, G. and Kwak, M.K. (1996), "Free vibrations of annular plates coupled with fluids", J. Sound Vib., 191(5), 825-846. https://doi.org/10.1006/jsvi.1996.0158.
  3. Askari, E., Jeong, K.H. and Amabili, M. (2013), "Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface", J. Sound Vib., 332(12), 3064-3085. https://doi.org/10.1016/j.jsv.2013.01.007.
  4. Askari, E., Jeong, K.H., Ahn, K.H. and Amabili, M. (2020), "A mathematical approach to study fluid-coupled vibration of eccentric annular plates", J. Fluid. Struct., 98, 103129. https://doi.org/10.1016/j.jfluidstructs.2020.103129.
  5. Bauer, H. and Komatsu, K. (2000), "Coupled frequencies of a frictionless liquid in a circular cylindrical tank with an elastic partial surface cover", J. Sound Vib., 230(5), 1147-1163. https://doi.org/10.1006/jsvi.1999.2662.
  6. Chen, G.W., Liao, C.Y., Lin, Y.Z. and Ma, C.C. (2021), "Analytic solution to the coupled characteristics of a rectangular plate partially immersed in a finite fluid container", J. Sound Vib., 515, 116446. https://doi.org/10.1016/j.jsv.2021.116446.
  7. Escaler, X. and De La Torre, O. (2018), "Axisymmetric vibrations of a circular Chladni plate in air and fully submerged in water", J. Fluid. Struct., 82, 432-445. https://doi.org/10.1016/j.jfluidstructs.2018.07.017.
  8. Hosseini, M., Goudarzi. M.A. and Soroor. A. (2017), "Reduction of seismic sloshing in floating roof liquid storage tanks by using a suspended annular baffle", J. Fluid. Struct., 71, 40-55. http://dx.doi.org/10.1016/j.jfluidstructs.2017.02.008.
  9. Jeong, K.H. (2006), "Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid", J. Fluid. Struct., 22(8), 1079-1096. https://doi.org/10.1016/j.jfluidstructs.2006.07.001.
  10. Jeong, K.H. and Kim, K.J. (2005), "Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid", J. Sound Vib., 283(1-2), 153-172. https://doi.org/10.1016/j.jsv.2004.04.029.
  11. Kim, Y.W. and Lee, Y.S. (2005), "Coupled vibration analysis of liquid-filled rigid cylindrical storage tank with an annular plate cover", J. Sound Vib., 279(1-2), 217-235. https://doi.org/10.1016/j.jsv.2003.10.032.
  12. Kwak, M.K. and Amabili, M. (1999), "Hydroelastic vibration of free-edge annular plates", ASME J. Vib. Acoust., 121, 26-32. https://doi.org/10.1115/1.2893944.
  13. Kwak, M.K. and Han, S.B. (2000), "Effect of fluid depth on the hydroelastic vibration of free-edge circular plate", J. Sound Vib., 230(1), 171-185. https://doi.org/10.1006/jsvi.1999.2608.
  14. Liang, C.C., Tai, Y.S. and Li, P.L. (1999), "Natural frequencies of annular plates having contact with fluid", J. Sound Vib., 228(5), 1167-1181. https://doi.org/10.1006/jsvi.1999.2463.
  15. Lin, G.Z., Yang, Y., He, Z.G. and Jiao, P.C. (2022), "Hydrodynamic optimization in high-acceleration underwater motions using added-mass coefficient", Ocean Eng., 263, 112274. https://doi.org/10.1016/j.oceaneng.2022.112274.
  16. Wang, P.G., Zhao, M. and Du, X.L. (2019), "A simple added mass model for simulating elliptical cylinder vibrating in water under earthquake action", Ocean Eng., 179, 351-360. https://doi.org/10.1016/j.oceaneng.2019.02.046.
  17. Zhang, J.R., Wei, K. and Qin, S.Q. (2022), "An efficient numerical model for hydrodynamic added mass of immersed column with arbitrary cross section", Ocean Eng., 187, 106192. https://doi.org/10.1016/j.oceaneng.2019.106192.