In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

References

References
1.
Finot
,
M.
, and
Suresh
,
S.
, 1996, “
Small and Large Deformation of Thick and Thin-Film Multilayers: Effect of Layer Geometry, Plasticity and Compositional Gradients
,”
J. Mech. Phys. Solids
,
44
, pp.
683
721
.
2.
Prakash
,
T.
, and
Ganapathi
,
M.
, 2006, “
Asymmetric Flexural Vibration and Thermoelastic Stability of FGM Circular Plates Using Finite Element Method
,”
Composites, Part B
,
37
, pp.
642
649
.
3.
Efraim
,
E.
, and
Eisenberger
,
M.
, 2007, “
Exact Vibration Analysis of Variable Thickness Thick Annular Isotropic and FGM Plates
,”
J. Sound Vib
.
299
, pp.
720
738
.
4.
Nie
,
G. J.
, and
Zhong
,
Z.
, 2007, “
Semi-Analytical Solution for Three-Dimensional Vibration of Functionally Graded Circular Plates
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
4901
4910
.
5.
Dong
,
C. Y.
, 2008, “
Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates Using the Chebyshev–Ritz Method
,”
Mater. Des.
,
29
, pp.
1518
1525
.
6.
Malekzadeh
,
P.
,
Shahpari
,
S. A.
, and
Ziaee
,
H. R.
,2010, “
Three-Dimensional Free Vibration of Thick Functionally Graded Annular Plates in Thermal Environment
,”
J. Sound Vib.
,
329
, pp.
425
442
.
7.
Jodaei
,
A.
,
Jalal
,
M.
, and
Yas
,
M. H.
, 2012, “
Free Vibration Analysis of Functionally Graded Annular Plates by State-Space Based Differential Quadrature Method and Comparative Modeling by ANN
,”
Composites, Part B
,
43
, pp.
340
353
.
8.
Xiang
,
Y.
,
Wang
,
C. M.
, and
Kitipornchai
,
S.
, 1994, “
Exact Vibration Solution for Initially Stressed Mindlin Plates on Pasternak Foundations
,”
Int. J. Mech. Sci.
,
36
, pp.
311
316
.
9.
Xiang
,
Y.
,
Kitipornchai
,
S.
, and
Liew
,
K. M.
, 1996, “
Buckling and Vibration of Thick Laminates on Pasternak Foundations
,”
ASCE J. Eng. Mech.
,
122
(
1
), pp.
54
63
.
10.
Malekzadeh
,
P.
, and
Karami
,
G.
, 2004, “
Vibration of Non-Uniform Thick Plates on Elastic Foundation by Differential Quadrature Method
,”
Eng. Struct.
,
26
, pp.
1473
1482
.
11.
Hosseini-Hashemi
,
Sh.
,
Rokni Damavandi Taher
,
H.
, and
Omidi
,
M.
, 2008, “
3-D Free Vibration Analysis of Annular Plates on Pasternak Elastic Foundation via p-Ritz Method
,”
J. Sound Vib.
,
311
, pp.
1114
1140
.
12.
Hosseini-Hashemi
,
Sh.
,
Omidi
,
M.
, and
Rokni Damavandi Taher
,
H.
, 2009, “
The Validity Range of CPT and Mindlin Plate Theory in Comparison With 3-D Vibrational Analysis of Circular Plates on the Elastic Foundation
,”
Eur. J. Mech. A, Solids
,
28
, pp.
289
304
.
13.
Ming-Hung
,
H.
, 2010, “
Vibration Analysis of Orthotropic Rectangular Plates on Elastic Foundations
,”
Compos. Struct.
,
92
, pp.
844
852
.
14.
Malekzadeh
,
P.
,
Afsari
,
A.
,
Zahedinejad
,
P.
, and
Bahadori
,
R.
, 2010, “
Three-Dimensional Layerwise-Finite Element Free Vibration Analysis of Thick Laminated Annular Plates on Elastic Foundation
,”
Appl. Math. Model.
,
34
, pp.
776
790
.
15.
Malekzadeh
,
P.
, 2009, “
Three-Dimensional Free Vibration Analysis of Thick Functionally Graded Plates on Elastic Foundations
,”
Compos. Struct.
,
89
, pp.
367
373
.
16.
Amini
,
M. H.
,
Soleimani
,
M.
, and
Rastgoo
,
A.
, 2009, “
Three-Dimensional Free Vibration Analysis of Functionally Graded Material Plates Resting on an Elastic Foundation
,”
Smart Mater. Struct.
,
18
, p.
085015
.
17.
Yas
,
M. H.
, and
Sobhani Aragh
,
B.
, 2010, “
Free Vibration Analysis of Continuous Grading Fiber Reinforced Plates on Elastic Foundation
,”
Int. J. Eng. Sci.
,
48
, pp.
1881
1895
.
18.
Hosseini-Hashemi
,
Sh.
,
Akhavan
,
H.
,
Rokni Damavandi Taher
,
H.
,
Daemi
,
N.
, and
Alibeigloo
,
A.
, 2010, “
Differential Quadrature Analysis of Functionally Graded Circular and Annular Sector Plates on Elastic Foundation
,”
Mater. Des.
,
31
, pp.
1871
1880
.
19.
Hosseini-Hashemi
,
Sh.
,
Rokni Damavandi Taher
,
H.
, and
Akhavan
,
H.
, 2010, “
Vibration Analysis of Radially FGM Sectorial Plates of Variable Thickness on Elastic Foundations
,”
Compos. Struct.
,
92
, pp.
1734
1743
.
20.
Nie
,
G. J.
, and
Zhong
,
Z.
, 2007, “
Semi-Analytical Solution for Three-Dimensional Vibration of Functionally Graded Circular Plates
,”
Compu. Methods Appl. Mech. Eng.
,
196
, pp.
4901
4910
.
21.
Chen
,
W. Q.
,
Lv
,
C. F.
, and
Bian
,
Z. G.
, 2003, “
Elasticity Solution for Free Vibration of Laminated Beams
,”
Compos. Struct.
,
62
(
1
), pp.
75
82
.
22.
Shu
,
C.
, and
Richards
,
B. E.
, 1992, “
Application of Generalized Differential Quadrature to Solve Two-Dimensional Incompressible Navier-Stoaks Equations
,”
Int. J. Numer. Methods Fluids
,
15
, pp.
791
798
.
23.
Malekzadeh
,
P.
,
Golbahar Haghighi
,
M. R.
, and
Atashi
,
M. M.
, 2010, “
Free Vibration Analysis of Elastically Supported Functionally Graded Annular Plates Subjected to Thermal Environment
,”
Meccanica
,
46
, pp.
893
913
.
24.
Nie
,
G. J.
, and
Zhong
,
Z.
, 2010, “
Dynamic Analysis of Multi-Directional Functionally Graded Annular Plates
,”
Appl. Math. Model.
,
34
, pp.
608
616
.
You do not currently have access to this content.