Structural Engineering and Mechanics

  • 제44권3호
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  • Pages.267-288
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  • 2012
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibrations of arbitrary quadrilateral thick plates with internal columns and uniform elastic edge supports by pb-2 Ritz method

  • Wu, L.H. (Department of Engineering Mechanics, Shijiazhuang Tiedao University)
  • 투고 : 2012.03.30
  • 심사 : 2012.09.26
  • 발행 : 2012.11.10
⟨ 이전 논문 다음 논문 ⟩

초록

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

키워드

참고문헌

  1. Cheung, Y.K. and Zhou, D. (1999), "The free vibration of rectangular composite plates with point supports using static beam functions", Compos. Struct., 44, 145-154. https://doi.org/10.1016/S0263-8223(98)00122-6
  2. Cheung, Y.K. and Zhou, D. (2000), "Vibrations of rectangular plates with elastic intermediate line-supports and edge constraints", Thin Wall. Struct., 37, 305-331. https://doi.org/10.1016/S0263-8231(00)00015-X
  3. Du, J., Li, W.L., Liu, Z., Yang, T. and Jin, G. (2011), "Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints", J. Sound Vib., 330(4), 788-804. https://doi.org/10.1016/j.jsv.2010.08.044
  4. Fan, S.C. and Cheung, Y.K. (1984), "Flexural free vibrations of rectangular plates with complex support conditions", J. Sound Vib., 93, 81-94. https://doi.org/10.1016/0022-460X(84)90352-3
  5. Gorman, D.J. (1999), "Accurate free vibration analysis of point supported Mindlin plates by the superposition method", J. Sound Vib., 219, 265-277. https://doi.org/10.1006/jsvi.1998.1874
  6. Huang, M.H. and Thambiratnam, D.P. (2001), "Free vibration analysis of rectangular plates on elastic intermediate supports", J. Sound Vib., 240, 567-580. https://doi.org/10.1006/jsvi.2000.3239
  7. Huang, M.H. and Zhao, M.Y. (2001), "Static and free vibration analysis of plate on column supports by different models", J. Nanchang Univ., 23(3), 18-25. (in Chinese)
  8. Karunasena, W., Liew, K.M. and Bermani, F.G.A. (1996), "Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method", J. Sound Vib., 196, 371-385. https://doi.org/10.1006/jsvi.1996.0489
  9. Kim, C.S. and Dickinson, S.M. (1987), "The flexural vibration of rectangular plates with point supports", J. Sound Vib., 117, 249-261. https://doi.org/10.1016/0022-460X(87)90537-2
  10. Kitipornchai, S., Xiang, Y. and Liew, K.M. (1994), "Vibration analysis of corner supported Mindlin plates of arbitrary shape using the Lagrange multiplier method", J. Sound Vib., 173(4), 457-470. https://doi.org/10.1006/jsvi.1994.1241
  11. Lee, L.T. and Lee, D.C. (1997), "Free vibration of rectangular plates on elastic point supports with the application of a new type of admissible function", Comput. Struct., 65, 149-156. https://doi.org/10.1016/S0045-7949(96)00426-9
  12. Liew, K.M., Xiang, Y., Kitipornchai, S. and Lim, M.K. (1994), "Vibration of Mindlin plates in point supports using constraint functions", J. Eng. Mech., 120, 499-513. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:3(499)
  13. Malekzadeh, P. and Karami, G. (2008), "Large amplitude flexural vibration analysis of tapered plates with edges elastically restrained against rotation using DQM", Eng. Struct., 30, 2850-2858. https://doi.org/10.1016/j.engstruct.2008.03.016
  14. Narita, Y. (1981), "Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions", J. Sound Vib., 77, 345-355. https://doi.org/10.1016/S0022-460X(81)80171-X
  15. Narita, Y. (1984), "Note on vibrations of point supported rectangular plates", J. Sound Vib., 93, 593-597. https://doi.org/10.1016/0022-460X(84)90428-0
  16. Narita, Y. (1985), "The effects of point constraints on transverse vibration of cantilever plates", J. Sound Vib., 102, 305-313. https://doi.org/10.1016/S0022-460X(85)80144-9
