Free vibration analysis of plates with steps and internal line supports by using a modified matched interface and boundary method

다국어 초록 (Multilingual Abstract)

This paper deals with free vibration of plates with steps and internal line supports by using a modified matched interface and boundary (MMIB) method. Different kinds of interfaces caused by steps, rigid and elastic line supports and their combinations are taken into account. Detailed MMIB procedures for dealing with these different interfaces are presented. Various examples are chosen to illustrate the accuracy and convergence of MMIB method. Numerical results show that the proposed MMIB is a highly accurate and convergent approach for solving the title issue. This study will extend the application range of MMIB method.

참고문헌 (Reference)

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

2 Mizusawa, T., "Vibration and buckling analysis of plates of abruptly varying stiffness" 12 : 689-693, 1980

3 Singhatanadgid, P., "Vibration analysis of stepped rectangular plates using the extended Kantorovich method" 23 : 201-215, 2014

4 Duan, G. H., "Vibration analysis of stepped rectangular plates by the discrete singular convolution algorithm" 82 : 100-109, 2014

5 Leissa, A. W., "The free vibration of rectangular plates" 31 : 257-293, 1973

6 Zienkiewicz, O.C., "The Finite Element Method" McGraw-Hill 1989

7 Wang, B., "Second order solving 3D elasticity equations with complex interfaces" 294 : 405-438, 2015

8 Song, Z. W., "Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method" 52 : 1159-1173, 2017

9 Gu, H., "On the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method" 202 (202): 452-459, 1997

10 Zhou, Y. C., "On the fictitious-domain and interpolation formulations of the matched interface and boundary(MIB)method" 219 : 228-246, 2006

11 Yu, S. N., "Matched interface and boundary(MIB)method for the vibration analysis of plates" 25 : 923-950, 2009

12 Yu, S. N., "Matched interface and boundary(MIB)method for elliptic problems with sharp-edged interfaces" 224 : 729-756, 2007

13 Zhao, S., "Matched interface and boundary(MIB)for the implementation of boundary conditions in high order central finite differences" 77 : 1690-1730, 2009

14 Xiang, Y., "Levy solutions for vibration of multi-span rectangular plates" 44 : 1195-1218, 2002

15 Zhou, Y. C., "High order matched interface and boundary(MIB)schemes for elliptic equations with discontinuous coefficients and singular sources" 213 : 1-30, 2006

16 Zhao, S., "High order FDTD methods via derivative matching for Maxwell's equations with material interfaces" 200 : 60-103, 2004

17 Wang, C, "Free vibration of stepped thickness rectangular plates using spectral finite element method" 332 : 4324-4338, 2013

18 Lü, C. F., "Free vibration of long-span continuous rectangular Kirchhoff plates with internal rigid line supports" 297 : 351-364, 2006

19 Duan, G. H., "Free vibration analysis of multiple-stepped beams by the discrete singular convolution" 219 : 11096-11109, 2013

20 Duan, G. H., "Free vibration analysis of circular thin plates with stepped thickness by the DSC element method" 85 : 25-33, 2014

21 Wu, T. Y., "Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule" 38 : 7967-7980, 2001

22 Wu, T. Y., "Free vibration analysis of circular plates using generalized differential quadrature rule" 191 : 5365-5380, 2002

23 Zhiwei Song, "Free vibration analysis of beams with various interfaces by using a modified matched interface and boundary method" 국제구조공학회 72 (72): 1-17, 2019

24 Cheung, Y. K., "Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions" 36 : 89-110, 2000

25 Xiang, Y., "Exact buckling and vibration solutions for stepped rectangular plates" 250 (250): 503-517, 2002

26 Li, W., "Discrete singular convolution method for dynamic stability analysis of beams under periodic axial forces" 141 : 04015033-04015031, 2015

27 Liu, F. L., "Differential quadrature element method : a new approach for free vibration analysis of polar Mindlin plates having discontinuities" 179 : 407-423, 1999

28 Shu, C., "Differential Quadrature and its Application in Engineering" Springer 2000

29 Zhao, S., "DSC analysis of free-edged beams by an iteratively matched boundary method" 284 : 487-493, 2005

30 Ng, C. H. W., "Comparison of discrete singular convolution and generalized differential quadrature for the vibration of analysis of rectangular plates" 193 : 2483-2506, 2004

31 Fornberg, B., "Calculation of weights in finite difference formulas" 40 : 685-691, 1998

32 Rajasekaran, S., "Buckling and vibration of stepped rectangular plates by element-based differential transform method" 6 (6): 51-64, 2013

33 Zhou, X. Q., "Band gap characteristics of periodically stiffened-thin-plate based on center finite difference method" 82 : 115-123, 2014

34 Khezri, M., "Application of RKP-FSM in the buckling and free vibration analysis of thin plates with abrupt thickness changes and internal supports" 104 : 125-156, 2015

35 Li, Q. S., "An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support" 45 : 669-685, 2003

36 Chai, Y. B., "A smoothed finite element method for exterior Helmholtz equation in two dimensions" 84 : 237-252, 2017

37 Wei, G. W., "A novel approach for the analysis of high-frequency vibrations" 257 (257): 207-246, 2002

38 Wu, F., "A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner-Mindlin plates" 53 : 333-352, 2018

39 Li, W., "A comparison study of HO-CFD and DSC-RSK for solving some classes of boundary-value and eigenvalue problems" 17 (17): 1950011-1950011, 2020