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

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 Cheung, Y.K., "Vibrations of rectangular plates with elastic intermediate line-supports and edge constraints" 37 : 305-331, 2000

2 Zhou, D., "Vibrations of point supported rectangular plates with variable thickness using a set of static tapered beam functions" 44 : 149-164, 2002

3 Zhou, D., "Vibrations of Mindlin rectangular plates with elastic restrained edges using static Timoshenko beam functions in Rayleigh-Ritz method" 38 : 5565-5580, 2001

4 Liew, K. M., "Vibration of Mindlin plates in point supports using constraint functions" 120 : 499-513, 1994

5 Xiang, Y., "Vibration analysis of rectangular plates resting on elastic edge supports" 204 (204): 1-16, 1997

6 Kitipornchai, S., "Vibration analysis of corner supported Mindlin plates of arbitrary shape using the Lagrange multiplier method" 173 (173): 457-470, 1994

7 Zhou, D., "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method" 39 : 6339-6353, 2002

8 Reddy, J. N., "Theory and Analysis of Elastic Plates" Taylor & Francis 1999

9 Cheung, Y.K., "The free vibration of rectangular composite plates with point supports using static beam functions" 44 : 145-154, 1999

10 Kim, C.S., "The flexural vibration of rectangular plates with point supports" 117 : 249-261, 1987

11 Narita, Y., "The effects of point constraints on transverse vibration of cantilever plates" 102 : 305-313, 1985

12 Huang, M.H., "Static and free vibration analysis of plate on column supports by different models" 23 (23): 18-25, 2001

13 Shufrin, I., "Stability and vibration of shear deformable plates—first order and higher order analyses" 42 : 1225-1251, 2005

14 Seyedemad, M., "On the free vibration response of rectangular plates, partially supported on elastic foundation" 36 : 4473-4482, 2012

15 Narita, Y., "Note on vibrations of point supported rectangular plates" 93 : 593-597, 1984

16 Karunasena, W., "Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method" 196 : 371-385, 1996

17 Malekzadeh, P., "Large amplitude flexural vibration analysis of tapered plates with edges elastically restrained against rotation using DQM" 30 : 2850-2858, 2008

18 Du, J., "Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints" 330 (330): 788-804, 2011

19 Zhou, D., "Free vibration of thick layered rectangular plates with point supports by finite layer method" 37 : 1483-1499, 2000

20 Zhou, D., "Free vibration of rectangular plates with internal column supports" 297 : 146-166, 2006

21 Lee, L.T., "Free vibration of rectangular plates on elastic point supports with the application of a new type of admissible function" 65 : 149-156, 1997

22 Wu, L. H., "Free vibration of arbitrary quadrilateral thick plates" 22 (22): 258-263, 2001

23 Wu, L.H., "Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method" 53 : 494-504, 2011

24 Huang, M.H., "Free vibration analysis of rectangular plates on elastic intermediate supports" 240 : 567-580, 2001

25 Wu, L.H., "Free vibration analysis of arbitrary shaped thick plates by differential cubature method" 47 : 63-81, 2005

26 Ohya, F., "Free vibration analysis by the superposition method of rectangular Mindlin plates with internal columns resting on uniform elastic edge supports" 289 : 1-24, 2006

27 Fan, S.C., "Flexural free vibrations of rectangular plates with complex support conditions" 93 : 81-94, 1984

28 Wang, Y., "Application of meshless method in the transverse vibration of rectangular thin plate with elastic point supports" 27 (27): 238-243, 2010

29 Narita, Y., "Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions" 77 : 345-355, 1981

30 Gorman, D. J., "Accurate free vibration analysis of point supported Mindlin plates by the superposition method" 219 : 265-277, 1999

31 Zhou, D., "3-D vibration analysis of skew thick plates using Chebyshev-Ritz method" 48 : 1481-1493, 2006

32 Zhou, D., "3-D vibration analysis of rectangular plates with mixed boundary conditions" 72 : 227-236, 2005