  17. Ohya, F., Ueda, M., Uchiyama, T. and Kikuchi, M. (2006), "Free vibration analysis by the superposition method of rectangular Mindlin plates with internal columns resting on uniform elastic edge supports", J. Sound Vib., 289, 1-24. https://doi.org/10.1016/j.jsv.2005.01.030
  18. Reddy, J.N. (1999), Theory and Analysis of Elastic Plates, Taylor & Francis, Philadephia.
  19. Seyedemad, M., Massood, M. and John, E.A. (2012), "On the free vibration response of rectangular plates, partially supported on elastic foundation" Appl. Math. Mode., 36, 4473-4482. https://doi.org/10.1016/j.apm.2011.11.076
  20. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates-first order and higher order analyses", Int. J. Solids Struct., 42, 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  21. Wang, Y., Wang, Z.M. and Ruan, M. (2010), "Application of meshless method in the transverse vibration of rectangular thin plate with elastic point supports", Chinese J. Comput. Mech., 27(2), 238-243. (in Chinese)
  22. Wu, L.H. (2001), " Free vibration of arbitrary quadrilateral thick plates", Chin. Quart. Mech., 22(2), 258-263.
  23. Wu, L.H. and Liu, J. (2005), "Free vibration analysis of arbitrary shaped thick plates by differential cubature method", Int. J. Mech. Sci., 47, 63-81. https://doi.org/10.1016/j.ijmecsci.2004.12.003
  24. Wu, L.H. and Lu, Y. (2011), "Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method", Int. J. Mech. Sci., 53, 494-504. https://doi.org/10.1016/j.ijmecsci.2011.04.006
  25. Xiang, Y., Liew, K.M. and Kitipornchai, S. (1997), "Vibration analysis of rectangular plates resting on elastic edge supports", J. Sound Vib., 204(1), 1-16. https://doi.org/10.1006/jsvi.1996.0922
  26. Zhou, D. (2002), "Vibrations of point supported rectangular plates with variable thickness using a set of static tapered beam functions", Int. J. Mech. Sci., 44, 149-164. https://doi.org/10.1016/S0020-7403(01)00081-9
  27. Zhou, D. and Ji, T. (2006), "Free vibration of rectangular plates with internal column supports", J. Sound Vib., 297, 146-166. https://doi.org/10.1016/j.jsv.2006.03.031
  28. Zhou, D., Cheung, Y.K. and Kong, J. (2000), "Free vibration of thick layered rectangular plates with point supports by finite layer method", Int. J. Solids Struct., 37, 1483-1499. https://doi.org/10.1016/S0020-7683(98)00316-3
  29. Zhou, D. (2001), "Vibrations of Mindlin rectangular plates with elastic restrained edges using static Timoshenko beam functions in Rayleigh-Ritz method", Int. J. Solids Struct., 38, 5565-5580. https://doi.org/10.1016/S0020-7683(00)00384-X
  30. Zhou, D., Lo, S.H., Au, F.T.K., Cheung, Y.K. and Liu, W.Q. (2006), "3-D vibration analysis of skew thick plates using Chebyshev-Ritz method", Int. J. Mech. Sci., 48, 1481-1493. https://doi.org/10.1016/j.ijmecsci.2006.06.015
  31. Zhou, D., Cheung, Y.K., Au, F.T.K. and Lo, S.H. (2002), "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solids Struct., 39, 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2
  32. Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2005), "3-D vibration analysis of rectangular plates with mixed boundary conditions", ASME J. Appl. Mech., 72, 227-236. https://doi.org/10.1115/1.1827250

피인용 문헌

  1. A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges vol.2018, pp.1875-9203, 2018, https://doi.org/10.1155/2018/8562079
  2. Dynamic response of thin plates on time-varying elastic point supports vol.62, pp.4, 2017, https://doi.org/10.12989/sem.2017.62.4.431
  3. Dynamic behaviour of thick plates resting on Winkler foundation with fourth order element vol.16, pp.3, 2012, https://doi.org/10.12989/eas.2019.16.3.359
  4. Dynamic Analysis of Thick Plates Resting on Winkler Foundation Using a New Finite Element vol.44, pp.1, 2012, https://doi.org/10.1007/s40996-019-00260-4