A unified approach to study the forced linear and geometrically nonlinear elastic vibrations of fiber-reinforced laminated composite plates subjected to uniform load on the entire plate as well as on a localized area is presented in this paper. To accommodate different shapes of the plate, the analytical procedure has two parts. The first part deals with the geometry which is interpolated by relatively low-order polynomials. In the second part, the displacement based $p$-type method is briefly presented where the displacement fields are defined by significantly higher-order polynomials than those used for the geometry. Simply supported square, rhombic, and annular circular sector plates are modeled. The equation of motion is obtained by the Hamilton’s principle and solved by beta-$m$ method along with the Newton–Raphson iterative scheme. Numerical procedure presented herein is validated successfully by comparing present results with the previously published data, convergence study, and fast Fourier transforms of the linear and nonlinear transient responses. The geometric nonlinearity is seen to cause stiffening of the plates and in turn significantly lowers the values of displacements and stresses. Also as expected, the frequencies are increased for the nonlinear cases.

1.
Sun
,
C. T.
,
Whitney
,
J. M.
, and
Whitford
,
L.
, 1975, “
Dynamic Response of Laminated Composite Plates
,”
AIAA J.
0001-1452,
13
(
10
), pp.
1259
1260
.
2.
Whitney
,
J. M.
, and
Sun
,
C. T.
, 1977, “
,”
J. Acoust. Soc. Am.
0001-4966,
61
(
1
), pp.
101
104
.
3.
Reddy
,
J. N.
, 1982, “
On the Solutions to Forced Motions of Rectangular Composite Plates
,”
ASME Trans. J. Appl. Mech.
0021-8936,
49
, pp.
403
408
.
4.
Reddy
,
J. N.
, 1983, “
Geometrically Nonlinear Transient Analysis of Laminated Composite Plates
,”
AIAA J.
0001-1452,
21
(
4
), pp.
621
629
.
5.
Khdeir
,
A. A.
, and
Reddy
,
J. N.
, 1988, “
,”
J. Sound Vib.
0022-460X,
126
(
3
), pp.
437
445
.
6.
Khdeir
,
A. A.
, and
Reddy
,
J. N.
, 1989, “
On the Forced Motions of Antisymmetric Cross-Ply Laminated Plates
,”
Int. J. Mech. Sci.
0020-7403,
31
(
7
), pp.
499
510
.
7.
Chen
,
J.
, and
Dawe
,
D. J.
, 1996, “
Linear Transient Analysis of Rectangular Laminated Plates by a Finite Strip-Mode Superposition Method
,”
Compos. Struct.
0263-8223,
35
, pp.
213
228
.
8.
Chen
,
J.
,
Dawe
,
D. J.
, and
Wang
,
S.
, 2000, “
Nonlinear Transient Analysis of Rectangular Laminated Composite Plates
,”
Compos. Struct.
0263-8223,
49
, pp.
129
139
.
9.
Tsouvalis
,
N. G.
, and
Papazoglou
,
V. J.
, 1996, “
Large Deflection Dynamic Response of Composite Laminated Plates Under Lateral Loads
,”
Mar. Struct.
0951-8339,
9
, pp.
825
848
.
10.
Nath
,
Y.
and
Shukla
,
K. K.
, 2001, “
Non-Linear Transient Analysis of Moderately Thick Laminated Composite Plates
,”
J. Sound Vib.
0022-460X,
247
(
3
), No. 3,
509
526
.
11.
,
T.
, and
Singh
,
A. V.
, 2004, “
A P-Type Solution for the Bending of Rectangular, Circular, Elliptic and Skew Plates
,”
Int. J. Solids Struct.
0020-7683,
41
, pp.
3977
3997
.
12.
Tanveer
,
M.
, and
Singh
,
A. V.
, 2006, “
,”
Second International Congress on Computational Mechanics and Simulation
, Indian Institute of Technology, Guwahati, India, pp.
12
18
.
13.
Singh
,
A. V.
, and
Elaghabash
,
Y.
, 2003, “
On the Finite Displacement Analysis of Quadrangular Plates
,”
Int. J. Non-Linear Mech.
0020-7462,
38
, pp.
1149
1162
.
14.
Weaver
,
W.
, and
Johnston
,
P. R.
, 1984,
Finite Elements for Structural Analysis
,
Prentice-Hall
,
Englewood Cliffs, NJ
, Chap. 3, pp.
115
126
.
15.
Katona
,
M. G.
, and
Zienkiewicz
,
O. C.
, 1985, “
A Unified Set of Single Step Algorithms-Part 3: The Beta-m Method, A Generalization of the Newmark Scheme
,”
Int. J. Numer. Methods Eng.
0029-5981,
21
, pp.
1345
1359
.
16.
Cook
,
R. D.
, 1974,
Concepts and Applications of Finite Element Analysis
,
Wiley
,
New York
, Chap. 14, pp.
279
285
.