A new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in this paper. By the DQEM, the complex plate domain is decomposed into small simple continuous subdomains (elements) and the differential quadrature method (DQM) is applied to each continuous subdomain to solve the problems. The detailed formulations for the DQEM and the connection conditions between each element are presented. Several numerical examples are analyzed to demonstrate the accuracy and applicability of this new method to the free vibration analysis of the Mindlin plate with various discontinuities which are not solvable directly using the differential quadrature method.
Issue Section:
Research Papers
1.
Ota
T.
Hamada
M.
1963
, “Fundamental Frequencies of Simply Supported But Partially Clamped Square Plates
,” Bull. Japan Soc. Mech. Engrs.
, Vol. 6
, pp. 397
–403
.2.
Stahl
B.
Keer
L. M.
1972
, “Vibration and Stability of Cracked Rectangular Plates
,” Int. J. Solids Struct
, Vol. 8
, No. 2
, pp. 69
–92
.3.
Ali
R.
Atwai
S. J.
1980
, “Prediction of Natural Frequencies of Vibration of Rectangular Plates with Rectangular Cutouts
,” Computers and Structures
, Vol. 12
, pp. 819
–826
.4.
Liew
K. M.
Hung
K. C.
Lim
M. K.
1993
, “Roles of Domain Decomposition Method in Plate Vibrations: Treatment of Mixed Discontinuous Periphery Boundaries
,” Int. J. Mech. Sci.
, Vol. 35
, No. 7
, pp. 615
–632
.5.
Liew
K. M.
Hung
K. C.
Lim
M. K.
1994
a, “A Solution Method for Analysis of Cracked Plates under Vibration
,” Engineering Fracture Mechanics
, Vol. 48
, No. 3
, pp. 393
–404
.6.
Bert
C. W.
Jang
S. K.
Striz
A. G.
1988
, “Two New Approximate Methods for Analyzing Free Vibration of Structural Components
,” AIAA Journal
, Vol. 26
, pp. 612
–618
.7.
Pandya
M. D.
Sherbourne
A. N.
1991
, “Buckling of Anisotropic Composite Plates under Stress Gradient
,” ASCE J. of Engineering Mechanics
, Vol. 117
, pp. 260
–275
.8.
Bert
C. W.
Malik
M.
1995
, “Differential Quadrature Analysis of Free Vibration of Symmetric Cross-ply Laminates with Shear Deformation and Rotatory Inertia
,” Shock and Vibration
, Vol. 2
, pp. 321
–338
.9.
Liew
K. M.
Han
J. -B.
Xiao
Z. M.
Du
H.
1996
, “Differential Quadrature Method for Mindlin Plates on Winkler Foundations
,” Int. J. Mech. Sci.
, Vol. 38
, pp. 405
–421
.10.
Liu, F. -L., and Liew, K. M., 1998, “Free Vibration Analysis of Mindlin Sector Plates: Numerical Solutions by Differential Quadrature Method,” Comput. Methods Appl. Mech. Engrg., in press.
11.
Liew, K. M., and Liu, F. -L., 1998, “Differential Quadrature Method for Vibration Analysis of Shear Deformable Annular Sector Plates,” J. of Sound and Vibration, in press.
12.
Striz
A. G.
Chen
W.
Bert
C. W.
1994
, “Static Analysis of Structures by the Quadrature Element Method (QEM)
,” Int. J. Solids Struct.
, Vol. 31
, pp. 2807
–2818
.13.
Chen
W.
Striz
A. G.
Bert
C. W.
1997
, “Free Vibration of High-accuracy Plate Elements by the Quadrature Element Method
,” J. of Sound and Vibration
, Vol. 202
, pp. 689
–702
.14.
Han, J. -B., and Liew, K. M., 1996, “The Differential Quadrature Element Method (DQEM) for Axisymmetric Bending of Thick Circular Plates,” Proc. of the Third Asian-Pacific Conference on Comput. Mechanics, pp. 2363–2368.
15.
Liu
F. -L.
Liew
K. M.
1998
, “Static Analysis of Reissner-Mindlin Plates by Differential Quadrature Element Method
,” ASME Journal of Applied Mechanics
, Vol. 65
, pp. 705
–710
.16.
Mindlin
R. D.
1951
, “Influence of Rotatory Inertia and Shear on Flexural Motion of Isotropic, Elastic Plates
,” ASME Journal of Applied Mechanics
, Vol. 18
, pp. 31
–38
.17.
Hutchinson
J. R.
1984
, “Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions
,” ASME Journal of Applied Mechanics
, Vol. 51
, pp. 580
–585
.18.
Yuan
J.
Dickinson
S. M.
1992
, “The Flexural Vibration of Rectangular Plate Systems Approached by Using Artificial Springs in the Rayleigh-Ritz Method
,” J. of Sound and Vibration
, Vol. 159
, pp. 39
–55
.19.
Dawe, D. J., 1985, “Buckling and Vibration of Plate Structures Including Shear Deformation and Related Effects,” Aspects of the Analysis of Plate Structures, Clarendon Press, Oxford, pp. 73–99.
20.
Leissa
A. W.
1973
, “The Free Vibration of Rectangular Plates
,” J. of Sound and Vibration
, Vol. 31
, pp. 257
–293
.21.
Liew
K. M.
Xiang
Y.
Kitipornchai
S.
1994
b, “Transverse Vibration of Thick Rectangular Plates—I: Comprehensive Sets of Boundary Conditions
,” Computers and Structures
, Vol. 49
, pp. 1
–29
.22.
Jayaraman
G.
Chen
P.
Snyder
V. W.
1990
, “Free Vibrations of Rectangular Orthotropic Plates with a Pair of Parallel Edges Simply Supported
,” Computers and Structures
, Vol. 34
, pp. 203
–214
.
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