In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

Issue Section:
Research Papers
Topics:
Composite materials, Vibration analysis, Finite element model, Degrees of freedom, Interpolation, Plates (structures), Vibration, Boundary-value problems, Damping, Displacement, Locks (Waterways), Rotation, Shear deformation
1.
Armanios
E. A.
, and
Negan
H. M.
,
1983
, “
An Improved Rectangular Element for Plate Bending Analysis
,”
Computers and Structures
, Vol.
16
, pp.
677
–
686
.
2.
Ghost
A. K.
, and
Dey
S. S.
,
1994
, “
Free Vibration of Laminated Composite Plates—A Simple Finite Element Based on Higher Order Theory
,”
Computers and Structures
, Vol.
52
, pp.
397
–
404
.
3.
Hinton, E., and Owen, D. R. J., 1984, Finite Element Software for Plates and Shells, Pineridge Press Limited.
4.
Hinton
E.
, and
Bicanic
N.
,
1979
, “
A Comparison of Lagrangian and Serendipity Mindlin Plate Elements for Free Vibration Analysis
,”
Computers and Structures
, Vol.
10
, pp.
483
–
493
.
5.
Hua, H. X., 1993, “Identification of Plate Rigities of Anisotropic Rectangular Plates, Sandwich Planets and Circular Orthotropic Disks Using Vibration Data,” Ph.D. thesis. Free University of Brussels, Belgium.
6.
Lin
D. X.
,
Ni
R. G.
, and
Adams
R. D.
,
1984
, “
Prediction and Measurement of the Vibrational Damping Parameters of Carbon and Glass Fibre-Reinforced Plastics Plates
,”
J. Composite Materials
, Vol.
18
, pp.
132
–
1521
.
7.
Malkus
D. S.
, and
Hughes
T. J. R.
,
1978
, “
Mixed Finite Element Methods—Reduced and Selective Integration Techniques: A Unification of Concepts
,”
Comput. Meth. Appl. Mech. Engng.
, Vol.
15
, pp.
63
–
81
.
8.
Mallikarjuna and Kant
T.
,
1989
, “
Free Vibration of Symmetrically Laminated Plates Using a Higher Order Theory With Finite Element Technique
,”
Int. J. Numer. Methods Engng.
, Vol.
28
, pp.
1875
–
1889
.
9.
Mottershead
J. E.
, and
Friswell
M. I.
,
1993
, “
Model Updating in Structural Dynamics: A Survey
,”
J. of Sound and Vib.
, Vol.
167
, pp.
347
–
375
.
10.
Noor
A. K.
, and
Burton
W. S.
,
1989
, “
Assessment of Shear Deformation Theories for Multilayered Composite Plates
,”
Appl. Mech. Rev.
, Vol.
42
, pp.
1
–
13
.
11.
Noor
A. K.
,
1973
, “
Free Vibration of Multi-layered Composite Plates
,”
AIAA J.
, Vol.
11
, pp.
1038
–
1039
.
12.
Panc, v., 1975, Theories of Elastic Plates, pp. 393–413, Noordhoff International Publishing.
13.
Phan
N. D.
, and
Reddy
J. N.
,
1985
, “
Analysis of Laminated Composite Plates Using a Higher-Order Shear Deformation Theory
,”
Int. J. for Numer. Meth. Engng.
, Vol.
21
, pp.
2201
–
2219
.
14.
Reddy
J. N.
, and
Robbins
D. H.
,
1994
“
Theories and Computational Models for Composite Laminates
,”
Appl. Mech. Rev.
, Vol.
47
, pp.
147
–
169
.
15.
Reddy
J. N.
,
1984
, “
A Simple Higher-Order Theory for Laminated Composite Plates
,”
ASME Journal of Applied Mechanics
, Vol.
54
, pp.
745
–
752
.
16.
Senthilnathan
N. R.
,
Lim
S. P.
,
Lee
K. H.
, and
Chow
S. T.
,
1988
, “
Vibration of Laminated Orthotropic Plates Using a Simplified Higher Order Deformation Theory
,”
Composite Structures
, Vol.
10
, pp.
211
–
229
.
17.
Sivakumaran
K. S.
,
1988
, “
Frequency Analysis of Symmetrically Laminated Plates With Free Edges
,”
J. Sound Vib.
, Vol.
125
, pp.
211
–
225
.
18.
Sol, H., 1986, “Identification of Anisotropic Plate Rigidities Using Free Vibration Data,” Ph.D. Thesis, Free University of Brussels, Belgium.
19.
Wiberg
N. E.
,
Bausys
R.
, and
Zeng
L. F.
,
1994
, “
Free Vibration Analysis of Reissner-Mindlin Plate Using a Linked Interpolated Mixed Element
,”
Computer and Structures
, Vol.
52
, pp.
979
–
986
.
20.
Wu
C. P.
, and
Chen
W. Y.
,
1994
, “
Vibration and Stability of Laminated Plates Based on a Local Higher-Order Plate Theory
,”
J. Sound Vib.
, Vol.
177
, pp.
503
–
520
.
21.
Zienkiewicz
O. C.
,
Xu
Z.
,
Zeng
L. F.
,
Samuelsson
A.
, and
Wiberg
N. E.
,
1993
, “
Linked Interpolation for Ressner-Mindlin Plate Elements, Part 1—A Simple Quadrilateral
,”
Int. J. Numer. Method Engng.
, Vol.
36
, pp.
3043
–
3056
.
22.
Zienkiewicz
O. C.
,
Too
J.
, and
Taylor
R. L.
,
1970
, “
Reduced Integration Technique in General Analysis of Plates and Shells
,”
Int. J. Numer. Method Engng.
, Vol.
2
, pp.
419
–
451
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.